BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:The Many Body Cercignani's Conjecture. - Dr Amit E
inav (DPMMS)
DTSTART;TZID=Europe/London:20141105T160000
DTEND;TZID=Europe/London:20141105T170000
UID:TALK55629AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/55629
DESCRIPTION:One of the most influential equations in the kinet
ic theory of gases is the so-called Boltzmann equa
tion\, describing the time evolution of the probab
ility density of a particle in dilute gas. While w
idely used\, and intuitive\, the Boltzmann equatio
n has no formal validation from Newtonian laws\, i
n macroscopic time scales.\nIn 1956 Marc Kac prese
nted an attempt to solve this problem in a particu
lar settings of the spatially homogeneous Boltzman
n equation. Kac considered a stochastic linear mod
el of N indistinguishable particles\, with one-dim
ensional velocities\, that undergo a random binary
collision process. Under the property of 'chaotic
ity' Kac managed to show that when one takes the n
umber of particles to infinity\, the limit of the
first marginal of the N-particle distribution func
tion satisfies a caricature of the Boltzmann equat
ion\, the so-called Boltzmann-Kac equation. Kac ho
ped that using this mean field approach will lead
to new results in the convergence to equilibrium o
f the limit equation using the simpler\, yet dimen
sion dependent\, linear ODE.\nIn our talk we will
introduce Kac's model and the concept of Chaoticit
y. We will then discuss possible trends to equilib
rium and review recent results in the matter. Time
permitting\, we will describe related research th
at has been done recently in connection to the abo
ve.\n\n
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Eavan Gleeson
END:VEVENT
END:VCALENDAR