Matches in SemOpenAlex for { <https://semopenalex.org/work/W2768225535> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W2768225535 abstract "The derivation of the Boltzmann equation from a particle model of a gas is currently a major area of research in mathematical physics. The standard approach to this problem is to study the BBGKY hierarchy, a system of equations that describe the distribution of the particles. A new method has recently been developed to tackle this problem by studying the probability of observing a specific history of events. We further develop this method to derive the linear Boltzmann equation in the Boltzmann-Grad scaling from two similar Rayleigh gas hard-sphere particle models. In both models the initial distribution of the particles is random and their evolution is deterministic. Validity is shown up to arbitrarily large times and with only moderate moment assumptions on the non-equilibrium initial data. The first model considers a Rayleigh gas whereby one tagged particle collides with a large number of background particles, which have no self interaction. The initial distribution of the background particles is assumed to be spatially homogeneous and at a collision between a background particle and the tagged particle only the tagged particle changes velocity. In the second model we make two changes: we allow the background particles to have a spatially non-homogeneous initial data and we assume that at collision both the tagged particle and background particle change velocity. The proof for each model follows the same general method, where we consider two evolution equations, the idealised and the empirical, on all possible collision histories. It is shown by a semigroup approach that there exists a solution to the idealised equation and that this solution is related to the solution of the linear Boltzmann equation. It is then shown that under the particle dynamics the distribution of collision histories solves the empirical equation. Convergence is shown by comparing the idealised and empirical equations." @default.
- W2768225535 created "2017-12-04" @default.
- W2768225535 creator A5033540905 @default.
- W2768225535 date "2017-09-01" @default.
- W2768225535 modified "2023-09-25" @default.
- W2768225535 title "Derivation of Kinetic Equations from Particle Models" @default.
- W2768225535 hasPublicationYear "2017" @default.
- W2768225535 type Work @default.
- W2768225535 sameAs 2768225535 @default.
- W2768225535 citedByCount "0" @default.
- W2768225535 crossrefType "dissertation" @default.
- W2768225535 hasAuthorship W2768225535A5033540905 @default.
- W2768225535 hasConcept C111368507 @default.
- W2768225535 hasConcept C121332964 @default.
- W2768225535 hasConcept C121704057 @default.
- W2768225535 hasConcept C121864883 @default.
- W2768225535 hasConcept C127313418 @default.
- W2768225535 hasConcept C165995430 @default.
- W2768225535 hasConcept C167312068 @default.
- W2768225535 hasConcept C186603090 @default.
- W2768225535 hasConcept C19979193 @default.
- W2768225535 hasConcept C2524010 @default.
- W2768225535 hasConcept C2778517922 @default.
- W2768225535 hasConcept C33332235 @default.
- W2768225535 hasConcept C33923547 @default.
- W2768225535 hasConcept C38652104 @default.
- W2768225535 hasConcept C41008148 @default.
- W2768225535 hasConcept C74650414 @default.
- W2768225535 hasConcept C97355855 @default.
- W2768225535 hasConcept C99844830 @default.
- W2768225535 hasConceptScore W2768225535C111368507 @default.
- W2768225535 hasConceptScore W2768225535C121332964 @default.
- W2768225535 hasConceptScore W2768225535C121704057 @default.
- W2768225535 hasConceptScore W2768225535C121864883 @default.
- W2768225535 hasConceptScore W2768225535C127313418 @default.
- W2768225535 hasConceptScore W2768225535C165995430 @default.
- W2768225535 hasConceptScore W2768225535C167312068 @default.
- W2768225535 hasConceptScore W2768225535C186603090 @default.
- W2768225535 hasConceptScore W2768225535C19979193 @default.
- W2768225535 hasConceptScore W2768225535C2524010 @default.
- W2768225535 hasConceptScore W2768225535C2778517922 @default.
- W2768225535 hasConceptScore W2768225535C33332235 @default.
- W2768225535 hasConceptScore W2768225535C33923547 @default.
- W2768225535 hasConceptScore W2768225535C38652104 @default.
- W2768225535 hasConceptScore W2768225535C41008148 @default.
- W2768225535 hasConceptScore W2768225535C74650414 @default.
- W2768225535 hasConceptScore W2768225535C97355855 @default.
- W2768225535 hasConceptScore W2768225535C99844830 @default.
- W2768225535 hasLocation W27682255351 @default.
- W2768225535 hasOpenAccess W2768225535 @default.
- W2768225535 hasPrimaryLocation W27682255351 @default.
- W2768225535 hasRelatedWork W1501394657 @default.
- W2768225535 hasRelatedWork W1973902846 @default.
- W2768225535 hasRelatedWork W1995753429 @default.
- W2768225535 hasRelatedWork W2019346186 @default.
- W2768225535 hasRelatedWork W2021894808 @default.
- W2768225535 hasRelatedWork W2023002920 @default.
- W2768225535 hasRelatedWork W2073837688 @default.
- W2768225535 hasRelatedWork W2103683187 @default.
- W2768225535 hasRelatedWork W2133884518 @default.
- W2768225535 hasRelatedWork W2143972299 @default.
- W2768225535 hasRelatedWork W2185919738 @default.
- W2768225535 hasRelatedWork W2461215054 @default.
- W2768225535 hasRelatedWork W2611197819 @default.
- W2768225535 hasRelatedWork W2979333694 @default.
- W2768225535 hasRelatedWork W3081053444 @default.
- W2768225535 hasRelatedWork W3086033969 @default.
- W2768225535 hasRelatedWork W3099591418 @default.
- W2768225535 hasRelatedWork W3100716934 @default.
- W2768225535 hasRelatedWork W39121094 @default.
- W2768225535 hasRelatedWork W77928113 @default.
- W2768225535 isParatext "false" @default.
- W2768225535 isRetracted "false" @default.
- W2768225535 magId "2768225535" @default.
- W2768225535 workType "dissertation" @default.