Related papers: Hybrid approaches for multiple-species stochastic …
We investigate predator-prey school interactions in aquatic environments using a stochastic differential equation (SDE)-based, particle-level model that incorporates attraction, repulsion, alignment, and environmental noise. Two predation…
Mass-conservative reaction-diffusion systems have recently been proposed as a general framework to describe intracellular pattern formation. These systems have been used to model the conformational switching of proteins as they cycle from…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
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…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Reactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular…
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…
Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…
This paper analyses of a stochastic model of a chemical reaction network with three types of chemical species ${\cal R}$, ${\cal M}$ and ${\cal U}$ that interact to transform a flow of external resources, the chemical species ${\cal Q}$, to…
The classical models for irreversible diffusion-influenced reactions can be derived by introducing absorbing boundary conditions to over-damped continuous Brownian motion (BM) theory. As there is a clear corresponding stochastic process,…
We consider a special type of fast reaction-diffusion systems in which the coefficients of the reaction terms of the two substances are much larger than those of the diffusion terms while the diffusive motion to the substrate is negligible.…
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…
Diffusion models have become the de facto framework for generating new datasets. The core of these models lies in the ability to reverse a diffusion process in time. The goal of this manuscript is to explain, from a PDE perspective, how…
Multiple time scales problems are investigated by combining geometrical and analytical approaches. More precisely, for fast-slow reaction-diffusion systems, we first prove the existence of slow manifolds for the abstract problem under the…
Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary…
Coupling diffusion process of signaling molecules with nonlinear interactions of intracellular processes and cellular growth/transformation leads to a system of reaction-diffusion equations coupled with ordinary differential equations…
The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the…
The aim of our study is to describe the dynamics of ant battles, with reference to laboratory experiments, by means of a chemical stochastic model. We focus on ants behavior as an interesting topic in order to predict the ecological…