10028
2016
2016
eng
18
article
IOP Publ.
London
Deutsche Physikalische Gesellschaft
1
--
2016-08-18
--
Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces
We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems.
New journal of physics : the open-access journal for physics
the nonlinear Poisson–Boltzmann approach
10.1088/1367-2630/18/8/083037
1367-2630
Universität Potsdam, Publikationsfonds
PA 2016_33
1390.30
online registration
083037
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100295">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 292</a>
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
eng
uncontrolled
polyelectrolyte adsorption
eng
uncontrolled
electrostatic interactions
eng
uncontrolled
critical phenomena
eng
uncontrolled
Debye screening
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
10029
2016
2016
eng
17
postprint
1
--
2016-08-18
--
Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces
We study the adsorption–desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye–Hückel approximation is often not feasible and the nonlinear Poisson–Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson–Boltzmann equation is smaller than the Debye–Hückel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical–chemical and biophysical systems.
the nonlinear Poisson–Boltzmann approach
urn:nbn:de:kobv:517-opus4-100295
online registration
New journal of physics 18 (2016). - DOI: 10.1088/1367-2630/18/8/083037
PA 2016_33
Universität Potsdam, Publikationsfonds
1392
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/10028">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
292
eng
uncontrolled
polyelectrolyte adsorption
eng
uncontrolled
electrostatic interactions
eng
uncontrolled
critical phenomena
eng
uncontrolled
Debye screening
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/10029/pmnr292_online.pdf
35261
2013
2013
eng
8
1
8
article
PLoS
San Fransisco
1
--
--
--
In vivo facilitated diffusion model
Under dilute in vitro conditions transcription factors rapidly locate their target sequence on DNA by using the facilitated diffusion mechanism. However, whether this strategy of alternating between three-dimensional bulk diffusion and one-dimensional sliding along the DNA contour is still beneficial in the crowded interior of cells is highly disputed. Here we use a simple model for the bacterial genome inside the cell and present a semi-analytical model for the in vivo target search of transcription factors within the facilitated diffusion framework. Without having to resort to extensive simulations we determine the mean search time of a lac repressor in a living E. coli cell by including parameters deduced from experimental measurements. The results agree very well with experimental findings, and thus the facilitated diffusion picture emerges as a quantitative approach to gene regulation in living bacteria cells. Furthermore we see that the search time is not very sensitive to the parameters characterizing the DNA configuration and that the cell seems to operate very close to optimal conditions for target localization. Local searches as implied by the colocalization mechanism are only found to mildly accelerate the mean search time within our model.
PLoS one
10.1371/journal.pone.0053956
1932-6203 (print)
wos:2011-2013
e53956
WOS:000313872800019
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); German Federal Ministry for
Education and Research
Maximilian Bauer
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
35268
2013
2013
eng
5
2
110
article
American Physical Society
College Park
1
--
--
--
Finite-Time effects and ultraweak ergodicity breaking in superdiffusive dynamics
We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement (delta x(2)) over bar around the ensemble value 3 - alpha (1 < alpha < 2) ranging from ballistic motion to subdiffusion, in strong contrast to the behavior of subdiffusive processes. In addition we find a significant dependence of the average of (delta x(2)) over bar over an ensemble of trajectories as a function of the finite measurement time. This so-called finite-time amplitude depression and the scatter of the scaling exponent is vital in the quantitative evaluation of superdiffusive processes. Comparing the long time average of the second moment with the ensemble mean squared displacement, these only differ by a constant factor, an ultraweak ergodicity breaking.
Physical review letters
10.1103/PhysRevLett.110.020603
0031-9007 (print)
wos:2011-2013
020603
WOS:000313421800002
Godec, A (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., aljaz.godec@ki.si; rmetzler@uni-potsdam.de
Academy of Finland; German Federal Ministry for Science and Education
Aljaz Godec
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35271
2013
2013
eng
5
2
110
article
American Physical Society
College Park
1
--
--
--
Aging effects and population splitting in single-particle trajectoryaverages
We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t(a) > 0 after initiation of the process at t = 0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external forces. Moreover, we discuss the implications of aging induced population splitting: with growing age ta of the process, an increasing fraction of particles remains motionless in a measurement of fixed duration. Consequences for single biomolecule tracking in live cells are discussed.
Physical review letters
10.1103/PhysRevLett.110.020602
0031-9007 (print)
1079-7114 (online)
wos:2011-2013
020602
WOS:000313336500003
Schulz, JHP (reprint author), Tech Univ Munich, Phys Dept T30G, D-85747 Garching, Germany.
CompInt graduate school; Academy of Finland (FiDiPro scheme); Israel
Science Foundation
Johannes H. P. Schulz
Eli Barkai
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35203
2013
2013
eng
12
2
87
article
American Physical Society
College Park
1
--
--
--
Anomalous statistics of random relaxations in random environments
We comprehensively analyze the emergence of anomalous statistics in the context of the random relaxation ( RARE) model [Eliazar and Metzler, J. Chem. Phys. 137, 234106 ( 2012)], a recently introduced versatile model of random relaxations in random environments. The RARE model considers excitations scattered randomly across a metric space around a reaction center. The excitations react randomly with the center, the reaction rates depending on the excitations' distances from this center. Relaxation occurs upon the first reaction between an excitation and the center. Addressing both the relaxation time and the relaxation range, we explore when these random variables display anomalous statistics, namely, heavy tails at zero and at infinity that manifest, respectively, exceptionally high occurrence probabilities of very small and very large outliers. A cohesive set of closed-form analytic results is established, determining precisely when such anomalous statistics emerge.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.87.022141
1539-3755 (print)
1550-2376 (online)
wos:2011-2013
022141
WOS:000315380200001
Eliazar, I (reprint author), Holon Inst Technol, POB 305, IL-58102 Holon, Israel., eliazar@post.tau.ac.il; rmetzler@uni-potsdam.de
Academy of Finland within the FiDiPro scheme
Iddo Eliazar
Ralf Metzler
Institut für Physik und Astronomie
Referiert
37424
2014
2014
eng
32
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2014/11/P11031
1742-5468 (print)
wos:2014
P11031
WOS:000345747600031
Palyulin, VV (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland within
the FiDiPro scheme; DAAD
Vladimir V. Palyulin
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
driven diffusive systems (theory)
eng
uncontrolled
fluctuations (theory)
eng
uncontrolled
stochastic processes (theory)
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
37388
2014
2014
eng
14
16
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < x(2)(t)> similar or equal to t(alpha) of the mean squared displacement with 0 < alpha < 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < x(2)(t)> similar or equal to log(1/2)t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < x(2)(t)> similar or equal to t(gamma) with 0 < gamma < 1/2, that is slower than the famed Harris law < x(2)(t)> similar or equal to t(1/2) without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/16/11/113050
1367-2630 (print)
wos:2014
113050
WOS:000346764000002
Sanders, LP (reprint author), Lund Univ, Dept Astron & Theoret Phys, Lund, Sweden.
Swedish Research Council [2009-2924, 2012-4526]; Academy of Finland
(FiDiPro scheme)
Lloyd P. Sanders
Michael A. Lomholt
Ludvig Lizana
Karl Fogelmark
Ralf Metzler
Tobias Ambjoernsson
eng
uncontrolled
single-file diffusion
eng
uncontrolled
continuous time random walks
eng
uncontrolled
ageing
Institut für Physik und Astronomie
Referiert
Open Access
37932
2014
2014
eng
1
14
140
other
American Institute of Physics
Melville
1
--
--
--
Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA
We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction epsilon(hb)(AT) for an AT base pair and the ring factor. turn out to be the most sensitive parameters. In addition, the stacking interaction epsilon(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4871297
0021-9606 (print)
1089-7690 (online)
wos:2014
149901
WOS:000334836600041
Chaudhury, P (reprint author), Univ Calcutta, Dept Chem, 92 A P C Rd, Kolkata 700009, India., rmetzler@uni-potsdam.de; skbanik@jcbose.ac.in; pinakc@rediffmail.com
Srijeeta Talukder
Shrabani Sen
Prantik Chakraborti
Ralf Metzler
Suman K. Banik
Pinaki Chaudhury
Institut für Physik und Astronomie
Referiert
37923
2014
2014
eng
5
4
89
article
American Physical Society
College Park
1
--
--
--
First-passage statistics for aging diffusion in systems with annealed and quenched disorder
Aging, the dependence of the dynamics of a physical process on the time t(a) since its original preparation, is observed in systems ranging from the motion of charge carriers in amorphous semiconductors over the blinking dynamics of quantum dots to the tracer dispersion in living biological cells. Here we study the effects of aging on one of the most fundamental properties of a stochastic process, the first-passage dynamics. We find that for an aging continuous time random walk process, the scaling exponent of the density of first-passage times changes twice as the aging progresses and reveals an intermediate scaling regime. The first-passage dynamics depends on t(a) differently for intermediate and strong aging. Similar crossovers are obtained for the first-passage dynamics for a confined and driven particle. Comparison to the motion of an aged particle in the quenched trap model with a bias shows excellent agreement with our analytical findings. Our results demonstrate how first-passage measurements can be used to unravel the age t(a) of a physical system.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.89.040101
24827169
1539-3755 (print)
1550-2376 (online)
wos:2014
040101
WOS:000339888000001
Krusemann, H (reprint author), Univ Potsdam, Inst Phys & Astron, D-14776 Potsdam Golm, Germany., rmetzler@uni-potsdam.de
Alexander von Humboldt Fellowship; Academy of Finland (FiDiPro scheme)
Henning Krüsemann
Aljaz Godec
Ralf Metzler
Institut für Physik und Astronomie
Referiert
37938
2014
2014
eng
13
2
4
article
American Physical Society
College Park
1
--
--
--
Sensing viruses by mechanical tension of DNA in responsive hydrogels
The rapid worldwide spread of severe viral infections, often involving novel mutations of viruses, poses major challenges to our health-care systems. This means that tools that can efficiently and specifically diagnose viruses are much needed. To be relevant for broad applications in local health-care centers, such tools should be relatively cheap and easy to use. In this paper, we discuss the biophysical potential for the macroscopic detection of viruses based on the induction of a mechanical stress in a bundle of prestretched DNA molecules upon binding of viruses to the DNA. We show that the affinity of the DNA to the charged virus surface induces a local melting of the double helix into two single-stranded DNA. This process effects a mechanical stress along the DNA chains leading to an overall contraction of the DNA. Our results suggest that when such DNA bundles are incorporated in a supporting matrix such as a responsive hydrogel, the presence of viruses may indeed lead to a significant, macroscopic mechanical deformation of the matrix. We discuss the biophysical basis for this effect and characterize the physical properties of the associated DNA melting transition. In particular, we reveal several scaling relations between the relevant physical parameters of the system. We promote this DNA-based assay as a possible tool for efficient and specific virus screening.
