Premium
Noise Prevents Collapse of Vlasov‐Poisson Point Charges
Author(s) -
Delarue François,
Flandoli Franco,
Vincenzi Dario
Publication year - 2014
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21476
Subject(s) - coalescence (physics) , statistical physics , noise (video) , mathematics , poisson distribution , point process , bounded function , point (geometry) , poisson point process , point particle , chaotic , classical mechanics , mathematical analysis , physics , computer science , geometry , statistics , artificial intelligence , astrobiology , image (mathematics)
We elucidate the effect of noise on the dynamics of N point charges in a Vlasov‐Poisson model with a singular bounded interaction force. A too simple noise does not affect the structure inherited from the deterministic system and, in particular, cannot prevent coalescence of point charges. Inspired by the theory of random transport of passive scalars, we identify a class of random fields generating random pulses that are chaotic enough to disorganize the structure of the deterministic system and prevent any collapse of particles. We obtain the strong unique solvability of the stochastic model for any initial configuration of distinct point charges. In the case where there are exactly two particles, we implement the “vanishing noise method” for determining the continuation of the deterministic model after collapse. © 2014 Wiley Periodicals, Inc.