相关论文: Anomalous transport in cellular flows: The role of…
The diffusion of a walk in the presence of traps is investigated. Different diffusion regimes are obtained considering the magnitude of the fluctuations in waiting times and jump distances. A constant velocity during the jump motion is…
A recent model of Ariel et al. [1] for explaining the observation of L\'evy walks in swarming bacteria suggests that self-propelled, elongated particles in a periodic array of regular vortices perform a super-diffusion that is consistent…
In this paper we study subdiffusion in a system with a thin membrane. At the beginning, the random walk of a particle is considered in a system with a discrete time and space variable and then the probability describing the evolution of the…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
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…
In both biological and artificial systems, concentration gradients can serve as a convenient mechanism for manipulating particles and generating motility. Particles that interact with a solute will move along its gradient; if they…
On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
The predictability, or lack thereof, of the solar cycle is governed by numerous separate physical processes that act in unison in the interior of the Sun. Magnetic flux transport and the finite time delay it introduces, specifically in the…
We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times $(t_w, t)$…
We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior.…
Non-reciprocal interactions play a key role in shaping transport in active and passive systems, giving rise to striking nonequilibrium behavior. Here, we study the dynamics of a tracer -- active or passive -- embedded in a bath of active or…
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…
Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…
In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…
Under rapid undercooling, glass forming liquids freeze in an amorphous state that can equilibrate only on enormously long time-scales, This is the characteristic sign of aging, which has been observed in a wide range of systems. Brownian…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal…
We analyze the diffusion of charged and neutral tracers suspended in an electrolyte embedded in a channel of varying cross-section. Making use of systematic approximations, the diffusion equation governing the motion of tracers is mapped…
Once the problem of ensemble averaging is removed, correlations between the response of a single molecule to an external driving field $F$, with the history of fluctuations of the particle, become detectable. Exact analytical theory for the…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…