相关论文: Convergence rates for energies of interacting part…
Densities of particles on $\Rn$ which interact pairwise through an attractive-repulsive power-law potential $W_{\al,\bt}(x) = |x|^\al/\al-|x|^\bt/\bt$ have often been used to explain patterns produced by biological and physical systems. In…
We give a general existence and convergence result for interacting particle systems on locally finite graphs with possibly unbounded degrees or jump rates. We allow the local state space to be Polish, and the jumps at a site to affect the…
We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a $\Gamma$-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we…
A nonlinear Fokker-Planck equation is obtained in the continuous limit of a one-dimensional lattice with an energy landscape of wells and barriers. Interaction is possible among particles in the same energy well. A parameter $\gamma$,…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
We present here exact results for a one-dimensional gas, or fluid, of hard-sphere particles with attractive boundaries. The particles, which can exchange with a bulk reservoir, mediate an interaction between the boundaries. A…
We consider a self-propelled particle system which has been used to describe certain types of collective motion of animals, such as fish schools and bird flocks. Interactions between particles are specified by means of a pairwise potential,…
This paper considers the equilibrium positions of $n$ particles in one dimension. Two forces act on the particles; a nonlocal repulsive particle-interaction force and an external force which pushes them to an impenetrable barrier. While the…
Systems of particles interacting via inverse-power law potentials have an invariance with respect to changes in length and temperature, implying a correspondence in the dynamics and thermodynamics between different `isomorphic' sets of…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
In this paper we consider three classes of interacting particle systems on $\mathbb Z$: independent random walks, the exclusion process, and the inclusion process. We allow particles to switch their jump rate (the rate identifies the type…
We report studies of the response of a massless particle confined by a potential. At large momentum transfer q it exhibits \tilde{y} or equivalently Nachtmann \xi scaling, and acquires a constant width independent of q. This width has a…
We investigate a diffusive motion of a system of interacting Brownian particles in quasi-one-dimensional micropores. In particular, we consider a semi-infinite 1D geometry with a partially absorbing boundary and the hard-core inter-particle…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics…
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…