TY - JOUR
A1 - Chechkin, Aleksei V.
A1 - Zaid, I. M.
A1 - Lomholt, M. A.
A1 - Sokolov, I. M.
A1 - Metzler, Ralf
T1 - Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
JF - Mathematical modelling of natural phenomena
N2 - 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.
KW - Bulk-mediated diffusion
KW - anomalous diffusion
KW - Levy flights
KW - stochastic processes
Y1 - 2013
U6 - http://dx.doi.org/10.1051/mmnp/20138208
SN - 0973-5348 (print)
VL - 8
IS - 2
SP - 114
EP - 126
PB - EDP Sciences
CY - Les Ulis
ER -
TY - GEN
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - paper 168
KW - adenoassociated virus
KW - anomalous diffusion
KW - cytoplasm
KW - endosomal escape
KW - escherichia-coli
KW - infection pathway
KW - intracellular-transport
KW - living cells
KW - models
KW - trafficking
Y1 - 2014
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-74021
IS - 168
SP - 1591
EP - 1601
ER -
TY - JOUR
A1 - Bodrova, Anna
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Quantifying non-ergodic dynamics of force-free granular gases
JF - Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies
N2 - 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.
Y1 - 2015
U6 - http://dx.doi.org/10.1039/C5CP02824H
SN - 1463-9084 (online)
IS - 17
SP - 21791
EP - 21798
ER -
TY - GEN
A1 - Bodrova, Anna
A1 - Chechkin, Aleksei V.
A1 - Cherstvy, Andrey G.
A1 - Metzler, Ralf
T1 - Quantifying non-ergodic dynamics of force-free granular gases
N2 - 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.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 206
Y1 - 2015
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-85200
ER -
TY - JOUR
A1 - Jeon, Jae-Hyung
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
JF - Physical chemistry, chemical physics : a journal of European Chemical Societies
N2 - 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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4cp02019g
SN - 1463-9076 (print)
SN - 1463-9084 (online)
VL - 16
IS - 30
SP - 15811
EP - 15817
PB - Royal Society of Chemistry
CY - Cambridge
ER -