Universal spectral features of different classes of random diffusivity processes

Sposini, V.; Grebenkov, D. S.; Metzler, R.; Oshanin, G.; Seno, F.

doi:10.48550/arxiv.1911.11661

Cited by 2 publications

(3 citation statements)

References 117 publications

(205 reference statements)

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“…We note that such a "deceptive" f -dependence has been previously reported for the running maximum of Brownian motion [68], diffusion in a periodic Sinai disorder [69], diffusion with stochastic reset [70] and also for a variety of diffusing diffusivity models [43]. Further on, the law µ(T, f ) ∼ T 1/3 /f 2 was observed for other super-diffusive processes, such as a fractional Brownian motion with the Hurst index H = 2/3 (i.e., γ = 4/3) [71] or a super-diffusive scaled Brownian motion Z t described by the Langevin equation Żt = t 1/6 ζ t [72], with ζ t being a Gaussian white-noise with zero mean.…”

Section: Spectral Analysis Of the Tp Trajectoriessupporting

confidence: 73%

“…Dynamical disorder emerges naturally when the TP's transition rates fluctuate randomly in time, as it happens, for instance, in physical processes underlying the socalled diffusing-diffusivity models [38][39][40][41][42][43][44] or the dynamic percolation [45][46][47]. Another pertinent case concerns the situations when the TP evolves in a dynamical environment of mobile steric obstacles -interacting crowders which impede its dynamics (see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

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Tracer diffusion on a crowded random Manhattan lattice

et al. 2020

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We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder-frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼t 4/3 , t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x-axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part ( ) -u exp 2 , where u=X/t 2/3 , and exhibits slower-than-Gaussian tails ( | | ) u exp 4 3 for sufficiently large t and u. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.

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Section: Spectral Analysis Of the Tp Trajectoriessupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Tracer diffusion on a crowded random Manhattan lattice

et al. 2020

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“…Brownian yet non-Gaussian dynamics was also derived from extreme value arguments [16] and for a model with ongoing tracer multimerisation [17]. Several random-diffusivity models based on Brownian motion were discussed in [18,19].…”

Section: Introductionmentioning

confidence: 99%

Unexpected crossovers in correlated random-diffusivity processes

Wang

Seno

Sokolov

et al. 2020

Preprint

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The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the strong non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of "viscoelastic yet non-Gaussian" diffusion.

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Universal spectral features of different classes of random diffusivity processes

Cited by 2 publications

References 117 publications

Tracer diffusion on a crowded random Manhattan lattice

Tracer diffusion on a crowded random Manhattan lattice

Unexpected crossovers in correlated random-diffusivity processes

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