35545
2012
2012
eng
5
5
86
article
IOP Publ. Ltd.
Bristol
1
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--
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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
--
--
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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
35899
2012
2012
eng
2321
2330
10
10
102
article
Cell Press
Cambridge
1
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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
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--
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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
35441
2012
2012
eng
9
23
137
article
American Institute of Physics
Melville
1
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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
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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
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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
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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
35613
2012
2012
eng
11
4
86
article
American Physical Society
College Park
1
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--
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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
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--
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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