BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.6.0//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1190@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20210601T082910 DTSTART;TZID=Europe/Zurich:20210602T141500 SUMMARY:Seminar Analysis and Mathematical Physics: Corentin Le Bihan (ENS L yon) DESCRIPTION:A simple model of gas is the hard spheres model. It is a billia rd of little particles which can interact very strongly at very small dist ance (think for example of real billiards with a lot of balls). Because un derstanding such system is an outstanding problem\, people tried to find a limiting process. A first equation governing the density of one particle was given by Boltzmann :∂tf+v⋅∇xf=Q(f\,f)\\r\\nIn its formal derivat ion Boltzmann supposed that two different particles are almost independent \, so the probability of having two particles at the same place is the the product of probability. The validity of such equation is a priori not cle ar since it adds some irreversibly that does not exist in the hard sphere model.\\r\\nLanford solved the problem in its ‘75 paper: Boltzmann’s e quation is true\, up to a time independent of the number of particles (how ever each particle will have in mean less than one collision).\\r\\nNow co mes the question of the boundary. We expect to find some “Lanfords” th eorem even if we add some boundary condition. A first example are the spec ular reflections\, for a deterministic law. An other example\, which would be very important in physics\, is the evolution of a gas between two hot plaques. Then the reflection condition is stochastic. I am interested in a third type of reflection\, also stochastic\, which is a modeling of a rou gh boundary.\\r\\nDuring my talk I will present some ideas of the proof of Boltzmann in the torus R^3/Z^3 and the adaptation in the case of a domain with boundaries. X-ALT-DESC:

A simple model of gas is the hard spheres model. It is a bill iard of little particles which can interact very strongly at very small di stance (think for example of real billiards with a lot of balls). Because understanding such system is an outstanding problem\, people tried to find a limiting process. A first equation governing the density of one particl e was given by Boltzmann :∂tf+v⋅ ∇xf=Q(f \,f)

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In its formal derivation Boltzman n supposed that two different particles are almost independent\, so the pr obability of having two particles at the same place is the the product of probability. The validity of such equation is a priori not clear since it adds some irreversibly that does not exist in the hard sphere mod el.

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Lanford solved the problem in its ‘75 paper: Boltzmann’s e quation is true\, up to a time independent of the number of particles (how ever each particle will have in mean less than one collision).

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Now comes the question of the boundary. We expect to find some “Lanfords” theorem even if we add some boundary condition. A first example are the s pecular reflections\, for a deterministic law. An other example\, which wo uld be very important in physics\, is the evolution of a gas between two h ot plaques. Then the reflection condition is stochastic. I am interested i n a third type of reflection\, also stochastic\, which is a modeling of a rough boundary.

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During my talk I will present some ideas of the pr oof of Boltzmann in the torus R^3/Z^3 and the adaptation in the case of a domain with boundaries.

DTEND;TZID=Europe/Zurich:20210602T160000 END:VEVENT END:VCALENDAR