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Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
We consider a model of fermions interacting via point interactions, defined via a certain weighted Dirichlet form. While for two particles the interaction corresponds to infinite scattering length, the presence of further particles…
We introduce an interacting particle system that models the spread of an epidemic in terms of heterogeneous diffusive dynamics, rather than exogenous contact and transmission rates at the population level as in classical compartmental…
In the framework of a final state interaction model, we show that the so-called radial flow, i.e. the almost linear increase of the inverse slope $T$ with the mass of the produced particle, is already contained in the initial condition --…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
We discuss the collective dynamics of self-propelled particles with selective attraction and repulsion interactions. Each particle, or individual, may respond differently to its neighbors depending on the sign of their relative velocity.…
In this paper a general theorem of constructing infinite particle systems of jump types with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses…
In this short survey we compare aspects of two different approaches for scaling limits of interacting particle systems, the hydrodynamic limit and the high density limit. We present some examples, comments and open problems on each approach…
We study thermodynamics properties of a one dimensional gas of hard elongated particles. The particle centers are restricted to a line, while they can rotate in two-dimensional space. Correlations between orientations of the objects are…
We consider a run-and-tumble particle on a finite interval $[a,b]$ with two absorbing end points. The particle has an internal velocity state that switches between three values $v,0,-v$ at exponential times, thus incorporating positive…
Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…
The dynamics of particles in turbulence when the particle-size is larger than the dissipative scale of the carrier flow is studied. Recent experiments have highlighted signatures of particles finiteness on their statistical properties,…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…
We study a system of interacting self-propelled particles whose walking velocity depends on the stage of the locomotion cycle. The model introduces a phase equation in the optimal velocity model for vehicular traffic. We find that the…