相关论文: A unifying approach to diffusive transport in hete…

Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the…

We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including…

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through…

This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a one-dimensional disordered system that employs the discrete…

Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of…

We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes…

We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a…

We show that anomalous diffusion can result when the steps of a random walk are not statistically independent. We present an algorithm that counts all the possible paths of particles diffusing on random graphs with arbitrary degree…

We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic…

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a…

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of…

We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple…

Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…

This is an easy-to-read introduction to foundations of deterministic chaos, deterministic diffusion and anomalous diffusion. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and…

The random propagation of molecules in a fluid medium is characterized by the spontaneous diffusion law as well as the interaction between the environment and molecules. In this paper, we embody the anomalous diffusion theory for modeling…

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…

Motivated by contemporary and rich applications of anomalous diffusion processes we propose a new statistical test for fractional Brownian motion, which is one of the most popular models for anomalous diffusion systems. The test is based on…

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites, where the diffusion of a single random walk presents an anomalous {\it anisotropic} behavior…