Physical review : X, Expanding access
10.1103/PhysRevX.4.021002
2160-3308 (print)
wos:2014
WOS:000334285100001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); German Research Council (DFG) [CH
707/5-1]; German Ministry for Education and Research
Jaeoh Shin
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
37985
2014
2014
eng
10
12
140
article
American Institute of Physics
Melville
1
--
--
--
Breathing dynamics based parameter sensitivity analysis of hetero-polymeric DNA
We study the parameter sensitivity of hetero-polymeric DNA within the purview of DNA breathing dynamics. The degree of correlation between the mean bubble size and the model parameters is estimated for this purpose for three different DNA sequences. The analysis leads us to a better understanding of the sequence dependent nature of the breathing dynamics of hetero-polymeric DNA. Out of the 14 model parameters for DNA stability in the statistical Poland-Scheraga approach, the hydrogen bond interaction epsilon(hb)(AT) for an AT base pair and the ring factor. turn out to be the most sensitive parameters. In addition, the stacking interaction epsilon(st)(TA-TA) for an TA-TA nearest neighbor pair of base-pairs is found to be the most sensitive one among all stacking interactions. Moreover, we also establish that the nature of stacking interaction has a deciding effect on the DNA breathing dynamics, not the number of times a particular stacking interaction appears in a sequence. We show that the sensitivity analysis can be used as an effective measure to guide a stochastic optimization technique to find the kinetic rate constants related to the dynamics as opposed to the case where the rate constants are measured using the conventional unbiased way of optimization. (c) 2014 AIP Publishing LLC.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4869112
24697480
0021-9606 (print)
1089-7690 (online)
wos:2014
125101
WOS:000334169000068
Chaudhury, P (reprint author), Univ Calcutta, Dept Chem, 92 A P C Rd, Kolkata 700009, India., rmetzler@uni-potsdam.de; skbanik@jcbose.ac.in; pinakc@rediffmail.com
Srijeeta Talukder
Shrabani Sen
Prantik Chakraborti
Ralf Metzler
Suman K. Banik
Pinaki Chaudhury
Institut für Physik und Astronomie
Referiert
34805
2013
2013
eng
13
15
15
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
We demonstrate the non-ergodicity of a simple Markovian stochastic process with space-dependent diffusion coefficient D(x). For power-law forms D(x) similar or equal to vertical bar x vertical bar(alpha), this process yields anomalous diffusion of the form < x(2)(t)> similar or equal to t(2/(2-alpha)). Interestingly, in both the sub- and superdiffusive regimes we observe weak ergodicity breaking: the scaling of the time-averaged mean-squared displacement <(delta(2)(Delta))over bar> remains linear in the lag time Delta and thus differs from the corresponding ensemble average < x(2)(t)>. We analyse the non-ergodic behaviour of this process in terms of the time-averaged mean- squared displacement (delta(2)) over bar and its random features, i.e. the statistical distribution of (delta(2)) over bar and the ergodicity breaking parameters. The heterogeneous diffusion model represents an alternative approach to non- ergodic, anomalous diffusion that might be particularly relevant for diffusion in heterogeneous media.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/15/8/083039
1367-2630 (print)
wos:2011-2013
083039
WOS:000323320400005
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Deutsche Forschungsgemeinschaft [CH
707/5-1]
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
34877
2013
2013
eng
11
11
1
7
66
other
AMER INST PHYSICS
MELVILLE
1
--
--
--
Electrostatic effects in living cells Reply
PHYSICS TODAY
0031-9228
(print)
1945-0699
(online)
wos:2011-2013
WOS:000327027700008
Barkai, E (reprint author), Bar Ilan Univ, Ramat Gan, Israel.
, rmetzler@uni-potsdam.de
Eli Barkai
Yuval Garini
Ralf Metzler
35545
2012
2012
eng
5
5
86
article
IOP Publ. Ltd.
Bristol
1
--
--
--
The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories
Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.
Physica scripta : an international journal for experimental and theoretical physics
10.1088/0031-8949/86/05/058510
0031-8949 (print)
wos:2011-2013
058510
WOS:000310910000035
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); European Science Foundation
Ralf Metzler
Jae-Hyung Jeon
Institut für Physik und Astronomie
Referiert
36117
2012
2012
eng
8
2
85
article
American Physical Society
College Park
1
--
--
--
Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.85.021147
1539-3755 (print)
wos:2011-2013
021147
WOS:000300939400002
Jeon, JH (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., jeonjh@gmail.com; rmetzler@uni-potsdam.de
Academy of Finland
Jae-Hyung Jeon
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38041
2014
2014
eng
24
1
4
article
American Physical Society
College Park
1
--
--
--
Aging renewal theory and application to random walks
We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval [0, t] statistically strongly differ from those observed at later times [t(a,) t(a) + t]. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.
Physical review : X, Expanding access
10.1103/PhysRevX.4.011028
2160-3308 (print)
wos:2014
011028
WOS:000332161500001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam Golm, Germany., rmetzler@uni-potsdam.de
Elitenetzwerk Bayern; Academy of Finland (FiDiPro scheme); Israel
Science Foundation
Johannes H. P. Schulz
Eli Barkai
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
38043
2014
2014
eng
2931
2936
6
8
111
article
National Acad. of Sciences
Washington
1
--
--
--
Levy flights do not always optimize random blind search for sparse targets
It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
Proceedings of the National Academy of Sciences of the United States of America
10.1073/pnas.1320424111
24516153
0027-8424 (print)
wos:2014
WOS:000332180900022
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland
(FiDiPro scheme)
Vladimir V. Palyulin
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
search optimization
eng
uncontrolled
stochastic processes
eng
uncontrolled
Levy foraging hypothesis
Institut für Physik und Astronomie
Referiert
37996
2014
2014
eng
7
3
9
article
PLoS
San Fransisco
1
--
--
--
How Molecular Motors Work in the Crowded Environment of Living Cells: Coexistence and Efficiency of Normal and Anomalous Transport
Recent experiments reveal both passive subdiffusion of various nanoparticles and anomalous active transport of such particles by molecular motors in the molecularly crowded environment of living biological cells. Passive and active microrheology reveals that the origin of this anomalous dynamics is due to the viscoelasticity of the intracellular fluid. How do molecular motors perform in such a highly viscous, dissipative environment? Can we explain the observed co-existence of the anomalous transport of relatively large particles of 100 to 500 nm in size by kinesin motors with the normal transport of smaller particles by the same molecular motors? What is the efficiency of molecular motors in the anomalous transport regime? Here we answer these seemingly conflicting questions and consistently explain experimental findings in a generalization of the well-known continuous diffusion model for molecular motors with two conformational states in which viscoelastic effects are included.
PLoS one
10.1371/journal.pone.0091700
24626511
1932-6203 (print)
wos:2014
e91700
WOS:000332851300124
Goychuk, I (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., igoychuk@uni-potsdam.de
Deutsche Forschungsgemeinschaft(DFG) [GO 2052/1-1, GO 2052/1-2]; Finland
Distinguished Professor program, Academy of Finland
Igor Goychuk
Vasyl O. Kharchenko
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
35899
2012
2012
eng
2321
2330
10
10
102
article
Cell Press
Cambridge
1
--
--
--
Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states
Transcription factors (TFs) such as the lac repressor find their target sequence on DNA at remarkably high rates. In the established Berg-von Hippel model for this search process, the TF alternates between three-dimensional diffusion in the bulk solution and one-dimensional sliding along the DNA chain. To overcome the so-called speed-stability paradox, in similar models the TF was considered as being present in two conformations (search state and recognition state) between which it switches stochastically. Combining both the facilitated diffusion model and alternating states, we obtain a generalized model. We explicitly treat bulk excursions for rodlike chains arranged in parallel and consider a simplified model for coiled DNA. Compared to previously considered facilitated diffusion models, corresponding to limiting cases of our generalized model, we surprisingly find a reduced target search rate. Moreover, at optimal conditions there is no longer an equipartition between the time spent by the protein on and off the DNA chain.
