6533b82bfe1ef96bd128e346
RESEARCH PRODUCT
A numerical study of attraction/repulsion collective behavior models: 3D particle analyses and 1D kinetic simulations
Jesús Rosado LinaresPauline LafitteFrancesco Vecilsubject
Collective behaviorParticle numberKinetic energy01 natural sciencesMSC 92B05 70F99 65P40 35L50symbols.namesakecollective behavior0103 physical sciences[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Statistical physics0101 mathematicsRayleigh scattering010306 general physicsParticle systemSelf-organizationPhysicsNumerical analysisStatistical and Nonlinear Physicsattractive/repulsive potentialCondensed Matter Physicsself-organizationswarming010101 applied mathematicsClassical mechanicssymbolsSPHERES[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]description
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, we describe the kinetic system derived as the limit from the particle model as N tends to infinity; we propose, in 1D, a numerical scheme for the simulations, and perform a numerical analysis devoted to trying to recover asymptotically patterns similar to those emerging for the equivalent particle systems, when particles originally evolved on a circle.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-10-01 |