Related papers: On the Reaction Diffusion Master Equation in the M…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
We consider the problem of droplet impact and droplet spreading on a smooth surface in the case of a viscous Newtonian fluid. We revisit the concept of the rim-lamella model, in which the droplet spreading is described by a system of…
This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient…
The Smoluchowski approach to diffusion-controlled reactions is generalized to interacting substrate particles by including the osmotic pressure and hydrodynamic interactions of the nonideal particles in the Smoluchoswki equation within a…
The Smoluchowski equation is a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers, or by positive…
Traditional chemical kinetics may be inappropriate to describe chemical reactions in micro-domains involving only a small number of substrate and reactant molecules. Starting with the stochastic dynamics of the molecules, we derive a…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
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…
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…
Mathematical models are important tools to study the excluded volume effects on reaction-diffusion systems, which are known to play an important role inside living cells. Detailed microscopic simulations with off-lattice Brownian dynamics…
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…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
The stochastic thermodynamics of a dilute, well-stirred mixture of chemically-reacting species is built on the stochastic trajectories of reaction events obtained from the Chemical Master Equation. However, when the molecular populations…
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…
We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…