Biophysical journal
10.1016/j.bpj.2012.04.008
0006-3495 (print)
wos:2011-2013
WOS:000304091100011
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland
Maximilian Bauer
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35910
2012
2012
eng
5
5
85
article
American Physical Society
College Park
1
--
--
--
Correlated continuous-time random walks in external force fields
We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T-i is equal to the previous waiting time Ti-1 plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.85.051103
1539-3755 (print)
1550-2376 (online)
wos:2011-2013
051103
WOS:000306440100001
Magdziarz, M (reprint author), Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, Wyspianskiego 27, PL-50370 Wroclaw, Poland., marcin.magdziarz@pwr.wroc.pl; rmetzler@uni-potsdam.de; wladyslaw.szczotka@math.uni.wroc.pl; piotr.zebrowski@math.uni.wroc.pl
Marcin Magdziarz
Ralf Metzler
Wladyslaw Szczotka
Piotr Zebrowski
Institut für Physik und Astronomie
Referiert
36426
2011
2011
eng
8
24
135
article
American Institute of Physics
Melville
1
--
--
--
First passage time distribution of chaperone driven polymer translocation through a nanopore homopolymer and heteropolymer cases
Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Peclet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Peclet number. We investigate the effect of the chaperone size on the translocation process. In particular, for large chaperone size, the translocation progress and the mean waiting time as function of the reaction coordinate exhibit pronounced sawtooth-shapes. The effects of a heterogeneous polymer sequence on the translocation dynamics is studied in terms of the translocation velocity, the probability distribution for the translocation progress, and the monomer waiting times. (C) 2011 American Institute of Physics.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.3669427
0021-9606 (print)
wos:2011-2013
245102
WOS:000298640500053
Abdolvahab, RH (reprint author), Sharif Univ Technol, Dept Phys, POB 11155-9161, Tehran, Iran., abdolvahab@physics.sharif.edu
CompInt graduate school at TUM; Academy of Finland; Sharif University of
Technology
Rouhollah Haji Abdolvahab
Ralf Metzler
Mohammad Reza Ejtehadi
Institut für Physik und Astronomie
Referiert
37307
2014
2014
eng
18
48
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ageing and confinement in non-ergodic heterogeneous diffusion processes
We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/48/485002
1751-8113 (print)
1751-8121 (online)
wos:2014
485002
WOS:000345229100004
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft (DFG) [CH 707/5-1]; Berlin Mathematical
Society; Academy of Finland (Suomen Akatemia)
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
stochastic processes
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
ageing
eng
uncontrolled
weak ergodicity breaking
Institut für Physik und Astronomie
Referiert
37299
2014
2014
eng
10
49
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Localisation and universal fluctuations in ultraslow diffusion processes
We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/49/492002
1751-8113 (print)
1751-8121 (online)
wos:2014
492002
WOS:000346266400002
Godec, A (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Alexander von Humboldt Foundation;
Berlin Mathematical Society; Israel Science Foundation
Aljaz Godec
Aleksei V. Chechkin
Eli Barkai
Holger Kantz
Ralf Metzler
eng
uncontrolled
Sinai diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
quenched energy landscape
Institut für Physik und Astronomie
Referiert
37336
2014
2014
eng
3287
3293
7
14
223
article
Springer
Heidelberg
1
--
--
--
Ageing single file motion
The European physical journal
10.1140/epjst/e2014-02333-5
1951-6355 (print)
1951-6401 (online)
wos:2014
WOS:000346416400018
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Swedish Research Council [2009-2924, 2012-4526]; Academy of Finland
Ralf Metzler
L. Sanders
M. A. Lomholt
L. Lizana
K. Fogelmark
Tobias Ambjoernsson
Institut für Physik und Astronomie
Referiert
37839
2014
2014
eng
19
16
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Mixing and segregation of ring polymers: spatial confinement and molecular crowding effects
During the life cycle of bacterial cells the non-mixing of the two ring-shaped daughter genomes is an important prerequisite for the cell division process. Mimicking the environments inside highly crowded biological cells, we study the dynamics and statistical behavior of two flexible ring polymers in the presence of cylindrical confinement and crowding molecules. From extensive computer simulations we determine the degree of ring-ring overlap and the number of inter-monomer contacts for varying volume fractions phi of crowders. We also examine the entropic demixing of polymer rings in the presence of mobile crowders and determine the characteristic times of the internal polymer dynamics. Effects of the ring length on ring-ring overlap are also analyzed. In particular, on systematic variation of the fraction of crowding molecules, a (1 - phi)-scaling is found for the ring-ring overlap length along the cylinder axis, and a non-monotonic dependence of the 3D ring-ring contact number with a maximum at phi approximate to 0.2 is obtained. Our results demonstrate that polymer rings are demixed and separated by particular entropy-favourable partitioning of crowders along the axis of the cylindrical simulation box. These findings help to rationalize the implications of macromolecular crowding for circular DNA molecules in confined spaces inside bacteria as well as in localized cellular compartments inside eukaryotic cells.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/16/5/053047
1367-2630 (print)
wos:2014
053047
WOS:000338940800001
Shin, J (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland; Deutsche Forschungsgemeinschaft (DFG) [CH 707/5-1];
German Federal Ministry for Education and Research
Jaeoh Shin
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
polymers
eng
uncontrolled
confinement
eng
uncontrolled
crowding
Institut für Physik und Astronomie
Referiert
Open Access
35074
2013
2013
eng
10
4
87
article
American Physical Society
College Park
1
--
--
--
Area coverage of radial Levy flights with periodic boundary conditions
We consider the area coverage of radial Levy flights in a finite square area with periodic boundary conditions. From simulations we show how the fractal path dimension d(f) and thus the degree of area coverage depends on the number of steps of the trajectory, the size of the area, and the resolution of the applied box counting algorithm. For sufficiently long trajectories and not too high resolution, the fractal dimension returned by the box counting method equals two, and in that sense the Levy flight fully covers the area. Otherwise, the determined fractal dimension equals the stable index of the distribution of jump lengths of the Levy flight. We provide mathematical expressions for the turnover between these two scaling regimes. As complementary methods to analyze confined Levy flights we investigate fractional order moments of the position for which we also provide scaling arguments. Finally, we study the time evolution of the probability density function and the first passage time density of Levy flights in a square area. Our findings are of interest for a general understanding of Levy flights as well as for the analysis of recorded trajectories of animals searching for food or for human motion patterns.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.87.042136
1539-3755 (print)
wos:2011-2013
042136
WOS:000319004700003
Vahabi, M (reprint author), Tech Univ Munich, Dept Phys, D-85747 Garching, Germany.
Academy of Finland (FiDiPro scheme); CompInt graduate school at TUM
Mahsa Vahabi
Johannes H. P. Schulz
Babak Shokri
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35081
2013
2013
eng
16
4
15
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions
We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 mu m after short-time normal diffusion turn over to perform anomalous diffusion of the form < r(2)(t)> similar or equal to t(alpha) with alpha approximate to 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/15/4/045011
1367-2630 (print)
wos:2011-2013
045011
WOS:000317590300002
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FIN-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Lundbeck Foundation Center for Biomembranes in Nanomedicine (CBN);
Academy of Finland within the Finland Distinguished Professor (FiDiPro)
programme
Jae-Hyung Jeon
Natascha Leijnse
Lene B. Oddershede
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
35404
2013
2013
eng
397
417
21
1
161
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes
Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concentration of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is observed to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent associated with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations associated with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically observed in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the physical limits of protein motion. Our results suggest that protein concentration is anything but constant in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.
Faraday discussions
10.1039/c2fd20085f
1359-6640 (print)
wos:2011-2013
WOS:000313970200021
Vattulainen, I (reprint author), Tampere Univ Technol, Dept Phys, POB 692, FI-33101 Tampere, Finland., ilpo.vattulainen@tut.fi
The Academy of Finland; European Research Council [290974
CROWDED-PRO-LIPIDS]
Matti Javanainen
Henrik Hammaren
Luca Monticelli
Jae-Hyung Jeon
Markus S. Miettinen
Hector Martinez-Seara
Ralf Metzler
Ilpo Vattulainen
Institut für Physik und Astronomie
Referiert
35441
2012
2012
eng
9
23
137
article
American Institute of Physics
Melville
1
--
--
--
The RARE model a generalized approach to random relaxation processes in disordered systems
This paper introduces and analyses a general statistical model, termed the RAndom RElaxations (RARE) model, of random relaxation processes in disordered systems. The model considers excitations that are randomly scattered around a reaction center in a general embedding space. The model's input quantities are the spatial scattering statistics of the excitations around the reaction center, and the chemical reaction rates between the excitations and the reaction center as a function of their mutual distance. The framework of the RARE model is versatile and a detailed stochastic analysis of the random relaxation processes is established. Analytic results regarding the duration and the range of the random relaxation processes, as well as the model's thermodynamic limit, are obtained in closed form. In particular, the case of power-law inputs, which turn out to yield stretched exponential relaxation patterns and asymptotically Paretian relaxation ranges, is addressed in detail.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4770266
0021-9606 (print)
1089-7690 (online)
wos:2011-2013
234106
WOS:000312780300008
Eliazar, I (reprint author), Holon Inst Technol, POB 305, IL-58102 Holon, Israel., eliazar@post.tau.ac.il; rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme)
Iddo Eliazar
Ralf Metzler
eng
uncontrolled
chemical relaxation
eng
uncontrolled
Pareto analysis
eng
uncontrolled
reaction kinetics theory
eng
uncontrolled
reaction rate constants
eng
uncontrolled
stochastic processes
Institut für Physik und Astronomie
Referiert
35980
2012
2012
eng
18
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Correlated continuous-time random walks-scaling limits and Langevin picture
In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2012/04/P04010
1742-5468 (print)
wos:2011-2013
P04010
WOS:000303545700012
Magdziarz, M (reprint author), Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, Wyspianskiego 27, PL-50370 Wroclaw, Poland., Marcin.Magdziarz@pwr.wroc.pl; rmetzler@uni-potsdam.de; Wladyslaw.Szczotka@math.uni.wroc.pl; Piotr.Zebrowski@math.uni.wroc.pl
Academy of Finland (FiDiPro)
Marcin Magdziarz
Ralf Metzler
Wladyslaw Szczotka
Piotr Zebrowski
eng
uncontrolled
stochastic processes (theory)
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
35967
2012
2012
eng
2527
2542
16
8
391
article
Elsevier
Amsterdam
1
--
--
--
Generalized space-time fractional diffusion equation with composite fractional time derivative
We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
Physica : europhysics journal ; A, Statistical mechanics and its applications
10.1016/j.physa.2011.12.035
0378-4371 (print)
1873-2119 (online)
wos:2011-2013
WOS:000301209400003
Tomovski, Z (reprint author), St Cyril & Methodius Univ, Fac Nat Sci & Math, Inst Math, Skopje 1000, Macedonia., tomovski@pmf.ukim.mk; trifce.sandev@drs.gov.mk; metz@ph.tum.de; j.l.a.dubbeldam@tudelft.nl
DAAD; NWO; Academy of Finland; Ministry of Education and Science of the
Republic of Macedonia
Zivorad Tomovski
Trifce Sandev
Ralf Metzler
Johan Dubbeldam
eng
uncontrolled
Fractional diffusion equation
eng
uncontrolled
Composite fractional derivative
eng
uncontrolled
Riesz-Feller fractional derivative
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
Fox H-function
eng
uncontrolled
Fractional moments
eng
uncontrolled
Asymptotic expansions
eng
uncontrolled
Grunwald-Letnikov approximation
Institut für Physik und Astronomie
Referiert
35989
2012
2012
eng
75
84
10
1
204
article
Springer
Heidelberg
1
--
--
--
Diffusion inside living human cells
Naturally occurring lipid granules diffuse in the cytoplasm and can be used as tracers to map out the viscoelastic landscape inside living cells. Using optical trapping and single particle tracking we found that lipid granules exhibit anomalous diffusion inside human umbilical vein endothelial cells. For these cells the exact diffusional pattern of a particular granule depends on the physiological state of the cell and on the localization of the granule within the cytoplasm. Granules located close to the actin rich periphery of the cell move less than those located towards to the center of the cell or within the nucleus. Also, granules in cells which are stressed by intense laser illumination or which have attached to a surface for a long period of time move in a more restricted fashion than those within healthy cells. For granules diffusing in healthy cells, in regions away from the cell periphery, occurrences of weak ergodicity breaking are observed, similar to the recent observations inside living fission yeast cells [1].
