Long-time-correlation effects and biased anomalous diffusion

Wang, K. G.

doi:10.1103/physreva.45.833

Cited by 101 publications

(73 citation statements)

References 10 publications

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“…Moreover, the amplitude-squared of the noise (diffusion coefficient) is related to the friction coefficient via the Einstein relation, which is an example of the fluctuation-dissipation theorem. It has been suggested that the Langevin equation can be generalized to the case of diffusion in complex heterogeneous media such as the cytoplasm or plasma membrane by considering a Brownian particle subject to frictional and fluctuating forces with long-time correlations that exhibit power-law behavior (Lutz, 2001;Porra et al, 1996;Wang, 1992;Wang and Lung, 1990). For example, consider the following generalized Langevin equation for a Brownian particle with unit mass moving in a 1D medium (Wang and Lung, 1990):…”

Section: A Anomalous Diffusionmentioning

confidence: 99%

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Stochastic models of intracellular transport

2013

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The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasisteady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.

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Section: A Anomalous Diffusionmentioning

confidence: 99%

“…Following Wang (1992); Wang and Lung (1990), the correlation function C(t) is governed by a power law,…”

Section: A Anomalous Diffusionmentioning

confidence: 99%

Stochastic models of intracellular transport

2013

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“…Several authors derived fractional diffusion equations for solutions to linear SIDE. (26,36,44,50) The drawback of these derivations is that they are restricted to the problem at hand; in order to construct the diffusion equation one has to know beforehand the evolution of the probability density. These fractional diffusion equations are not used as a predictive tool; they are merely a reformulation of a result that can be obtained independently.…”

Section: Comparison With the Fractional Fokker-planck Equationmentioning

confidence: 99%

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Kupferman

2004

Journal of Statistical Physics

143

135

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We study a variant of the Kac-Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n Q . the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation-a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f a -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of nonMarkovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker-Planck equation in the present context. All results are supported by direct numerical experiments.

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“…In the literature, pure power-law correlation functions have been employed to investigate the anomalous diffusion behavior of the particle that is related to the long time tail correlations. [35][36][37][38] Recently, Viñales and Despósito 39 have considered a Mittag-Leffler noise given by…”

Section: Thermostat Described By An 1d Glementioning

confidence: 99%

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

Batra

Swaminathan

Ayyaswamy

et al. 2011

The Journal of Chemical Physics

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A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.

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Long-time-correlation effects and biased anomalous diffusion

Cited by 101 publications

References 10 publications

Stochastic models of intracellular transport

Stochastic models of intracellular transport

Fractional Kinetics in Kac–Zwanzig Heat Bath Models

Generalized Langevin dynamics of a nanoparticle using a finite element approach: Thermostating with correlated noise

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