English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The focus of this work is to create benchmark simulations of decay rates tostatistical equilibrium in transport plasma models for Coulomb particleinteractions given by a coupled Vlasov-Poisson Fokker-Planck-Landau equation,as well as with Maxwell type and hard sphere interactions. The qualitativedecay to the equilibrium Maxwell-Boltzmann distribution through relativeentropy is studied in detail for all three types of particle interactions bymeans of a conservative hybrid spectral and discontinuous Galerkin schemeadapted from previous work. More precisely, the Coulomb case shows that thereis a degenerate spectrum, with a decay rate close to the law of two thirdspredicted by upper estimates in a work of Strain and Guo in 2006, while theMaxwell type and hard sphere examples both exhibit a spectral gap as predictedby Desvillettes and Villani in 2000. Such decay rate behavior indicates thatthe analytical estimates for the Coulomb case is sharp while, still to thisdate, there is no analytical proof of sharp degenerate spectral behaviour forthe Fokker-Planck-Landau operator.  Simulations are presented, both for the space-homogeneous case of justparticle potential interactions and the space-inhomogeneous case for the meanfield coupling through the Poisson equation for total charges in periodicdomains. New explicit derivations of spectral collisional weights are presentedin the case of Maxwell type and hard sphere interactions and the stability ofall three scenarios, including Coulomb interactions, is investigated.

Entropy Decay Rates for Conservative Spectral Schemes Modeling Fokker-Planck-Landau Type Flows in the Mean Field Limit