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We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
In this article, we investigate an interacting particle system featuring random intensities, individual noise, and environmental noise, commonly referred to as stochastic point vortex model. The model serves as an approximation for the…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Despite the diversity of materials designated as active matter, virtually all active systems undergo a form of dynamic arrest when crowding and activity compete, reminiscent of the dynamic arrest observed in colloidal and molecular fluids…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
We study analytically the emergence of spontaneous collective motion within large bidimensional groups of self-propelled particles with noisy local interactions, a schematic model for assemblies of biological organisms. As a central result,…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
We consider an exclusion process with finite-range interactions in the microscopic interval $[0,N]$. The process is coupled with the simple symmetric exclusion processes in the intervals $[-N,-1]$ and $[N+1,2N]$, which simulate reservoirs.…
Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
A recently introduced particle-based model for fluid dynamics with effective excluded volume interactions is analyzed in detail. The interactions are modeled by means of stochastic multiparticle collisions which are biased and depend on…
Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…