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DTSTART:19700329T010000
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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Semigroup methods for the derivation of Boltzmann-
type equations from deterministic particle dynamic
s - Karsten Matthies (University of Bath)
DTSTART;TZID=Europe/London:20220215T133000
DTEND;TZID=Europe/London:20220215T141500
UID:TALK170132AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170132
DESCRIPTION:In this talk we will revisit the classical questio
ns of understanding the statistics of various dete
rministic dynamics of n hard spheres of diameter a
with random initial data in the Boltzmann-Grad sc
aling as a tends to zero and n tends to infinity.
I will present some ideas to replace the analysis
of the BBGKY hierarchy. The convergence of the emp
iric dynamics to the Boltzmann-type dynamics is sh
own using semigroup methods to analyse Kolmogorov
equations for associated probability measures on g
enuine collision histories. \; \;\nDetails
are given for a Rayleigh gas where a tagged parti
cle is undergoing collisions with background parti
cles\, which do not interact among each other. In
the Boltzmann-Grad scaling\, we derive the validit
y of a linear Boltzmann equation for arbitrary lon
g times under moderate assumptions on the initial
distributions of the tagged particle and the possi
bly non-equilibrium distribution of the background
. I aim to give various current and future questio
ns. Based on work with George Stone\, Theodora Syn
taka and Florian Theil.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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