Related papers: Feynman-Kac Equations for Reaction and Diffusion P…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
We further develop the general theory of the area reactivity model that provides an alternative description of the diffusion-influenced reaction of an isolated receptor-ligand pair in terms of a generalized Feynman-Kac equation. We analyze…
Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic…
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
In this article we prove the existence of Bernstein processes which we associate in a natural way with a class of linear parabolic initial-and final boundary value problems defined in bounded convex subsets of Euclidean space of arbitrary…
This is a brief review on Brownian functionals in one dimension and their various applications, a contribution to the special issue ``The Legacy of Albert Einstein" of Current Science. After a brief description of Einstein's original…
A numerical study of the role of anomalous diffusion in front propagation in reaction-diffusion systems is presented. Three models of anomalous diffusion are considered: fractional diffusion, tempered fractional diffusion, and a model that…
The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different…
We study three basic diffusion-controlled reaction processes -- annihilation, coalescence, and aggregation. We examine the evolution starting with the most natural inhomogeneous initial configuration where a half-line is uniformly filled by…
This article develops a methodology allowing application of the complete machinery of particle-based inference methods upon the class of continuous-discrete State Space Models (CD-SSMs). Such models correspond to a latent continuous-time…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
We study theoretically and numerically the steady state diffusion controlled reaction $A+B\rightarrow\emptyset$, where currents $J$ of $A$ and $B$ particles are applied at opposite boundaries. For a reaction rate $\lambda$, and equal…
We present a study of atom-wall interactions in non-relativistic quantum electrodynamics by functional integral methods. The Feynman-Kac path integral representation is generalized to the case when the particle interacts with a radiation…
Equation of long-range particle drift and diffusion on three-dimensional physical lattice is suggested. This equation can be considered as a lattice analogof space-fractional Fokker-Planck equation for continuum. The lattice approach gives…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…
Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply…