Related papers: Realistic boundary conditions for stochastic simul…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
Absorbing boundary condition approach to nuclear breakup reactions is investigated. A key ingredient of the method is an absorbing potential outside the physical area, which simulates the outgoing boundary condition for scattered waves.…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
An encounter-based approach consists in using the boundary local time as a proxy for the number of encounters between a diffusing particle and a target to implement various surface reaction mechanisms on that target. In this paper, we…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…
Reaction networks are mathematical models of interacting chemical species that are primarily used in biochemistry. There are two modeling regimes that are typically used, one of which is deterministic and one that is stochastic. In…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two…
The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…
We propose a general theoretical description of chemical reactions occurring on a catalytic surface with heterogeneous reactivity. The propagator of a diffusion-reaction process with eventual absorption on the heterogeneous partially…
This paper is devoted to the anomalous diffusion limit of kinetic equations with a fractional Fokker-Planck collision operator in a spatially bounded domain. We consider two boundary conditions at the kinetic scale: absorption and specular…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
In recent years, several particle-based stochastic simulation algorithms (PSSA) have been developed to study the spatially resolved dynamics of biochemical networks at a molecular scale. A challenge all these approaches have to address is…
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…
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…
We study a random process with reinforcement, which evolves following the dynamics of a given diffusion process in a bounded domain and is resampled according to its occupation measure when it reaches the boundary. We show that its…
In many biological situations, a species arriving from a remote source diffuses in a domain confined between two parallel surfaces until it finds a binding partner. Since such a geometric shape falls in between two- and three-dimensional…
This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an…