相关论文: Pattern formation of a pathway-based diffusion mod…

The stability of asymptotic profiles of solutions to the Cauchy-Dirichlet problem for Fast Diffusion Equation (FDE, for short) is discussed. The main result of the present paper is the stability of any asymptotic profiles of least energy.…

Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only…

In this letter we present a measurement of the phase-space density distribution (PSDD) of ultra-cold \Rb atoms performing 1D anomalous diffusion. The PSDD is imaged using a direct tomographic method based on Raman velocity selection. It…

This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…

In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…

We present analytic solutions for steady flow of the Johnson-Segalman (JS) model with a diffusion term in various geometries and under controlled strain rate conditions, using matched asymptotic expansions. The diffusion term represents a…

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of…

A suspension of swimming microorganisms often generates a large-scale convective pattern known as bioconvection. In contrast to the thermal Rayleigh-Benard system, recent experimental studies report an emergence of steady localized…

An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of…

Equivariant diffusion policies (EDPs) combine the generative expressivity of diffusion models with the strong generalization and sample efficiency afforded by geometric symmetries. While steering these policies with reinforcement learning…

We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a…

In this work, we design and analyze an asymptotic preserving (AP), semi-implicit finite volume scheme for the scaled compressible isentropic Euler system with a singular pressure law known as the congestion pressure law. The congestion…

In recent years, diffusion models have become the leading approach for distribution learning. This paper focuses on structure-preserving diffusion models (SPDM), a specific subset of diffusion processes tailored for distributions with…

The vertical transport of solid material in a stratified medium is fundamental to a number of environmental applications, with implications for the carbon cycle and nutrient transport in marine ecosystems. In this work, we study the…

Synthesizing fully developed three-dimensional turbulent velocity fields remains a long-standing problem in fluid mechanics and an open challenge for generative modeling. The difficulty arises from the coexistence of extreme dimensionality,…

We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…

In this work, we propose an asymptotic preserving scheme for a non-linear kinetic reaction-transport equation, in the regime of sharp interface. With a non-linear reaction term of KPP-type, a phenomenon of front propagation has been proved…

We have studied the persistence probability $p(t)$ of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the the probability of a stochastic variable that has not changed it's sign…

We present a positive and asymptotic preserving numerical scheme for solving linear kinetic, transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard…

We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a conditional expectation of an associated diffusion process.…