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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Directed Percolation: Lecture 1 - Mike Cates (Univ
ersity of Cambridge)
DTSTART;TZID=Europe/London:20240409T160000
DTEND;TZID=Europe/London:20240409T170000
UID:TALK215413AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/215413
DESCRIPTION:Directed percolation (DP) is a specific model whos
e significance is that it shares behaviour (specif
ically\, a set of critical phenomena\, characteriz
ed by universal exponents) with a large class of o
ther models\, many of reaction-diffusion type. A f
amous conjecture asserts that the DP universality
class contains all models with a handful of broadl
y defined features\, such as the existence of a un
ique 'absorbing state' which the system can enter
but not escape. The onset of turbulence by prolife
ration of puffs appears to satisfy these criteria\
, allowing many pre-existing results to be asserte
d without further reference to the underlying flui
d mechanics. In these two lectures I will give a b
rief overview of the DP class\, and some of its pr
operties. I will start from discrete models but so
on move onto coarse-grained ones described by stoc
hastic PDEs. These can be used to make specific pr
edictions concerning the critical exponents\, incl
uding their exact values in spatial dimensions d >
4 and\, via the renormalization group (RG)\, esti
mates for d < 4. I will not go into the details of
how the RG works\, but will outline how it explai
ns universality: models in the same universality c
lass differ by terms that are 'irrelevant' in a pr
ecisely defined sense. If time allows I will also
discuss some models that superficially resemble DP
but are not in its universality class. These incl
ude so-called parity-conserving DP (with two absor
bing states) and conserved DP (with infinitely man
y). \;
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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