Related papers: Analytical Investigation of Long-time Diffusion Dy…
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-tumble process to the intracellular reaction where the…
We apply expansion methods to obtain an approximate expression in terms of elementary functions for the space and time dependence of wave packets in a dispersive medium. The specific application to pulses in a cold plasma is considered in…
Synaptic transmission between neurons is governed by a cascade of stochastic reaction-diffusion events that lead to calcium-induced vesicle release of neurotransmitter. Since experimental measurements of such systems are challenging due…
The large scale behaviour of a population of cells that grow and interact through the concentration field of the chemicals they secrete is studied using dynamical renormalization group methods. The combination of the effective long-range…
We consider the evolution of a passive scalar advected by a parallel shear flow in an infinite cylinder with bounded cross section, in arbitrary space dimension. The essential parameters of the problem are the molecular diffusivity $\nu$,…
The manner in which signals propagate through dense granular systems in both space and time is not well understood. In order to learn more about this process, we carry out discrete element simulations of the system response to excitations…
One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…
We study the asymptotic long-range behavior of the time-dependent correlation function of the surface charge density induced on the interface between two media of distinct dielectric functions which are in thermal equilibrium with one…
Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…
We present an analytical and computational study characterizing the structural and dynamical properties of an active filament confined in cylindrical channels. We first outline the effects of the interplay between confinement and polar…
Molecular dynamics simulations are used to show that strong magnetization significantly increases the space and time scales associated with interparticle correlations. The physical mechanism responsible is a channeling effect whereby…
We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of many potentials which are involved (donor - bridge…
Transport and dispersion of active particles in structured environments such as corrugated channels and porous media are important for the understanding of both natural and engineered active systems. Owing to their continuous…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
We perform a linear perturbation analysis of expanding shells driven by expansions of HII regions. The ambient gas is assumed to be uniform. As an unperturbed state, we develop a semi-analytic method for deriving the time evolution of the…
Self-diffusion along the longitudinal coordinate in a channel of varying cross section is considered. The starting point is the two-dimensional Enskog-Boltzmann-Lorentz kinetic equation with appropriated boundary conditions. It is…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
Diffusion models have demonstrated remarkable performance in generation tasks. Nevertheless, explaining the diffusion process remains challenging due to it being a sequence of denoising noisy images that are difficult for experts to…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We use analytical methods and particle-in-cell simulation to investigate the origin of electrons accelerated by the process of direct laser acceleration driven by high-power laser pulses in preformed narrow cylindrical plasma channels. The…