Search results for "Particle system"
showing 10 items of 24 documents
Entropies and Equilibria of Many-Particle Systems: An Essay on Recent Research
2004
International audience; .This essay is intended to present a fruitful collaboration which has developed among a group of people whose names are listed above: entropy methods have proved over the last years to be an efficient tool for the understanding of the qualitative properties of physically sound models, for accurate numerics and for a more mathematical understanding of nonlinear PDEs. The goal of this essay is to sketch the historical development of the concept of entropy in connection with PDEs of continuum mechanics, to present recent results which have been obtained by the members of the group and to emphasize the most striking achievements of this research. The presentation is by n…
A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations
2013
39p; International audience; We study at particle and kinetic level a collective behavior model based on three phenomena: self-propulsion, friction (Rayleigh effect) and an attractive/repulsive (Morse) potential rescaled so that the total mass of the system remains constant independently of the number of particles N . In the first part of the paper, we introduce the particle model: the agents are numbered and described by their position and velocity. We iden- tify five parameters that govern the possible asymptotic states for this system (clumps, spheres, dispersion, mills, rigid-body rotation, flocks) and perform a numerical analysis on the 3D setting. Then, in the second part of the paper…
Collision Theory for Two- and Three-Particle Systems Interacting via Short-Range and Coulomb Forces
1996
In two- and three-particle reactions with light nuclei, a rich body of precise experimental data exists in which both projectile and target and/or the fragments occurring in the final state are charged. In order to make optimal use of these data for extracting physically interesting information about the nuclear interactions, the effects of the Coulomb force must be separated out in a reliable manner. For this purpose the mastering of the intricacies of charged-particle scattering theory is of vital importance.
A SIMPLE PARTICLE MODEL FOR A SYSTEM OF COUPLED EQUATIONS WITH ABSORBING COLLISION TERM
2011
We study a particle model for a simple system of partial differential equations describing, in dimension $d\geq 2$, a two component mixture where light particles move in a medium of absorbing, fixed obstacles; the system consists in a transport and a reaction equation coupled through pure absorption collision terms. We consider a particle system where the obstacles, of radius $\var$, become inactive at a rate related to the number of light particles travelling in their range of influence at a given time and the light particles are instantaneously absorbed at the first time they meet the physical boundary of an obstacle; elements belonging to the same species do not interact among themselves…
Large Number Asymptotics for Two-Component Systems with Self-Consistent Coupling
2014
We shall consider the large number asymptotics of particle models for partial differential equations describing two component mixtures with simplest kind of self-consistent couplings. We shall recall in particular two examples related to different classes of models, the first one having both particle-like components and the second one having only one particle-like component (the other being described as a fluid); for these examples, different techniques on the probabilistic and analytic point of view are to be used to rigorously prove the convergence to a limit of the self-consistent terms in a “mean-field”-like asymptotics. The two models were analysed resp. in Bernardin and Ricci (Kinet R…
The kinetics of defect accumulation under irradiation: many-particle effects
1993
The kinetics of Frenkel defect accumulation under permanent particle source (irradiation) is discussed with special emphasis on many-particle effects. Defect accumulation is restricted by their diffusion and annihilation, A + B → 0, if the relative distance is less than the critical distance r0. A novel formalism of many-point particle densities based on Kirkwood's superposition approximation is developed to take into account aggregation of similar defects (A−A, B−B). The dependence of the saturation concentration after a prolonged irradiation upon spatial dimension ( = 1, 2, 3), defect mobility and the initial correlation within geminate pairs is analyzed. It is shown that the defect conce…
Cluster size distributions in particle systems with asymmetric dynamics
2001
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.
Non Markovian Behavior of the Boltzmann-Grad Limit of Linear Stochastic Particle Systems
2007
We will review some results which illustrate how the distribution of obstacles and the shape of the characteristic curves influence the convergence of the probability density of linear stochastic particle systems to the one particle probability density associated with a Markovian process in the Boltzmann-Grad asymptotics.
CP Violation in Correlated Production and Decay of Unstable Particles
2011
We study resonant CP-violating Einstein--Podolsky--Rosen correlations that may take place in the production and decay of unstable scalar particles at high-energy colliders. We show that as a consequence of unitarity and CPT invariance of the S-matrix, in 2 --> 2 scatterings mediated by mixed scalar particles, at least three linearly independent decay matrices associated with the unstable scalar states are needed to obtain non-zero CP-odd observables that are also odd under C-conjugation. Instead, for the correlated production and decay of two unstable particle systems in 2 --> 4 processes, we find that only two independent decay matrices are sufficient to induce a net non-vanishing CP…