Related papers: Transport Equations for Subdiffusion with Nonlinea…
Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and…
We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between…
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
We study the dynamics of micron-sized particles on a layer of motile cells. This cell carpet acts as an active bath that propels passive tracer particles via direct mechanical contact. The resulting nonequilibrium transport shows a…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
Superdiffusion is an anomalous transport behavior. Recently, a new mechanism, termed the ``nodal mechanism," has been proposed to induce superdiffusion in quantum models. However, existing realizations of the nodal mechanism have so far…
We propose a reaction-transport model for CTRW with non-linear reactions and non-exponential waiting time distributions. We derive non-linear evolution equation for mesoscopic density of particles. We apply this equation to the problem of…
Excluded-volume effects can play an important role in determining transport properties in diffusion of particles. Here, the diffusion of finite-sized hard-core interacting particles in two or three dimensions is considered systematically…
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
The purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transport that involves chemotactic substance affecting the cells at all time, not only during the jump. This leads the random waiting time to be…
Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
Many living and physical systems such as cell aggregates, tissues or bacterial colonies behave as unconventional systems of particles that are strongly constrained by volume exclusion and shape interactions. Understanding how these…
This Chapter contains an overview of the effects of nonlinear interactions in selected problems of non-equilibrium statistical mechanics. Most of the emphasis is put on open setups, where energy is exchanged with the environment. With…