Hierarchical foliation of one-dimensional Vlasov-Poisson system

TL;DR

This paper explores the algebraic structure of the one-dimensional Vlasov-Poisson system to bridge the gap between fluid and kinetic models using a hierarchical approach based on the water-bag model.

Contribution

It introduces a hierarchy of sub-algebras that interpolate between fluid and kinetic models, providing a new framework for understanding microscopic effects as symmetry breaking.

Findings

Hierarchical sub-algebras form a bridge between fluid and kinetic models.

The water-bag model helps characterize the microscopic effects.

The analysis reveals symmetry breaking as a key microscopic effect.

Abstract

We elucidate the intermediate of the macroscopic fluid model and the microscopic kinetic model by studying the Poisson algebraic structure of the one-dimensional Vlasov-Poisson system. The water-bag model helps formulating the hierarchy of sub-algebras, which interpolates the gap between the fluid and kinetic models. By analyzing the embedding of the sub-manifold of an intermediate hierarchy in a more microscopic hierarchy, we characterize the microscopic effect as the symmetry breaking pertinent to a macroscopic invariant.