in a class of parabolic SPDEs

Nils Berglund

Description

Niveau: Supérieur
Metastability in a class of parabolic SPDEs Nils Berglund MAPMO, Universite d'Orleans CNRS, UMR 6628 et Federation Denis Poisson Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld Grenoble, 2 decembre 2010

• configuration space


• transition path


• free energy


• stochastic lattice


• order parameter


• µ?


• supersaturated gas


• gibbs measure

Sujets

• Barret
• Poisson
• Berglund
• École polytechnique
• Olivieri
• Fernández
• Cambridge University
• Configuration space
• Free energy
• Phase transition

Informations

• Publié par: chaeh
• Publié le: 01 décembre 2010
• Nombre de lectures: 12
• Langue: English

Extrait

Metastability

in a class of parabolic SPDEs

Nils Berglund MAPMO,Universit´ed’Orl´eans CNRS,UMR6628etFe´d´erationDenisPoisson www.univ-orleans.fr/mapmo/membres/berglund

Collaborators: Florent Barret, Ecole Polytechnique, Palaiseau Bastien Fernandez, CPT, CNRS, Marseille Barbara Gentz, University of Bielefeld

Grenoble,2d´ecembre2010

Metastability in

Examples:

•

•

•

Supercooled

physics

liquid

Supersaturated gas

Wrongly

magnetised

ferromagnet

1

Metastability in physics

Examples:

•Supercooled liquid •Supersaturated gas •Wrongly magnetised ferromagnet

.Near first-order phase transition .Nucleation implies crossing energy

barrier

1-a

Metastability in stochastic lattice models

.aLttice:Λ⊂⊂

Z d .Configuration space:X=S Λ ,Sfinite set (e.g.{−1,1}) .an:HlimainotH:X → R  or lattice gas)(e.g. Ising .Gibbs measure:µ β (x) = e −βH(x) /Z β . chain with invariant measureDynamics: Markovµ β (e.g. Metropolis: Glauber or Kawasaki)

2

Metastability in stochastic lattice models

.Lattice:Λ⊂⊂ Z d .Configuration space:X=S Λ ,Sfinite set (e.g.{−1,1}) .imaH:nainotlH:X → R  or lattice gas)(e.g. Ising .Gibbs measure:µ β (x) = e −βH(x) /Z β .Dynamics: Markov chain with invariant measureµ β (e.g. Metropolis: Glauber or Kawasaki)

Results (forβ1) on •Transition time between + and− or empty and full configuration •Transition path •Shape of critical droplet

.Frank den Hollander,Metastability under stochastic dynamics, Stochastic Process. Appl.114(2004), 1–26. .s,reivierianEnzoOl´llaaiaVMdraaiuELarge deviations and metastability, Cambridge University Press, Cambridge, 2005.

2-a