European physical journal special topics
10.1140/epjst/e2012-01553-y
1951-6355 (print)
wos:2011-2013
WOS:000302814400007
Leijnse, N (reprint author), Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark., oddershede@nbi.dk
Lundbeck Foundation 'Center for Biomembranes in Nanomedicine';
University of Copenhagen; Academy of Finland
N. Leijnse
J. -H. Jeon
S. Loft
Ralf Metzler
L. B. Oddershede
Institut für Physik und Astronomie
Referiert
35005
2013
2013
eng
5
20
110
article
American Physical Society
College Park
1
--
--
--
Microscopic origin of the logarithmic time evolution of aging processes in complex systems
There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its full theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on nonrenewal, aging waiting times. Each state n of the system follows a local clock initiated at t = 0. The random time tau between clock ticks follows the waiting time density psi (tau). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by psi (tau). For power-law forms psi (tau) similar or equal to tau(-1-alpha) (0 < alpha < 1) we obtain a logarithmic time evolution of the state number < n(t)> similar or equal to log(t/t(0)), while for alpha > 2 the process becomes normal in the sense that < n(t)> similar or equal to t. In the intermediate range 1 < alpha < 2 we find the power-law growth < n(t)> similar or equal to t(alpha-1). Our model provides a universal description for transition dynamics between aging and nonaging states.
Physical review letters
10.1103/PhysRevLett.110.208301
0031-9007 (print)
wos:2011-2013
208301
WOS:000319064100017
Lomholt, MA (reprint author), Univ Southern Denmark, Dept Phys Chem & Pharm, MEMPHYS, DK-5230 Odense M, Denmark.
Knut and Alice Wallenberg (KAW) foundation; Academy of Finland
Michael A. Lomholt
Ludvig Lizana
Ralf Metzler
Tobias Ambjoernsson
Institut für Physik und Astronomie
Referiert
35007
2013
2013
eng
5
19
110
article
American Physical Society
College Park
1
--
--
--
Distance matters the impact of gene proximity in bacterial gene regulation
Following recent discoveries of colocalization of downstream-regulating genes in living cells, the impact of the spatial distance between such genes on the kinetics of gene product formation is increasingly recognized. We here show from analytical and numerical analysis that the distance between a transcription factor (TF) gene and its target gene drastically affects the speed and reliability of transcriptional regulation in bacterial cells. For an explicit model system, we develop a general theory for the interactions between a TF and a transcription unit. The observed variations in regulation efficiency are linked to the magnitude of the variation of the TF concentration peaks as a function of the binding site distance from the signal source. Our results support the role of rapid binding site search for gene colocalization and emphasize the role of local concentration differences.
Physical review letters
10.1103/PhysRevLett.110.198101
0031-9007 (print)
wos:2011-2013
198101
WOS:000322735100012
Pulkkinen, O (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland.
Academy of Finland
Otto Pulkkinen
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35613
2012
2012
eng
11
4
86
article
American Physical Society
College Park
1
--
--
--
Bulk-mediated diffusion on a planar surface full solution
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.86.041101
1539-3755 (print)
wos:2011-2013
041101
WOS:000309350400001
Chechkin, AV (reprint author), Inst Theoret Phys NSC KIPT, Akad Skaya St 1, UA-61108 Kharkov, Ukraine.
Academy of Finland within FiDiPro scheme
Aleksei V. Chechkin
Irwin M. Zaid
Michael A. Lomholt
Igor M. Sokolov
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35571
2012
2012
eng
5
18
109
article
American Physical Society
College Park
1
--
--
--
Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.
Physical review letters
10.1103/PhysRevLett.109.188103
0031-9007 (print)
wos:2011-2013
188103
WOS:000310434400041
Jeon, JH (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland.
Academy of Finland
Jae-Hyung Jeon
Hector Martinez-Seara Monne
Matti Javanainen
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35632
2012
2012
eng
8
3
86
article
American Physical Society
College Park
1
--
--
--
First passages in bounded domains When is the mean first passage time meaningful?
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(omega) distribution of the random variable omega = tau(1)/(tau(1) + tau(2)), which is a measure for how similar the first passage times tau(1) and tau(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.86.031143
1539-3755 (print)
wos:2011-2013
031143
WOS:000309338900001
Mattos, TG (reprint author), Max Planck Inst Intelligent Syst, Heisenbergstr 3, D-70569 Stuttgart, Germany., tgmattos@is.mpg.de
European Science Foundation; Marie Curie International Research Staff
Exchange Scheme Fellowship within the 7th European Community Framework
Programme [PIRSES-GA-2010-269139]; Academy of Finland within the FiDiPro
program; ESF Research Network "Exploring the Physics of Small Devices"
Thiago G. Mattos
Carlos Mejia-Monasterio
Ralf Metzler
Gleb Oshanin
Institut für Physik und Astronomie
Referiert
36362
2012
2012
eng
6
2
97
article
EDP Sciences
Mulhouse
1
--
--
--
A solution to the subdiffusion-efficiency paradox inactive states enhance reaction efficiency at subdiffusion conditions in living cells
Macromolecular crowding in living biological cells effects subdiffusion of larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion in terms of random walks on a critical percolation cluster, we here present a case study of EcoRV restriction enzymes involved in vital cellular defence. We show that due to its so far elusive propensity to an inactive state the enzyme avoids non-specific binding and remains well-distributed in the bulk cytoplasm of the cell. Despite the reduced volume exploration capability of subdiffusion processes, this mechanism guarantees a high efficiency of the enzyme. By variation of the non-specific binding constant and the bond occupation probability on the percolation network, we demonstrate that reduced nonspecific binding are beneficial for efficient subdiffusive enzyme activity even in relatively small bacteria cells. Our results corroborate a more local picture of cellular regulation.
epl : a letters journal exploring the frontiers of physics
10.1209/0295-5075/97/20008
0295-5075 (print)
wos:2011-2013
20008
WOS:000300259100008
Sereshki, LE (reprint author), Tech Univ Munich, Dept Phys, James Franck Str, D-85747 Garching, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Center for Nanoscience; Academy of
Finland; Danish National Research Foundation
L. E. Sereshki
M. A. Lomholt
Ralf Metzler
Institut für Physik und Astronomie
Referiert
36288
2012
2012
eng
8651
8658
8
33
8
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Quantifying supercoiling-induced denaturation bubbles in DNA
In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.
Soft matter
10.1039/c2sm26089a
1744-683X (print)
wos:2011-2013
WOS:000307021300014
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Academy of Finland
Jozef Adamcik
Jae-Hyung Jeon
Konrad J. Karczewski
Ralf Metzler
Giovanni Dietler
Institut für Physik und Astronomie
Referiert
37703
2014
2014
eng
11
1
90
article
American Physical Society
College Park
1
--
--
--
Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes
We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence D(x) similar to vertical bar x vertical bar(alpha) of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on statistical measures such as the amplitude scatter of the time-averaged mean-squared displacement of individual realizations, the ergodicity breaking and non-Gaussianity parameters, as well as the probability density function P(x, t), we analyze the weakly nonergodic character of the heterogeneous diffusion process and, particularly, the degree of irreproducibility of individual realizations. As we show, the fluctuations between individual realizations increase with growing modulus vertical bar alpha vertical bar of the scaling exponent. The fluctuations appear to diverge when the critical value alpha = 2 is approached, while for even larger alpha the fluctuations decrease, again. At criticality, the power-law behavior of the mean-squared displacement changes to an exponentially fast growth, and the fluctuations of the time-averaged mean-squared displacement do not converge for increasing number of realizations. From a systematic comparison we observe some striking similarities of the heterogeneous diffusion process with the familiar subdiffusive continuous time random walk process with power-law waiting time distribution and diverging characteristic waiting time.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.90.012134
25122278
1539-3755 (print)
1550-2376 (online)
wos:2014
012134
WOS:000339992200007
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany.
Academy of Finland; German Research Council (DFG) [CH 707/5-1]
Andrej G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
37628
2014
2014
eng
9
7
141
article
American Institute of Physics
Melville
1
--
--
--
Deformation propagation in responsive polymer network films
We study the elastic deformations in a cross-linked polymer network film triggered by the binding of submicron particles with a sticky surface, mimicking the interactions of viral pathogens with thin films of stimulus-responsive polymeric materials such as hydrogels. From extensive Langevin Dynamics simulations we quantify how far the network deformations propagate depending on the elasticity parameters of the network and the adhesion strength of the particles. We examine the dynamics of the collective area shrinkage of the network and obtain some simple relations for the associated characteristic decay lengths. A detailed analysis elucidates how the elastic energy of the network is distributed between stretching and compression modes in response to the particle binding. We also examine the force-distance curves of the repulsion or attraction interactions for a pair of sticky particles in the polymer network film as a function of the particle-particle separation. The results of this computational study provide new insight into collective phenomena in soft polymer network films and may, in particular, be applied to applications for visual detection of pathogens such as viruses via a macroscopic response of thin films of cross-linked hydrogels. (C) 2014 AIP Publishing LLC.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4893056
25149813
0021-9606 (print)
1089-7690 (online)
wos:2014
074903
WOS:000340714600048
Ghosh, SK (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany.
