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SUMMARY:Different flavours of the mean-field theory - Virga\, E (Universit
  degli Studi di Pavia)
DTSTART:20130320T115000Z
DTEND:20130320T124000Z
UID:TALK44020@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Since the proposal for a remarkably simple theory of ferromagn
 etism made by Weiss in 1906\, under the assumption that each molecule suff
 ered an effective magnetic field (le champ intrieur\, in Weiss' words) mim
 icking the average action of all other molecules\, the notion of mean fiel
 d has grown and acquired a life of its own. The most striking application 
 to liquid crystal science of the mean-field formalism is perhaps the Maier
 -Saupe theory for the nematic phase. Many other models and approximations 
 are comprised under the general heading of mean-field theory\, though ofte
 n one may hardly find any trace of an average\, collective field there\, i
 ts place being taken instead by a generalized order field. Some theories i
 n this ample catalogue are variational\, while others are not. All feature
  a key self-consistency condition\, which may involve a probability distri
 bution density as well as an order field. The lecture will attempt to just
 ify the key self-consistency equatio n in a rigorous way for the different
  flavours that theory has taken.\n\n
LOCATION:Seminar Room 1\, Newton Institute
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