Anomalous diffusion: Testing ergodicity breaking in experimental data

Magdziarz, Marcin; Weron, Aleksander

doi:10.1103/physreve.84.051138

Cited by 78 publications

(86 citation statements)

References 39 publications

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“…The results we report below show clearly how long-range memory effects can change H and the propagator independently. Our results also have a bearing on the family of autoregressive and heteroscedastic processes, some of which have a bearing on anomalous diffusion [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

mentioning

confidence: 95%

Weakly anomalous diffusion with non-Gaussian propagators

Cressoni

Viswanathan²,

Ferreira³

et al. 2012

Phys. Rev. E

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confidence: 95%

Weakly anomalous diffusion with non-Gaussian propagators

Cressoni

Viswanathan²,

Ferreira³

et al. 2012

Phys. Rev. E

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“…This is because the same power-law exponent in the MSD does not imply that the physical mechanism in the anomalous diffusion is also the same. Therefore, clarifying the origin of anomalous diffusion is an important subject, and many researches on this issue have been conducted extensively [23,29,30,32,41]. One of the key properties characterizing anomalous diffusion is ergodicity, i.e., time-averaged observables being equal to a constant (the ensemble average).…”

Section: Introductionmentioning

confidence: 99%

Phase Diagram in Stored-Energy-Driven Lévy Flight

Akimoto

Miyaguchi

2014

J Stat Phys

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Phase diagram based on the mean square displacement (MSD) and the distribution of diffusion coefficients of the time-averaged MSD for the stored-energy-driven Lévy flight (SEDLF) is presented. In the SEDLF, a random walker cannot move while storing energy, and it jumps by the stored energy. The SEDLF shows a whole spectrum of anomalous diffusions including subdiffusion and superdiffusion, depending on the coupling parameter between storing time (trapping time) and stored energy. This stochastic process can be investigated analytically with the aid of renewal theory. Here, we consider two different renewal processes, i.e., ordinary renewal process and equilibrium renewal process, when the mean trapping time does not diverge. We analytically show the phase diagram according to the coupling parameter and the power exponent in the trapping-time distribution. In particular, we find that distributional behavior of time-averaged MSD intrinsically appears in superdiffusive as well as normal diffusive regime even when the mean trapping time does not diverge.

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“…If we consider a random walk within such a crowded environment, with a motile agent being placed in such a closed region, then the agent will remain within the closed region for all time. This observation is enough to indicate that a random walk process through this kind of crowded environment can be non-ergodic [44], even when φ is below the percolation threshold.…”

Section: Constant Distributionmentioning

confidence: 90%

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Ellery

Baker

McCue

et al. 2016

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• Stochastic simulations of individual and collective motion through a crowded environment. • Crowded environments populated by mixtures of obstacles of different shapes and sizes.• Transport properties depend on the obstacle volume fraction and details of the obstacle shape and size distribution. • Standard fractional diffusion equation descriptions ought to be used with care. a b s t r a c tMany biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

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Anomalous diffusion: Testing ergodicity breaking in experimental data

Cited by 78 publications

References 39 publications

Weakly anomalous diffusion with non-Gaussian propagators

Weakly anomalous diffusion with non-Gaussian propagators

Phase Diagram in Stored-Energy-Driven Lévy Flight

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

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