Academy of Finland (FiDiPro scheme); German Research Council (DFG) [CH
707/5-1]; Federal Ministry of Education and Research
Surya K. Ghosh
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
37631
2014
2014
eng
16524
16535
12
31
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion
The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp01234h
24985765
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000340075700023
Goychuk, I (reprint author), Univ Potsdam, Inst Phys & Astron, Karl Liebknecht Str 24-25, D-144766 Potsdam, Germany., igoychuk@uni-potsdam.de
German Research Foundation [GO 2052/1-2]; Academy of Finland
Igor Goychuk
Vasyl O. Kharchenko
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35363
2013
2013
eng
114
126
13
2
8
article
EDP Sciences
Les Ulis
1
--
--
--
Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
Mathematical modelling of natural phenomena
10.1051/mmnp/20138208
0973-5348 (print)
wos:2011-2013
WOS:000318215200008
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme)
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-415480">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 593</a>
Aleksei V. Chechkin
I. M. Zaid
M. A. Lomholt
I. M. Sokolov
Ralf Metzler
eng
uncontrolled
Bulk-mediated diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
Levy flights
eng
uncontrolled
stochastic processes
Institut für Chemie
Referiert
35315
2013
2013
eng
20220
20235
16
46
15
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c3cp53056f
1463-9076 (print)
1463-9084 (online)
wos:2011-2013
WOS:000326747200032
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., a.cherstvy@gmail.com; rmetzler@uni-potsdam.de
Academy of Finland; German Research Council (DFG) [CH 707/5-1];
Mathematical Institute of the University of Oxford
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
35689
2012
2012
eng
426
450
25
3
15
article
Versita
Warsaw
1
--
--
--
Velocity and displacement correlation functions for fractional generalized Langevin equations
We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.
Fractional calculus and applied analysis : an international journal for theory and applications
10.2478/s13540-012-0031-2
1311-0454 (print)
wos:2011-2013
WOS:000305912000007
Sandev, T (reprint author), Radiat Safety Directorate, Partizanski Odredi 143,POB 22, Skopje 1020, Macedonia., trifce.sandev@drs.gov.mk; rmetzler@uni-potsdam.de; tomovski@pmf.ukim.mk
Ministry of Education and Science of the Republic of Macedonia; NWO
Trifce Sandev
Ralf Metzler
Zivorad Tomovski
eng
uncontrolled
fractional generalized Langevin equation
eng
uncontrolled
frictional memory kernel
eng
uncontrolled
variances
eng
uncontrolled
mean square displacement
eng
uncontrolled
anomalous diffusion
Institut für Physik und Astronomie
Referiert
35732
2012
2012
eng
29
35
7
8
65
article
American Institute of Physics
Melville
1
--
--
--
Strange Kinetics of single molecules in living cells
Physics today
0031-9228 (print)
wos:2011-2013
WOS:000307614600020
Barkai, E (reprint author), Bar Ilan Univ, Ramat Gan, Israel.
Israel Science Foundation; Academy of Finland
Eli Barkai
Yuval Garini
Ralf Metzler
Institut für Physik und Astronomie
Referiert
36072
2012
2012
eng
10
1
article
IOP Publ. Ltd.
Bristol
1
--
--
--
How a finite potential barrier decreases the mean first-passage time
We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2012/03/L03001
1742-5468 (print)
wos:2011-2013
L03001
WOS:000302246400002
Palyulin, VV (reprint author), Tech Univ Munich, Dept Phys, D-85747 Garching, Germany., vladimir.palyulin@tum.de; rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Academy of Finland
Vladimir V. Palyulin
Ralf Metzler
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
37545
2014
2014
eng
13
16
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Collective dynamics effect transient subdiffusion of inert tracers in flexible gel networks
Based on extensive Brownian dynamics simulations we study the thermal motion of a tracer bead in a cross-linked, flexible gel in the limit when the tracer particle size is comparable to or even larger than the equilibrium mesh size of the gel. The analysis of long individual trajectories of the tracer demonstrates the existence of pronounced transient anomalous diffusion. From the time averaged mean squared displacement and the time averaged van Hove correlation functions we elucidate the many-body origin of the non-Brownian tracer bead dynamics. Our results shed new light onto the ongoing debate over the physical origin of steric tracer interactions with structured environments.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/16/9/092002
1367-2630 (print)
wos:2014
092002
WOS:000342050200001
Godec, A (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Alexander von Humboldt Fellowship; Academy of Finland (FiDiPro scheme);
German Ministry for Education and Research
Aljaz Godec
Maximilian Bauer
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
gel network
eng
uncontrolled
van Hove correlation
Institut für Physik und Astronomie
Referiert
Open Access
38080
2014
2014
eng
23
2
55
article
American Institute of Physics
Melville
1
--
--
--
Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise
We study generalized fractional Langevin equations in the presence of a harmonic potential. General expressions for the mean velocity and particle displacement, the mean squared displacement, position and velocity correlation functions, as well as normalized displacement correlation function are derived. We report exact results for the cases of internal and external friction, that is, when the driving noise is either internal and thus the fluctuation-dissipation relation is fulfilled or when the noise is external. The asymptotic behavior of the generalized stochastic oscillator is investigated, and the case of high viscous damping (overdamped limit) is considered. Additional behaviors of the normalized displacement correlation functions different from those for the regular damped harmonic oscillator are observed. In addition, the cases of a constant external force and the force free case are obtained. The validity of the generalized Einstein relation for this process is discussed. The considered fractional generalized Langevin equation may be used to model anomalous diffusive processes including single file-type diffusion.
Journal of mathematical physics
10.1063/1.4863478
0022-2488 (print)
1089-7658 (online)
wos:2014
023301
WOS:000332486500022
Sandev, T (reprint author), Radiat Safety Directorate, Partizanski Odredi 143,POB 22, Skopje 1020, Macedonia., trifce.sandev@drs.gov.mk; rmetzler@uni-potsdam.de; tomovski@pmf.ukim.mk
Academy of Finland within the FiDiPro programme
Trifce Sandev
Ralf Metzler
Zivorad Tomovski
Institut für Physik und Astronomie
Referiert
40053
2017
2017
eng
1
11
11
19
article
IOP
London
1
--
2017-06-30
--
Time averaging, ageing and delay analysis of financial time series
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
New journal of physics
10.1088/1367-2630/aa7199
1367-2630
Universität Potsdam, Publikationsfonds
PA 2017_27
1299.48
online registration
063045
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-400541">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 347</a>
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
time averaging
eng
uncontrolled
diffusion
eng
uncontrolled
geometric Brownian motion
eng
uncontrolled
financial time series
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
40054
2017
2017
eng
11
postprint
1
--
2017-09-01
--
Time averaging, ageing and delay analysis of financial time series
We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.
urn:nbn:de:kobv:517-opus4-400541
online registration
New journal of physics 19 (2017) 063045. - DOI: 10.1088/1367-2630/aa7199
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40053">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Andrey G. Cherstvy
Deepak Vinod
Erez Aghion
Aleksei V. Chechkin
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
347
eng
uncontrolled
diffusion
eng
uncontrolled
financial time series
eng
uncontrolled
geometric Brownian motion
eng
uncontrolled
time averaging
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/40054/pmn347_online.pdf
38449
2015
2015
eng
12
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions
We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction phi of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational-but not rotational-diffusivity of the particles Dis a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law D(phi) similar to (1 - phi/phi*)(2 ... 2.4) with the area fraction phi occupied by the crowders and the critical value phi*. Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/11/113028
1367-2630 (print)
wos:2015
113028
WOS:000365896200004
Shin, J (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., jshin@pks.mpg.de; rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia, Finland Distinguished
Professorship); Deutsche Forschungsgemeinschaft (DFG); Federal Ministry
of Education and Research (BMBF Project)
Jaeoh Shin
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
crowded fluids
eng
uncontrolled
stochastic processes
Institut für Physik und Astronomie
Referiert
Open Access
38501
2015
2015
eng
12
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Facilitation of polymer looping and giant polymer diffusivity in crowded solutions of active particles
We study the dynamics of polymer chains in a bath of self-propelled particles (SPP) by extensive Langevin dynamics simulations in a two-dimensional model system. Specifically, we analyse the polymer looping properties versus the SPP activity and investigate how the presence of the active particles alters the chain conformational statistics. We find that SPPs tend to extend flexible polymer chains, while they rather compactify stiffer semiflexible polymers, in agreement with previous results. Here we show that higher activities of SPPs yield a higher effective temperature of the bath and thus facilitate the looping kinetics of a passive polymer chain. We explicitly compute the looping probability and looping time in a wide range of the model parameters. We also analyse the motion of a monomeric tracer particle and the polymer's centre of mass in the presence of the active particles in terms of the time averaged mean squared displacement, revealing a giant diffusivity enhancement for the polymer chain via SPP pooling. Our results are applicable to rationalising the dimensions and looping kinetics of biopolymers at constantly fluctuating and often actively driven conditions inside biological cells or in suspensions of active colloidal particles or bacteria cells.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/11/113008
1367-2630 (print)
wos:2015
113008
WOS:000365901300002
Shin, J (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., jshin@pks.mpg.de
Academy of Finland (Suomen Akatemia, Finland Distinguished
Professorship); Deutsche Forschungsgemeinschaft (DFG)
Jaeoh Shin
Andrey G. Cherstvy
Won Kyu Kim
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
active transport
eng
uncontrolled
polymers
Institut für Physik und Astronomie
Referiert
Open Access
38517
2015
2015
eng
19
4
92
article
American Physical Society
College Park
1
--
--
--
Distributed-order diffusion equations and multifractality: Models and solutions
We study distributed-order time fractional diffusion equations characterized by multifractal memory kernels, in contrast to the simple power-law kernel of common time fractional diffusion equations. Based on the physical approach to anomalous diffusion provided by the seminal Scher-Montroll-Weiss continuous time random walk, we analyze both natural and modified-form distributed-order time fractional diffusion equations and compare the two approaches. The mean squared displacement is obtained and its limiting behavior analyzed. We derive the connection between the Wiener process, described by the conventional Langevin equation and the dynamics encoded by the distributed-order time fractional diffusion equation in terms of a generalized subordination of time. A detailed analysis of the multifractal properties of distributed-order diffusion equations is provided.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.92.042117
26565178
1539-3755 (print)
1550-2376 (online)
wos:2015
042117
WOS:000362446200004
Sandev, T (reprint author), Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany.
