Related papers: Fractional Chemotaxis Diffusion Equations
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
Subdiffusive fractional equations are not structurally stable with respect to spatial perturbations to the anomalous exponent (Phys. Rev. E 85, 031132 (2012)). The question arises of applicability of these fractional equations to model real…
Anomalous transport processes in which the variance of the distance travelled does not necessarily increase linearly with time are modelled using the formalism of continuous time random walks. We compute particle propagators which have the…
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…
Cells encounter a diverse array of physical and chemical signals as they navigate their natural surroundings. However, their response to the simultaneous presence of multiple cues remains elusive. Particularly, the impact of topography…
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a…
The classical macroscopic chemotaxis equations have previously been derived from an individual-based description of the tactic response of cells that use a "run-and-tumble" strategy in response to environmental cues. Here we derive…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We propose a computational method to simulate anomalous self-diffusion in a simple liquid. The method is based on a molecular dynamics simulation on which we impose the following two conditions: firstly, the inter-particle interaction is…
The life of a cell is governed by highly dynamical microscopic processes. Two notable examples are the diffusion of membrane receptors and the kinetics of transcription factors governing the rates of gene expression. Different fluorescence…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
Aerotaxis is the particular form of chemotaxis in which oxygen plays the role of both the attractant and the repellent. Aerotaxis occurs without methylation adaptation, and it leads to fast and complete aggregation toward the most favorable…
Random-walk Monte Carlo simulations are widely used to predict the optical properties of complex, disordered materials. In presence of large heterogeneities (e.g., spatially-extended nonscattering regions in a turbid environment), an…
In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biological chemotaxis phenomenon in the fluid environment and…
Microorganisms often perform chemotaxis, (i.e., sensing and moving toward a region with a higher concentration of an attractive chemical) by changing the rate of tumbling for random walk. We studied several models with internal adaptive…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
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…