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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…

Statistical Mechanics · Physics 2017-07-04 Jordan M. Horowitz

We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signalling molecules, which are diffused over the medium, to the…

Computational Engineering, Finance, and Science · Computer Science 2015-03-20 Chun Tung Chou

Biochemical reaction networks are widely applied across scientific disciplines to model complex dynamic systems. We investigate the diffusion approximation of reaction networks with mass-action kinetics, focusing on the identifiability of…

Probability · Mathematics 2026-04-29 Louis Faul , Linard Hoessly , Panqiu Xia

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…

Numerical Analysis · Mathematics 2019-03-13 Maria Chiara D'Autilia , Ivonne Sgura , Valeria Simoncini

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…

Analysis of PDEs · Mathematics 2025-01-24 Yahya Alnashri

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal…

Quantitative Methods · Quantitative Biology 2018-10-03 Wei-Xiang Chew , Kazunari Kaizu , Masaki Watabe , Sithi V. Muniandy , Koichi Takahashi , Satya N. V. Arjunan

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…

Probability · Mathematics 2025-07-15 Francesca Arceci , Francesco Carlo De Vecchi , Daniela Morale , Stefania Ugolini

We study reaction diffusion equations with a deterministic reaction term as well as two random reaction terms, one that acts on the interior of the domain, and another that acts only on the boundary of the domain. We are interested in the…

Probability · Mathematics 2018-04-16 Sandra Cerrai , Nicholas Paskal

Reaction-diffusion PDEs and particle-based stochastic reaction-diffusion (PBSRD) models are commonly-used approaches for modeling the spatial dynamics of chemical and biological systems. Standard reaction-diffusion PDE models ignore the…

Analysis of PDEs · Mathematics 2021-06-02 Samuel A Isaacson , Jingwei Ma , Konstantinos Spiliopoulos

We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete…

Analysis of PDEs · Mathematics 2025-04-10 Georg Heinze , Alexander Mielke , Artur Stephan

Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…

Quantum Physics · Physics 2008-01-23 Alexander Romanenko , Leonid Yatsenko

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…

Computational Engineering, Finance, and Science · Computer Science 2016-05-06 Daljit Singh J. Dhillon , Michel C. Milinkovitch , Matthias Zwicker

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…

Analysis of PDEs · Mathematics 2018-02-19 Emilie Blanc , Stefan Engblom , Andreas Hellander , Per Lötstedt

We present the spatial regime conversion method (SRCM), a novel hybrid modelling framework for simulating reaction-diffusion systems that adaptively combines stochastic discrete and deterministic continuum representations. Extending the…

Quantitative Methods · Quantitative Biology 2025-07-08 Charles G. Cameron , Cameron A. Smith , Christian A. Yates

In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion depends on subtle assumptions…

Statistical Mechanics · Physics 2020-10-23 Sean D Lawley

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

Graphics · Computer Science 2025-05-20 Javier E. Santos , Agnese Marcato , Roman Colman , Nicholas Lubbers , Yen Ting Lin

The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the…

Quantitative Methods · Quantitative Biology 2015-10-01 Alexander Andreychenko , Luca Bortolussi , Ramon Grima , Philipp Thomas , Verena Wolf

In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this…

Emerging Technologies · Computer Science 2023-01-18 Sebastian Lotter , Maximilian Schäfer , Robert Schober

We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…

Probability · Mathematics 2019-05-02 Wenqing Hu , Michael Salins , Konstantinos Spiliopoulos

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…

Computational Physics · Physics 2016-03-02 Fabian Spill , Pilar Guerrero , Tomas Alarcon , Philip K. Maini , Helen Byrne