IMU Berlin Einstein Foundation; Academy of Finland (Suomen Akatemia)
through the FiDiPro scheme
Trifce Sandev
Aleksei V. Chechkin
Nickolay Korabel
Holger Kantz
Igor M. Sokolov
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38913
2015
2015
eng
17
5
91
article
American Physical Society
College Park
1
--
--
--
Optimization and universality of Brownian search in a basic model of quenched heterogeneous media
The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so-called mean first-passage time ( MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous random walk can significantly and universally enhance the search in any spatial dimension. In a generic minimal model we consider a spherically symmetric system comprising two concentric regions with piecewise constant diffusivity. The MFPT is analyzed under the constraint of conserved average dynamics, that is, the spatially averaged diffusivity is kept constant. Our analytical calculations and extensive numerical simulations demonstrate the existence of an optimal heterogeneity minimizing the MFPT to the target. We prove that the MFPT for a random walk is completely dominated by what we term direct trajectories towards the target and reveal a remarkable universality of the spatially heterogeneous search with respect to target size and system dimensionality. In contrast to intermittent strategies, which are most profitable in low spatial dimensions, the spatially inhomogeneous search performs best in higher dimensions. Discussing our results alongside recent experiments on single-particle tracking in living cells, we argue that the observed spatial heterogeneity may be beneficial for cellular signaling processes.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.91.052134
26066146
1539-3755 (print)
1550-2376 (online)
wos:2015
052134
WOS:000354986700001
Godec, A (reprint author), Univ Potsdam, Inst Phys & Astron, D-14776 Potsdam, Germany., agodec@uni-potsdam.de; rmetzler@uni-potsdam.de
Alexander von Humboldt Foundation Fellowship; Academy of Finland (Suomen
Akatemia, FiDiPro scheme)
Aljaz Godec
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38953
2015
2015
eng
20
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity
We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) similar to D-0x(alpha)t(beta) depends on both the position x of the test particle and the process time t. This process thus combines the features of scaled Brownian motion and heterogeneous diffusion parent processes. We compute the ensemble and time averaged mean squared displacements of this generalized diffusion process. The scaling exponent of the ensemble averaged mean squared displacement is shown to be the product of the critical exponents of the parent processes, and describes both subdiffusive and superdiffusive systems. We quantify the amplitude fluctuations of the time averaged mean squared displacement as function of the length of the time series and the lag time. In particular, we observe a weak ergodicity breaking of this generalized diffusion process: even in the long time limit the ensemble and time averaged mean squared displacements are strictly disparate. When we start to observe this process some time after its initiation we observe distinct features of ageing. We derive a universal ageing factor for the time averaged mean squared displacement containing all information on the ageing time and the measurement time. External confinement is shown to alter the magnitudes and statistics of the ensemble and time averaged mean squared displacements.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2015/05/P05010
1742-5468 (print)
wos:2015
P05010
WOS:000355588600010
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Golm, Germany., a.cherstvy@gmail.com; rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Deutsche Forschungsgemeinschaft [CH
707/5-1]
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
39417
2015
2015
eng
472
488
17
3
11
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size
The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.
Soft matter
10.1039/c4sm02007c
25413029
1744-683X (print)
1744-6848 (online)
wos:2015
WOS:000346911600006
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Deutsche Forschungsgemeinschaft
(DFG) [CH 707/5-1]; Federal Ministry of Education and Research (BMBF
Project)
Jaeoh Shin
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
39344
2015
2015
eng
4430
4443
14
22
11
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Inverted critical adsorption of polyelectrolytes in confinement
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sigma(c)-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sigma(c) for the concave interfaces versus the Debye screening length 1/kappa and the extent of confinement a for these three interfaces for small kappa a values. For large kappa a the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/kappa. We also rationalize how sigma(c)(kappa) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Soft matter
10.1039/c5sm00635j
25940939
1744-683X (print)
1744-6848 (online)
wos:2015
WOS:000355555100011
de Carvalho, SJ (reprint author), Sao Paulo State Univ, Inst Biosci Letters & Exact Sci, BR-15054000 Sao Jose Do Rio Preto, Brazil., sidneyjc@ibilce.unesp.br; rmetzler@uni-potsdam.de; a.cherstvy@gmail.com
Academy of Finland (FiDiPro scheme); German Research Foundation (DFG)
[CH 707/5-1]
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Institut für Physik und Astronomie
Referiert
39421
2015
2015
eng
1847
1858
12
3
17
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Non-universal tracer diffusion in crowded media of non-inert obstacles
We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp03599b
25474476
1463-9076 (print)
1463-9084 (online)
wos:2015
WOS:000346473600038
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); German Research Foundation (DFG)
[CH 707/5-1]; German Ministry of Education and Research (BMBF Grant)
Surya K. Ghosh
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38210
2014
2014
eng
9016
9037
22
45
10
review
Royal Society of Chemistry
Cambridge
1
--
--
--
Polymer translocation: the first two decades and the recent diversification
Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.
Soft matter
10.1039/c4sm01819b
25301107
1744-683X (print)
1744-6848 (online)
wos:2014
WOS:000344469700001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland
(FiDiPro scheme); Academy of Finland through its COMP Center of
Excellence [251748]
Vladimir V. Palyulin
Tapio Ala-Nissila
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38215
2014
2014
eng
24128
24164
37
44
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp03465a
25297814
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000344249400001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland; Israel Science Foundation; Deutsche
Forschungsgemeinschaft [CH 707/5-1]
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Institut für Chemie
Referiert
38146
2014
2014
eng
13
3
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/3/032002
1751-8113 (print)
1751-8121 (online)
wos:2014
032002
WOS:000329042400002
Palyulin, VV (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA2042/1-1]; Academy of Finland within
the FiDiPro scheme
Vladimir V. Palyulin
Ralf Metzler
eng
uncontrolled
first passage
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
potential landscape
eng
uncontrolled
polymer translocation
Institut für Physik und Astronomie
Referiert
38154
2014
2014
eng
9
2
140
article
American Institute of Physics
Melville
1
--
--
--
Numerical approach to unbiased and driven generalized elastic model
From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM) that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent beta characterizing the growth of the mean squared displacement <(delta h)(2)> of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments <vertical bar delta h vertical bar(q)> with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4858425
0021-9606 (print)
1089-7690 (online)
wos:2014
024106
WOS:000329925200007
Nezhadhaghighi, MG (reprint author), Sharif Univ Technol, Dept Phys, POB 11365-9161, Tehran, Iran.
University of Potsdam; German Academic Exchange Service [A/13/03073];
Academy of Finland
M. Ghasemi Nezhadhaghighi
Aleksei V. Chechkin
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38319
2014
2014
eng
1591
1601
11
10
10
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
Soft matter
10.1039/c3sm52846d
24652104
1744-683X (print)
1744-6848 (online)
wos:2014
WOS:000332461800015
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Golm, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Deutsche Forschungsgemeinschaft [CH
707/5-1]; German Academic Exchange Service [A/13/03073]
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38257
2014
2014
eng
15811
15817
7
30
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < alpha < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp02019g
24968336
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000339628400011
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Jae-Hyung Jeon
Aleksei V. Chechkin
Ralf Metzler
Institut für Chemie
Referiert
38264
2014
2014
eng
15539
15550
12
29
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Critical adsorption of polyelectrolytes onto charged Janus nanospheres
Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physicochemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp02207f
24954361
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000339173700057
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., a.cherstvy@gmail.com
Academy of Finland (FiDiPro scheme); German Research Foundation (DFG)
[CH 707/5-1]
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Institut für Physik und Astronomie
Referiert
38309
2014
2014
eng
6118
6128
11
13
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Diffusion of finite-size particles in two-dimensional channels with random wall configurations
Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c3cp55160a
24556939
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000332474700029
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
German Federal Ministry for Education and Research; Academy of Finland
within the FiDiPro scheme
Maximilian Bauer
Aljaz Godec
Ralf Metzler
Institut für Chemie
Referiert
38715
2015
2015
eng
1006
1038
33
4
18
article
De Gruyter
Berlin
1
--
--
--
Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel
We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
Fractional calculus and applied analysis : an international journal for theory and applications
10.1515/fca-2015-0059
1311-0454 (print)
1314-2224 (online)
wos:2015
WOS:000359161800010
Sandev, T (reprint author), Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany., sandev@pks.mpg.de; chechkin@pks.mpg.de; kantz@pks.mpg.de; rmetzler@uni-potsdam.de
IMU Berlin Einstein Foundation; Academy of Finland within the FiDiPro
programme
Trifce Sandev
Aleksei V. Chechkin
Holger Kantz
Ralf Metzler
eng
uncontrolled
continuous time random walk (CTRW)
eng
uncontrolled
Fokker-Planck-Smoluchowski equation
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
multi-scaling
Institut für Physik und Astronomie
Referiert
38756
2015
2015
eng
13
5
article
Nature Publ. Group
London
1
--
--
--
Real sequence effects on the search dynamics of transcription factors on DNA
Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.
