7618
2014
2014
eng
6118
6128
13
16
article
RSC Publications
Cambridge
1
2015-04-28
2014-02-06
--
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 [J. Chem. Phys., 2012, 137, 024107].
Physical chemistry, chemical physics : PCCP ; a journal of European chemical societies
10.1039/C3CP55160A
1463-9084 (online)
1463-9076 (print)
online registration
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 177</a>
Au-006422
Maximilian Bauer
Aljaž Godec
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
fractional dynamics
eng
uncontrolled
transport
eng
uncontrolled
nonergodicity
eng
uncontrolled
coefficient
Physik
Institut für Physik und Astronomie
Referiert
Open Access
RSC
Universität Potsdam
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
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
7400
2014
2014
eng
1591
1601
11
10
2014
article
Royal Society of Chemistry
1
--
2014-01-02
--
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
2046-2069 (online)
online registration
Au-006605
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 168</a>
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
intracellular-transport
eng
uncontrolled
adenoassociated virus
eng
uncontrolled
infection pathway
eng
uncontrolled
escherichia-coli
eng
uncontrolled
endosomal escape
eng
uncontrolled
living cells
eng
uncontrolled
trafficking
eng
uncontrolled
cytoplasm
eng
uncontrolled
models
Chemie und zugeordnete Wissenschaften
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
RSC
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
38753
2015
2015
eng
14
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/7/075004
1367-2630 (print)
wos:2015
075004
WOS:000359128100001
Klages, R (reprint author), Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England., peter.dieterich@tu-dresden.de; r.klages@qmul.ac.uk; chechkin@pks.mpg.de
Peter Dieterich
Rainer Klages
Aleksei V. Chechkin
eng
uncontrolled
fluctuation relations
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
stochastic thermodynamics
eng
uncontrolled
Fokker-Planck equations
Institut für Physik und Astronomie
Referiert
Open Access
7711
2014
eng
1847
1858
12
17
3
article
The Royal Society of Chemistry
Cambridge
1
--
2014-11-26
--
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
1463-9076
online registration
Au-006431
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77128">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Humanwissenschaftliche Reihe ; 186</a>
Surya K. Ghosh
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
fluorescence correlation spectroscopy
eng
uncontrolled
single-particle tracking
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
living cells
eng
uncontrolled
physiological consequences
eng
uncontrolled
langevin equation
eng
uncontrolled
infection pathway
eng
uncontrolled
excluded volume
eng
uncontrolled
brownian-motion
eng
uncontrolled
random-walks
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
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
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
43665
2019
2019
eng
13
21
article
Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
Bad Honnef und London
1
2019-02-28
2019-02-28
--
Fractional Brownian motion in a finite interval
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite interval with reflecting boundary conditions. The probability density function of this reflected FBM at long times converges to a stationary distribution showing distinct deviations from the fully flat distribution of amplitude 1/L in an interval of length L found for reflected normal Brownian motion. While for superdiffusion, corresponding to a mean squared displacement (MSD) 〈X² (t)〉 ⋍ tᵅ with 1 < α < 2, the probability density function is lowered in the centre of the interval and rises towards the boundaries, for subdiffusion (0 < α < 1) this behaviour is reversed and the particle density is depleted close to the boundaries. The MSD in these cases at long times converges to a stationary value, which is, remarkably, monotonically increasing with the anomalous diffusion exponent α. Our a priori surprising results may have interesting consequences for the application of FBM for processes such as molecule or tracer diffusion in the confines of living biological cells or organelles, or other viscoelastic environments such as dense liquids in microfluidic chambers.
New Journal of Physics
correlations effect depletion or accretion zones of particles near boundaries
10.1088/1367-2630/ab075f
1367-2630
Universität Potsdam
PA 2019_19
1299.48
022002
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436665">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 755</a>
false
false
Tobias Guggenberger
Gianni Pagnini
Thomas Vojta
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
fractional Brownian motion
eng
uncontrolled
reflecting boundary conditions
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access