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We investigate the obstructed motion of tracer (test) particles in crowded environments by carrying simulations of two-dimensional Gaussian random walk in model fibrinogen monolayers of different orientational ordering. The fibrinogen…

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…

The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…

The diffusive transport of biased Brownian particles in a two-dimensional symmetric channel is investigated numerically considering both the no-flow and the reflection boundary conditions at the channel boundaries. Here, the geometrical…

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…

In this work we investigate discrete-time transport in a generic U(1)-symmetric disordered model tuned across an array of different dynamical regimes. We develop an aggregate quantity, a circular statistical moment, which is a simple…

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and long-time non-Gaussian diffusive motion, unless interrupted. Despite its relevance to numerous…

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is…

A recently developed non-linear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However the diffusion and the noise terms present in this theory are not derived from…

We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive…

Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of…

The non-Markovian continuous-time random walk model, featuring fat-tailed waiting times and narrow distributed displacements with a non-zero mean, is a well studied model for anomalous diffusion. Using an analytical approach, we recently…

From the spread of pollutants in the atmosphere to the transmission of nutrients across cell membranes, anomalous diffusion processes are ubiquitous in natural systems. The ability to understand and control the mechanisms guiding such…

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…

We study fluctuating tilt Brownian ratchets based on fractional subdiffusion in sticky viscoelastic media characterized by a power law memory kernel. Unlike the normal diffusion case the rectification effect vanishes in the adiabatically…

Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…

We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the…

Fractional Brownian motion, a stochastic process with long-time correlations between its increments, is a prototypical model for anomalous diffusion. We analyze fractional Brownian motion in the presence of a reflecting wall by means of…

Recent progresses in single particle tracking have shown evidences of non-Gaussian distribution of displacements in living cells, both near the cellular membrane and inside the cytoskeleton. A similar behavior has also been observed in…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…