相关论文: Analysis of a cross-diffusion model for rival gang…

Reaction-diffusion equation model for a 2-dimensional gas discharge system is introduced in close relationship with the recent experiment by Nasuno. The model shows formation of spots, molecule-like organization of a cluster of spots,…

This paper studies the derivation of the quadratic porous medium equation and a class of cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a nonlocal interaction equation, resp. system, to solutions of…

The transition from localized to systemic spreading of bacteria, viruses and other agents is a fundamental problem that spans medicine, ecology, biology and agriculture science. We have conducted experiments and simulations in a simple…

The existence and stability of localized patterns of criminal activity are studied for the reaction-diffusion model of urban crime that was introduced by Short et. al. [Math. Models. Meth. Appl. Sci., 18, Suppl. (2008), pp. 1249--1267].…

The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…

This paper is devoted to the study of systems of reaction-cross diffusion equations arising in population dynamics. New results of existence of weak solutions are presented, allowing to treat systems of two equations in which one of the…

Recent developments in text-to-image models, particularly Stable Diffusion, have marked significant achievements in various applications. With these advancements, there are growing safety concerns about the vulnerability of the model that…

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing…

The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…

A microscopic approach to macroeconomic features is intended. A model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed. A birth-death lattice gas model taking into account the influence of an economic…

We study a stochastic system of $N$ interacting particles which models bimolecular chemical reaction-diffusion. In this model, each particle $i$ carries two attributes: the spatial location $X_t^i\in \mathbb{T}^d$, and the type $\Xi_t^i\in…

A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…

A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-moving constant-temperature background the macroscopic limit to…

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all…

Established theoretical studies of diffusion in rugged (or rough) potential surfaces have largely focused on quenched energy landscapes. Here we study diffusion on a rugged energy landscape in the presence of dynamic disorder, a situation…

We present a novel study on enhancing the capability of preserving the content in world models, focusing on a property we term World Stability. Recent diffusion-based generative models have advanced the synthesis of immersive and realistic…

We introduce a stochastic individual model for the spatial behavior of an animal population of dispersive and competitive species, considering various kinds of biological effects, such as heterogeneity of environmental conditions, mutual…

The spread of traffic jams in urban networks has long been viewed as a complex spatio-temporal phenomenon that often requires computationally intensive microscopic models for analysis purposes. In this study, we present a framework to…

In this study, a spatially distributed reaction-diffusion-advection (RDA) model with harvesting is investigated to signify the outcome of a competition between two competing species in a heterogeneous environment. The study builds upon the…