Related papers: Diffusion approximation for a simple kinetic model…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material,…
In this work we study a branching particle system of diffusion processes on the real line interacting through their rank in the system. Namely, each particle follows an independent Brownian motion, but only K $\ge$ 1 particles on the far…
The Brownian motion of a particle in a harmonic potential, which is simultaneously exposed either to a linear shear flow or to a plane Poiseuille flow is investigated. In the shear plane of both flows the probability distribution of the…
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…
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant…
Overdamped Brownian motion of a self-propelled particle is studied by solving the Langevin equation analytically. On top of translational and rotational diffusion, in the context of the presented model, the "active" particle is driven along…
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…
We develop diffusion models for time-varying correlation using stochastic processes defined on the unit circle. Specifically, we study Brownian motion on the circle and the von Mises diffusion, and propose their use as continuous-time…
A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical…
Hypothesis: Diffusion in confinement is an important fundamental problem with significant implications for applications of supported liquid phases. However, resolving the spatially dependent diffusion coefficient, parallel and perpendicular…
Diffusion through semipermeable interfaces has a wide range of applications, ranging from molecular transport through biological membranes to reverse osmosis for water purification using artificial membranes. At the single-particle level,…
We introduce the stochastic process of incremental multifractional Brownian motion (IMFBM), which locally behaves like fractional Brownian motion with a given local Hurst exponent and diffusivity. When these parameters change as function of…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
Understanding the spread of infectious diseases requires integrating movement, physical constraints, and spatial configurations into epidemiological models. In this study, we investigate how particle diffusivity, hardcore interactions, and…
We consider a processor sharing queue where the number of jobs served at any time is limited to $K$, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this…
The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Stochastically gated interfaces play an important role in a variety of cellular diffusion processes. Examples include intracellular transport via stochastically gated ion channels and pores in the plasma membrane of a cell, intercellular…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…