Related papers: Kinetic Model for Myxobacteria with Directional Di…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
In this paper, we discuss the existence and uniqueness of coexistence states for a class of non-local elliptic system. This problem models the behaviour of a bacteria and a living nutrient, whose diffusion depends on the population of the…
In the present paper the macroscopic limits of the kinetic model for inter-acting entities (individuals, organisms, cells) are studied. The kinetic model is one-dimensional and entities are characterized by their position and orientation…
Motivated by observations of the dynamics of {\it Myxococcus xanthus}, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but…
Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion…
We study the evolution of fronts in a bistable reaction-diffusion system when the nonlinear reaction term is spatially non-homogeneous. This equation has been used to model wave propagation in various biological systems. Extending previous…
We experimentally investigate how aerotactic bacteria, confined within a thin liquid film between two solid substrates, respond to a controlled oxygen gradient. We find that the total bacterial number density dictates which mechanism…
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking…
Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal…
We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimension subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria, for example, track in a…
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tumble phase in which they change their orientation. When…
We study analytically and numerically a bistable reaction-diffusion equation on an arbitrary finite network. We prove that stable fixed points (multi-fronts) exist for any configuration as long as the diffusion is small. We also study fold…
Contemporary epidemiological models often involve spatial variation, providing an avenue to investigate the averaged dynamics of individual movements. In this work, we extend a recent model by Vaziry, Kolokolnikov, and Kevrekidis [Royal…
In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion…
We investigate numerically a model consisting in a kinetic equation for the biased motion of bacteria following a run-and-tumble process, coupled with two reaction-diffusion equations for chemical signals. This model exhibits asymptotic…
Soft surfaces, spanning vastly different environmental and biomedical settings, are frequently colonised by surface-associated bacteria. Yet, how soft surfaces govern bacterial dynamics and their self-organisation into colonies remains…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…