Related papers: A stochastic branching particle method for solving…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
In this paper we prove the well-posedness of non-autonomous deterministic and stochastic reaction-diffusion equations with a polynomial reaction term. Concerning the stochastic problem, we also prove a new result on the space-time…
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…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through…
We study a multigrid method for solving large linear systems of equations with tensor product structure. Such systems are obtained from stochastic finite element discretization of stochastic partial differential equations such as the…
We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical…
This paper presents a space-time interface-fitted finite element method for solving a parabolic advection-diffusion problem with a nonstationary interface. The jumping diffusion coefficient gives rise to the discontinuity of the solution…
In this paper a reaction-diffusion type equation is the starting point for setting up a genuine thermodynamic reduction, i.e. involving a finite number of parameters or collective variables, of the initial system. This program is carried…
In this paper, we present splitting algorithms to solve multicomponent transport models with Maxwell-Stefan-diffusion approaches. The multicomponent models are related to transport problems, while we consider plasma processes, in which the…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
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…
In this work, we have discretized a system of time-dependent nonlinear convection-diffusion-reaction equations with the virtual element method over the spatial domain and the Euler method for the temporal interval. For the nonlinear…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…