Related papers: On the Reaction Diffusion Master Equation in the M…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
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…
We study a one-dimensional class of reaction-diffusion models on a $10-$parameters manifold. The equations of motion of the correlation functions close on this manifold. We compute exactly the long-time behaviour of the density and…
We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero.…
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-known Smoluchowski--Kramers diffusion approximation result…
A system of stochastic differential equations describing diffusive phenomena, which has arbitrary friction depending on both state and distribution is investigated. The Smoluchowski-Kramers approximation is seen to describe dynamics in the…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producing a solution that concentrates at a…
In a stochastic reaction network setting we consider the problem of tracking the fate of individual molecules. We show that using the classical large volume limit results, we may approximate the dynamics of a single tracked molecule in a…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
Stochastic evolution of Chemical Reactions Networks (CRNs) over time is usually analysed through solving the Chemical Master Equation (CME) or performing extensive simulations. Analysing stochasticity is often needed, particularly when some…
Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…
Direct interactions between the flow field and the chemical reaction in premixed flames occur when the reaction zone thickness is comparable to, or greater than flow length scales. To study such interactions, a laminar model is considered…
Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to…
We study a model for unimolecular reaction on a supported catalyst including reactant diffusion and desorption, using analytical methods and scaling concepts. For rapid reactions, enhancing surface diffusion or increasing particle size…