Scientific reports
10.1038/srep10072
26154484
2045-2322 (print)
wos:2015
10072
WOS:000357570500001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland
Maximilian Bauer
Emil S. Rasmussen
Michael A. Lomholt
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
38747
2015
2015
eng
20
28
48
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ageing first passage time density in continuous time random walks and quenched energy landscapes
We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function Psi (t) similar or equal to t(-1-alpha) (0 <= alpha <= 2). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time t(a), the time elapsed between its preparation and the start of the observation. Subdiffusive ageing CTRWs with 0 < alpha < 1 describe systems such as charge carriers in amorphous semiconducters, tracer dispersion in geological and biological systems, or the dynamics of blinking quantum dots. We derive the exact forms of the first passage time density for an ageing subdiffusive CTRW in the semi-infinite, confined, and biased case, finding different scaling regimes for weakly, intermediately, and strongly aged systems: these regimes, with different scaling laws, are also found when the scaling exponent is in the range 1 < alpha < 2, for sufficiently long ta. We compare our results with the ageing motion of a test particle in a quenched energy landscape. We test our theoretical results in the quenched landscape against simulations: only when the bias is strong enough, the correlations from returning to previously visited sites become insignificant and the results approach the ageing CTRW results. With small bias or without bias, the ageing effects disappear and a change in the exponent compared to the case of a completely annealed landscape can be found, reflecting the build-up of correlations in the quenched landscape.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/28/285001
1751-8113 (print)
1751-8121 (online)
wos:2015
285001
WOS:000357281400002
Krusemann, H (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia) within the Finland Distinguished
Professor (FiDiPro) programme
Henning Krüsemann
Aljaz Godec
Ralf Metzler
eng
uncontrolled
first passage
eng
uncontrolled
random walks
eng
uncontrolled
anomalous diffusion
Institut für Physik und Astronomie
Referiert
39193
2015
2015
eng
202
206
5
2
4
article
American Chemical Society
Washington
1
--
--
--
Polymer looping is controlled by macromolecular crowding, spatial confinement, and chain stiffness
We study by extensive computer simulations the looping characteristics of linear polymers with varying persistence length inside a spherical cavity in the presence of macromolecular crowding. For stiff chains, the looping probability and looping time reveal wildly oscillating patterns as functions of the chain length. The effects of crowding differ dramatically for flexible versus stiff polymers. While for flexible chains the looping kinetics is slowed down by the crowders, for stiffer chains the kinetics turns out to be either decreased or facilitated, depending on the polymer length. For severe confinement, the looping kinetics may become strongly facilitated by crowding. Our findings are of broad impact for DNA looping in the crowded and compartmentalized interior of living biological cells.
ACS Macro Letters
10.1021/mz500709w
2161-1653 (print)
wos:2015
WOS:000349814100013
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland; Deutsche Forschungsgemeinschaft (DFG) [CH 707/5-1];
German Federal Ministry of Education and Research (BMBF Project)
Jaeoh Shin
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38383
2015
2015
eng
11
5
article
Nature Publ. Group
London
1
--
--
--
Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation
Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E. coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
Scientific reports
10.1038/srep17820
26635080
2045-2322 (print)
wos:2015
17820
WOS:000365883200002
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., rmetzler@uni-potsdam.de
University of Potsdam; Academy of Finland (Suomen Akatemia) within the
Finland Distinguished Professor (FiDiPro) program
Otto Pulkkinen
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
38812
2015
2015
eng
14
5
article
Nature Publ. Group
London
1
--
--
--
Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii
Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.
Scientific reports
10.1038/srep11690
26123798
2045-2322 (print)
wos:2015
11690
WOS:000357097200001
Selhuber-Unkel, C (reprint author), Univ Kiel, Inst Mat Sci, Biocompatible Nanomat, Kaiserstr 2, D-24143 Kiel, Germany., cse@tf.uni-kiel.de
Academy of Finland (Suomen Akatemia) within the Finland Distinguished
Professorship program; "Cluster of Excellence Inflammation at
Interfaces", Cluster laboratory X, of the German Research Foundation
(DFG); German National Academy of Sciences Leopoldina [LPD 9901/8-164];
DFG [SE-1801/2-1, SFB 677]
Julia F. Reverey
Jae-Hyung Jeon
Han Bao
Matthias Leippe
Ralf Metzler
Christine Selhuber-Unkel
Institut für Physik und Astronomie
Referiert
Open Access
38814
2015
2015
eng
16
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ultraslow scaled Brownian motion
We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/6/063038
1367-2630 (print)
wos:2015
063038
WOS:000358930400003
Bodrova, AS (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
EUIRSES DCP-PhysBio [N269139]; Academy of Finland (Suomen Akatemia,
Finland Distinguished Professorship); Berlin Mathematical Society;
Deutsche Forschungsgemeinschaft (DFG) [CH707/5-1]; Open Access
Publication Fund of the University of Potsdam
Anna S. Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
ageing
Institut für Physik und Astronomie
Referiert
Open Access
39283
2015
2015
eng
30134
30147
14
44
17
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law similar to T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c5cp03548a
26503611
1463-9076 (print)
1463-9084 (online)
wos:2015
WOS:000364639700077
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., jeonjh@kias.re.kr; rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia) within the Finland Distinguished
Professor (FiDiPro) programme
Yousof Mardoukhi
Jae-Hyung Jeon
Ralf Metzler
Institut für Physik und Astronomie
Referiert
39317
2015
2015
eng
21791
21798
8
34
17
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Quantifying non-ergodic dynamics of force-free granular gases
Brownian motion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat-depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions-both a constant and a velocity-dependent (viscoelastic) restitution coefficient epsilon. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of epsilon on the impact velocity of particles.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c5cp02824h
26252559
1463-9076 (print)
1463-9084 (online)
wos:2015
WOS:000359971300004
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
EU IRSES grant [DCP-PhysBio N269139]; IMU Berlin Einstein Foundation;
DFG grant [CH 707/5-1]; Academy of Finland (Suomen Akatemia, Finland
Distinguished Professor programme)
Anna Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38596
2015
2015
eng
18
37
48
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Quantifying the non-ergodicity of scaled Brownian motion
We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/37/375002
1751-8113 (print)
1751-8121 (online)
wos:2015
375002
WOS:000361551700004
Safdari, H (reprint author), Shahid Beheshti Univ, Dept Phys, GC, Tehran 19839, Iran., rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia, Finland Distinguished
Professorship); Deutsche Forschungsgemeinschaft; IMU Berlin Einstein
Foundation
Hadiseh Safdari
Andrey G. Cherstvy
Aleksei V. Chechkin
Felix Thiel
Igor M. Sokolov
Ralf Metzler
eng
uncontrolled
scaled Brownian motion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
ageing
Institut für Physik und Astronomie
Referiert
39005
2015
2015
eng
11
14
142
article
American Institute of Physics
Melville
1
--
--
--
Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes
We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) similar to D-0 vertical bar x vertical bar (alpha 0) in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent a in time and space. In the case of annealed disorder, for which effectively alpha(0) = alpha(0)(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages. (C) 2015 AIP Publishing LLC.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4917077
25877560
0021-9606 (print)
1089-7690 (online)
wos:2015
144105
WOS:000352969600007
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., a.cherstvy@gmail.com; rmetzler@uni-potsdam.de
Academy of Finland; Deutsche Forschungsgemeinschaft [CH 707/5-1]
Andrey G. Cherstvy
Ralf Metzler
Institut für Physik und Astronomie
Referiert
39007
2015
2015
eng
9
4
91
article
American Physical Society
College Park
1
--
--
--
Aging scaled Brownian motion
Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly nonstationary process governed by the Langevin equation for Brownian motion, however, with a power-law time dependence of the noise strength. Here we study the aging properties of SBM for both unconfined and confined motion. Specifically, we derive the ensemble and time averaged mean squared displacements and analyze their behavior in the regimes of weak, intermediate, and strong aging. A very rich behavior is revealed for confined aging SBM depending on different aging times and whether the process is sub- or superdiffusive. We demonstrate that the information on the aging factorizes with respect to the lag time and exhibits a functional form that is identical to the aging behavior of scale-free continuous time random walk processes. While SBM exhibits a disparity between ensemble and time averaged observables and is thus weakly nonergodic, strong aging is shown to effect a convergence of the ensemble and time averaged mean squared displacement. Finally, we derive the density of first passage times in the semi-infinite domain that features a crossover defined by the aging time.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.91.042107
25974439
1539-3755 (print)
1550-2376 (online)
wos:2015
042107
WOS:000352259200004
Safdari, H (reprint author), Shahid Beheshti Univ, Dept Phys, Tehran 19839, Iran., rmetzler@uni-potsdam.de
IMU Berlin Einstein Foundation; Academy of Finland (Suomen Akatemia)
Hadiseh Safdari
Aleksei V. Chechkin
Gholamreza R. Jafari
Ralf Metzler
Institut für Physik und Astronomie
Referiert
39009
2015
2015
eng
14
13
48
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Conformational properties of complex polymers: rosette versus star-like structures
Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f(1) loops (petals) and f(2) linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius R-g and asphericity (A) over cap of typical conformation as functions of parameters f(1), f(2). In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/13/135001
1751-8113 (print)
1751-8121 (online)
wos:2015
135001
WOS:000351920800001
Blavatska, V (reprint author), Natl Acad Sci Ukraine, Inst Condensed Matter Phys, UA-79011 Lvov, Ukraine., viktoria@icmp.lviv.ua
FP7 EU IRSES [N269139, N295302]; Academy of Finland
Viktoria Blavatska
Ralf Metzler
eng
uncontrolled
polymers
eng
uncontrolled
path integration
eng
uncontrolled
conformational properties
Institut für Physik und Astronomie
Referiert
9714
2016
2016
eng
6
article
Nature Publishing Group
London
1
--
2016-07-27
--
Underdamped scaled Brownian motion
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
Scientific reports
(non-)existence of the overdamped limit in anomalous diffusion
10.1038/srep30520
2045-2322
Universität Potsdam, Publikationsfonds
PA 2016_32
1386.35
online registration
30520
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-97158">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 267</a>
30520
Creative Commons - Namensnennung, 4.0 International
Anna S. Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Hadiseh Safdari
Igor M. Sokolov
Ralf Metzler
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
9715
2016
2016
eng
16
postprint
1
--
2016-07-27
--
Underdamped scaled Brownian motion
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
(non-)existence of the overdamped limit in anomalous diffusion
urn:nbn:de:kobv:517-opus4-97158
online registration
Universität Potsdam, Publikationsfonds
PA 2016_32
1386,35
Scientific reports (2016) 6:30520. - DOI: 10.1038/srep30520
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/9714">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Creative Commons - Namensnennung, 4.0 International
Anna S. Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Hadiseh Safdari
Igor M. Sokolov
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
267
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/9715/pmnr267online.pdf
9446
2013
2013
eng
20220
20235
postprint
1
--
2013-09-09
--
Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependent diffusion coefficient and the initial conditions of the diffusing particles are vital for their statistical and ergodic properties. In all three cases a weak ergodicity breaking between the time and ensemble averaged mean squared displacements is observed. We also demonstrate a population splitting of the time averaged traces into fast and slow diffusers for the case of exponential variation of the diffusivity as well as a particle trapping in the case of the logarithmic diffusivity. Our analysis is complemented by the quantitative study of the space coverage, the diffusive spreading of the probability density, as well as the survival probability.
urn:nbn:de:kobv:517-opus4-94468
online registration
Phys. Chem. Chem. Phys. (2013) Nr. 15, S. 20220-20235. DOI: 10.1039/C3CP53056F
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Andrey G. Cherstvy
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
236
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
disordered media
eng
uncontrolled
fractional dynamics
eng
uncontrolled
infection pathway
eng
uncontrolled
inhomogeneous-media
eng
uncontrolled
intracellular-transport
eng
uncontrolled
langevin equation
eng
uncontrolled
living cells
eng
uncontrolled
random-walks
eng
uncontrolled
single-particle tracking
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/9446/pmnr236_online.pdf
8518
2015
eng
21791
21798
8
17
article
1
--
--
--
Quantifying non-ergodic dynamics of force-free granular gases
Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann–
Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent (viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles.
Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies
10.1039/C5CP02824H
1463-9084 (online)
online registration
Au 018919
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85200">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 206</a>
Anna Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Ralf Metzler
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
Universität Potsdam
8520
2015
2015
eng
postprint
1
--
2015-07-27
--
Quantifying non-ergodic dynamics of force-free granular gases
Brownianmotion is ergodic in the Boltzmann–Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent
(viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles.
urn:nbn:de:kobv:517-opus4-85200
online registration
Au 018919
Physical Chemistry Chemical Physics (2015) Nr. 17, S. 21791-21798 - DOI: 10.1039/C5CP02824H
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/8518">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Anna Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
206
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/8520/pmnr206.pdf
8523
2015
2015
eng
30134
30147
17
article
Wiley-VCH Verl.
Weinheim
1
--
2015-10-07
--
Geometry controlled anomalous diffusion in random fractal geometries
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of
purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies
looking beyond the infinite cluster
10.1039/c5cp03548a
1439-7641 (online)
online registration
Au 018531
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85247">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 207</a>
Yousof Mardoukhi
Jae-Hyung Jeon
Ralf Metzler
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
Universität Potsdam
8524
2015
2015
eng
postprint
1
--
2015-10-07
--
Geometry controlled anomalous diffusion in random fractal geometries
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of
purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
looking beyond the infinite cluster
urn:nbn:de:kobv:517-opus4-85247
online registration
Au 018531
Phys. Chem. Chem. Phys. (2015) Nr. 17, S. 30134-30147 - DOI: 10.1039/c5cp03548a
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/8523">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Yousof Mardoukhi
Jae-Hyung Jeon
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
207
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/8524/pmnr207.pdf
8955
2015
2015
eng
4430
4443
11
article
Royal Society of Chemistry
London
1
--
2015-04-22
--
Inverted critical adsorption of polyelectrolytes in confinement
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer–surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption–desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
Soft matter
10.1039/C5SM00635J
1744-6848 (online)
1744-683X (print)
online registration
Au 018920
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89562">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 214</a>
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
Universität Potsdam
8956
2015
2015
eng
4430
4443
postprint
1
--
2015-04-22
--
Inverted critical adsorption of polyelectrolytes in confinement
What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer–surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption–desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.
urn:nbn:de:kobv:517-opus4-89562
online registration
Au 018920
Soft Matter (2015) Nr. 11, 4430-4443. - DOI: 10.1039/C5SM00635J
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/8955">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
214
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/8956/pmnr_214.pdf
9587
2016
2016
eng
article
RSC
London
1
--
2016-07-28
--
Interactions of rod-like particles on responsive elastic sheets
What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.
Soft matter
10.1039/C6SM01522K
1744-6848 (online)
1744-683X (print)
online registration
Au 032777
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95882">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 256</a>
Surya K. Ghosh
Andrey G. Cherstvy
Eugene P. Petrov
Ralf Metzler
Physik
Institut für Physik und Astronomie
Referiert
Open Access
RSC
Universität Potsdam
9588
2016
2016
eng
postprint
1
--
2016-07-28
--
Interactions of rod-like particles on responsive elastic sheets
What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive–repulsive rod–rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.
urn:nbn:de:kobv:517-opus4-95882
online registration
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/9587">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Au 032777
Soft matter (2016). DOI: 10.1039/C6SM01522K
Surya K. Ghosh
Andrey G. Cherstvy
Eugene P. Petrov
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
256
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/9588/pmnr256_online.pdf
9589
2016
2016
eng
23840
23852
18
article
RSC Publ.
Cambridge
1
--
2016-08-08
--
Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.
Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies
10.1039/C6CP03101C
1463-9084 (online)
1463-9076 (print)
online registration
Au 032780
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95901">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 257</a>
Andrey G. Cherstvy
Ralf Metzler
Chemie und zugeordnete Wissenschaften
Institut für Physik und Astronomie
Referiert
Open Access
RSC
Universität Potsdam
9590
2016
2016
eng
23840
23852
postprint
1
--
2016-08-08
--
Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.
urn:nbn:de:kobv:517-opus4-95901
online registration
Au 032780
Phys. Chem. Chem. Phys. (2016) Nr. 18, S. 23840-23852. - DOI: 10.1039/C6CP03101C
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/9589">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Andrey G. Cherstvy
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
257
Chemie und zugeordnete Wissenschaften
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/9590/pmnr257_online.pdf
9878
2014
2014
eng
12
postprint
1
--
2014-06-20
--
Critical adsorption of polyelectrolytes onto charged Janus nanospheres
Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption–desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.
urn:nbn:de:kobv:517-opus4-98783
online registration
Phys. Chem. Chem. Phys. (2014) Nr. 16, S. 15539-15550. - DOI: 10.1039/C4CP02207F
Keine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Sidney J. de Carvalho
Ralf Metzler
Andrey G. Cherstvy
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
278
Chemie und zugeordnete Wissenschaften
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/9878/pmnr278_online.pdf
40931
2018
2018
eng
25
postprint
1
2018-03-28
2018-03-28
--
Superstatistical generalised Langevin equation
Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.
non-Gaussian viscoelastic anomalous diffusion
urn:nbn:de:kobv:517-opus4-409315
online registration
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40932">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
New Journal of Physics 20 (2018) Nr. 023026, S. 1–25 DOI: 10.1088/1367-2630/aaa3d4
Jakub Ślęzak
Ralf Metzler
Marcin Magdziarz
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
413
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
generalised langevin equation
eng
uncontrolled
superstatistics
eng
uncontrolled
non-Gaussian diffusion
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/40931/pmnr_413.online.pdf
40373
2017
2017
eng
1
17
7
article
Springer Nature
London
1
--
2017-10-11
--
A self-avoiding walk with neural delays as a model of fixational eye movements
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
Scientific reports
10.1038/s41598-017-13489-8
2045-2322
29021548
Universität Potsdam, Publikationsfonds
PA 2017_55
1552.95
online registration
12958
WOS:000412781300026
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403742">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 392</a>
Creative Commons - Namensnennung, 4.0 International
Carl J. J. Herrmann
Ralf Metzler
Informatik, Informationswissenschaft, allgemeine Werke
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
40374
2017
2017
eng
17
postprint
1
--
2017-11-16
--
A self-avoiding walk with neural delays as a model of fixational eye movements
Fixational eye movements show scaling behaviour of the positional mean-squared displacement with a characteristic transition from persistence to antipersistence for increasing time-lag. These statistical patterns were found to be mainly shaped by microsaccades (fast, small-amplitude movements). However, our re-analysis of fixational eye-movement data provides evidence that the slow component (physiological drift) of the eyes exhibits scaling behaviour of the mean-squared displacement that varies across human participants. These results suggest that drift is a correlated movement that interacts with microsaccades. Moreover, on the long time scale, the mean-squared displacement of the drift shows oscillations, which is also present in the displacement auto-correlation function. This finding lends support to the presence of time-delayed feedback in the control of drift movements. Based on an earlier non-linear delayed feedback model of fixational eye movements, we propose and discuss different versions of a new model that combines a self-avoiding walk with time delay. As a result, we identify a model that reproduces oscillatory correlation functions, the transition from persistence to antipersistence, and microsaccades.
urn:nbn:de:kobv:517-opus4-403742
online registration
Scientific reports 7 (2017). - DOI: 10.1038/s41598-017-13489-8
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40373">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Creative Commons - Namensnennung, 4.0 International
Carl J. J. Herrmann
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
392
Informatik, Informationswissenschaft, allgemeine Werke
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/40374/pmnr392_online.pdf
40209
2017
2017
eng
18
7
article
Macmillan Publishers Limited
London
1
--
2017-06-20
--
Quantifying non-ergodicity of anomalous diffusion with higher order moments
Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
Scientific reports
10.1038/s41598-017-03712-x
28634366
Universität Potsdam, Publikationsfonds
PA 2017_26
1552.95
online registration
3878
WOS:000403643900031
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-402109">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 382</a>
Creative Commons - Namensnennung, 4.0 International
Maria Schwarzl
Aljaž Godec
Ralf Metzler
Informatik, Informationswissenschaft, allgemeine Werke
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
40210
2017
2017
eng
18
postprint
1
--
2017-10-19
--
Quantifying non-ergodicity of anomalous diffusion with higher order moments
Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
urn:nbn:de:kobv:517-opus4-402109
online registration
Scientific reports 7 (2017). - DOI: 10.1038/s41598-017-03712-x
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40209">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Creative Commons - Namensnennung, 4.0 International
Maria Schwarzl
Aljaž Godec
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
382
Informatik, Informationswissenschaft, allgemeine Werke
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/40210/pmnr382_online.pdf