Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

Abstract

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...

Tumor spheroids accelerate persistently invading cancer cells

“…2 A), which would yield slightly different values, see Ref. 15 for a discussion and an overview. Nevertheless, the spheroid seems to induce a repulsion that drives cells persistently and fast away from it.…”

Coexistence of ergodicity and nonergodicity in the aging two-state random walks

“…The TSRW model discussed in this manuscript enriches the armamentarium of theories applicable to the description of stochastic phenomena. Moreover, the aging and nonergodicity of the TSRW model discussed in this manuscript, which are particularly useful for selecting the most appropriate models of anomalous and nonergodic diffusion in a statistical analysis of single particle tracking observations, 52 can provide new thoughts for the relevant experimental studies which have certain aspects of both the CTRW state and LW state. For instance, the aging and nonergodicity of the memoryless selfreinforcing directional transport in living cells can be studied under the framework of the random walk theory, 45 the intermittent search strategy can be described and studied by the TSRW model, 14,15 and the TSRW model can provide a second theoretical scheme to discuss the transport of neuronal mRNP in neuronal systems, especially the aging and nonergodic properties of the motion.…”

“…In addition, in recent years, with the aid of fast-developing experimental techniques such as single particle tracking, 42 more and more nontrivial anomalous diffusive behaviors (including the two-state stochastic phenomenon) are observed in the physical and biological systems, 9,13,[43][44][45][46][47][48][49] which cannot be sufficiently described by the single theoretical model. 44 Hence, hybrid models such as a combination of heterogeneous diffusion processes (HDP) and fractional Brownian motion (FBM), 50,51 a combination of scaled Brownian motion (SBM) and FBM, 52 a combination of CTRW and FBM, 44 the scheme of heavytailed CTRW on fractal structures, 53 and switching between different modes, [22][23][24][25] have been presented. Moreover, the nonergodicity and aging properties of these hybrid models, which are particularly useful when selecting the most appropriate models of anomalous and nonergodic diffusion in a statistical analysis of single particle tracking datasets, 52 were discussed as well.…”

It\^o--distribution from Gibbs measure and a comparison with experiment

“…The method presented here is general enough to find application in other problems where local characteristics of fluctuating diffusion is important. Diffusing diffusion is an idea of contemporary interest [29][30][31][32][33] particularly in the context of some non-ergodic, transient diffusion processes [34][35][36][37] and the present work could be of relevance there.…”