Complexity reduction in many particle systems with random initial data

Leonid V. Berlyand, Pierre Emmanuel Jabin, Mykhailo Potomkin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider the motion of interacting particles governed by a coupled system of ODEs with random initial conditions. Direct computations for such systems are prohibitively expensive due to a very large number of particles and randomness requiring many realizations in their locations in the presence of strong interactions. While there are several approaches that address the above difficulties, none addresses all three simultaneously. Our goal is to develop such a computational approach in order to capture the experimentally observed emergence of correlations in the collective state (patterns due to strong interactions). Our approach is based on the truncation of the BBGKY hierarchy that allows one to go beyond the classical mean field limit and capture correlations while drastically reducing the computational complexity. Finally, we provide an example showing a numerical solution of this nonlinear and nonlocal system.

Original languageEnglish (US)
Pages (from-to)446-474
Number of pages29
JournalSIAM-ASA Journal on Uncertainty Quantification
Volume4
Issue number1
DOIs
StatePublished - Jan 1 2016

Fingerprint

Many-particle System
Computational complexity
BBGKY Hierarchy
Mean-field Limit
Classical Limit
Interaction
Truncation
Randomness
Coupled System
Computational Complexity
Initial conditions
Numerical Solution
Motion

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Complexity reduction in many particle systems with random initial data. / Berlyand, Leonid V.; Jabin, Pierre Emmanuel; Potomkin, Mykhailo.

In: SIAM-ASA Journal on Uncertainty Quantification, Vol. 4, No. 1, 01.01.2016, p. 446-474.

Research output: Contribution to journalArticle

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