Keith Promislow - Correlation as a Source of Stochasticity in Continuum Models - IPAM at UCLA
Recorded 04 September 2025. Keith Promislow of Michigan State University presents "Correlation as a Source of Stochasticity in Continuum Models" at IPAM's Transitioning from Deterministic to Stochastic Interaction Modeling in Electrochemistry Tutorials.Abstract: Molecular dynamics models resolve material properties in terms of pairwise interactions between N particles. These can be characterized via a partial differential equation for the N-particle probability distribution function. The BBGKY hierarchy represents the coupled interaction of the partially integrated marginals of the probability distribution. Under ideal circumstances, as N grows the effective interactions can be modeled by coupling a single particle to a mean-field generated by the other particles – in this situation the joint probability distributions reduce to tensor products of a single particle distribution. This represents a tremendous reduction in complexity. This mean-field limit is not universal, and it generally breaks down when small groups of particles have successive interactions with each other such as between the water molecules in a hydration shell of an ion. These repeated interactions generate correlations described by 2 and 3 particle joint distributions. We will review the BBGKY framework, and the impact of correlation on the hydrodynamic limits that provide a further reduction to continuum systems. Our focus will be on models of interactions of particles with dipole moments, such as water.
Learn more online at: https://www.ipam.ucla.edu/programs/workshops/bridging-the-gap-transitioning-from-deterministic-to-stochastic-interaction-modeling-in-electrochemistry-tutorials/?tab=overview Receive SMS online on sms24.me
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