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SUMMARY:Directed Percolation: Lecture 2 - Mike Cates (University of Cambri
 dge)
DTSTART:20240410T150000Z
DTEND:20240410T160000Z
UID:TALK215416@talks.cam.ac.uk
DESCRIPTION:Directed percolation (DP) is a specific model whose significan
 ce is that it shares behaviour (specifically\, a set of critical phenomena
 \, characterized by universal exponents) with a large class of other model
 s\, many of reaction-diffusion type. A famous conjecture asserts that the 
 DP universality class contains all models with a handful of broadly define
 d features\, such as the existence of a unique 'absorbing state' which the
  system can enter but not escape. The onset of turbulence by proliferation
  of puffs appears to satisfy these criteria\, allowing many pre-existing r
 esults to be asserted without further reference to the underlying fluid me
 chanics. In these two lectures I will give a brief overview of the DP clas
 s\, and some of its properties. I will start from discrete models but soon
  move onto coarse-grained ones described by stochastic PDEs. These can be 
 used to make specific predictions concerning the critical exponents\, incl
 uding their exact values in spatial dimensions d > 4 and\, via the renorma
 lization group (RG)\, estimates for d < 4. I will not go into the details 
 of how the RG works\, but will outline how it explains universality: model
 s in the same universality class differ by terms that are 'irrelevant' in 
 a precisely defined sense. If time allows I will also discuss some models 
 that superficially resemble DP but are not in its universality class. Thes
 e include so-called parity-conserving DP (with two absorbing states) and c
 onserved DP (with infinitely many).&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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