Related papers: Reaction-diffusion systems derived from kinetic th…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
This paper deals with the micro-macro derivation of virus models coupled with a reaction diffusion models that generates the dynamics in space of the virus particles. The first part of the presentation focuses, starting from [5, 6] on a…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
We investigate a recently proposed cross-diffusion system modelling the growth of gliobastoma taking into account size exclusion both in the migration and proliferation process. In addition to degenerate nonlinear cross-diffusion the model…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
In this paper we perform a formal asymptotic analysis on a kinetic model for reactive mixtures in order to derive a reaction-diffusion system of Maxwell-Stefan type. More specifically, we start from the kinetic model of simple reacting…
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe the phenomenon are the celebrated Keller-Segel equation and a…
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with…
The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion…
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour…
A novel approach to simulate simple protein-ligand systems at large time- and length-scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD…
Image-based personalized medicine has the potential to transform healthcare, particularly for diseases that exhibit heterogeneous progression such as Multiple Sclerosis (MS). In this work, we introduce the first treatment-aware…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
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 propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanical stress, or both. The…
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…