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Research talks;Partial Differential Equations;Probability and Statistics;Numerical Analysis and Scientific Computing

The aim of this two-hour lecture is to present the mathematical underpinnings of some common numerical approaches to compute average properties as predicted by statistical physics. The first part provides an overview of the most important concepts of statistical physics (in particular thermodynamic ensembles). The aim of the second part is to provide an introduction to the practical computation of averages with respect to the Boltzmann-Gibbs measure using appropriate stochastic dynamics of Langevin type. Rigorous ergodicity results as well as elements on the estimation of numerical errors are provided. The last part is devoted to the computation of transport coefficients such as the mobility or autodiffusion in fluids, relying either on integrated equilibrium correlations à la Green-Kubo, or on the linear response of nonequilibrium dynamics in their steady-states. The aim of this two-hour lecture is to present the mathematical underpinnings of some common numerical approaches to compute average properties as predicted by statistical physics. The first part provides an overview of the most important concepts of statistical physics (in particular thermodynamic ensembles). The aim of the second part is to provide an introduction to the practical computation of averages with respect to the Boltzmann-Gibbs ...

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Documents 82B31 | enregistrements trouvés : 21

An introduction to molecular dynamics Stoltz, Gabriel | CIRM H Nouveau

Advances in structural reliabilityproceedings of the advanced seminar on structural reliability, held at the joint research center, Ispra, Italy, 4-8 June 1984 Lucia, Alfredo C. | D. Reidel Publishing Company 1987 Nouveau

Stochastic dynamicsworkshop on ...on the occasion of Werner Ebeling 60th birthday Pöschel, Thorsten ; Schimansky-Geier, Lutz | Springer 1997 Nouveau

Lectures on probability theory and statistics :école d'été de probabilités de Saint-Flour XXXIII - 2003#July 6-23 Dembo, Amir ; Funaki, Tadahisa ; Picard, Jean | Springer 2005 Nouveau

Methods of contemporary mathematical statistical physics.lecture notes presented at the 5th Prague summer school on mathematical statistical physicsPrague # september 2006 Kotecky, Roman | Springer 2009 Nouveau

Random walks, brownian motion, and interacting particle systems :a festschrift in honor of frank spitzer Durrett, Rick ; Kesten, Harry | Birkhäuser 1991 Nouveau

Statistical mechanics and fractals Dobrushin, R. L. ; Kusuoka, S. | Springer-Verlag 1993 Nouveau

Statistical mechanics and fractals Dobrushin, R. L. ; Kusuoka, S. | Springer-Verlag 1993 Nouveau

Ideas and methods in quantum and statistical physics Albeverio, Sergio ; Fenstad, J. E. ; Holden, H. ; Lindstrøm, T. | Cambridge University Press 1992 Nouveau

Path integral approach to quantum physics :an introduction Roepstorff, G. | Springer-Verlag 1994 Nouveau

Computer simulation methods :In theoretical physics Heermann, Dieter w. | Springer-Verlag 1990 Nouveau

Large deviations den Hollander, Frank | American Mathematical Society 2000 Nouveau

Statistical mechanics of disordered systems :a mathematical perspective Bovier, Anton | Cambridge University Press 2006 Nouveau

Collected papers I:limit theorems, review articles Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau

Collected papers II:PDE, SDE, diffusions, random media Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau

Collected papers III:large deviations Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau

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Advances in structural reliability
proceedings of the advanced seminar on structural reliability, held at the joint research center, Ispra, Italy, 4-8 June 1984 Lucia, Alfredo C. | D. Reidel Publishing Company 1987 Nouveau

Stochastic dynamics
workshop on ...
on the occasion of Werner Ebeling 60th birthday Pöschel, Thorsten ; Schimansky-Geier, Lutz | Springer 1997 Nouveau

Lectures on probability theory and statistics :
école d'été de probabilités de Saint-Flour XXXIII - 2003#July 6-23 Dembo, Amir ; Funaki, Tadahisa ; Picard, Jean | Springer 2005 Nouveau

Methods of contemporary mathematical statistical physics.
lecture notes presented at the 5th Prague summer school on mathematical statistical physics
Prague # september 2006 Kotecky, Roman | Springer 2009 Nouveau

Random walks, brownian motion, and interacting particle systems :
a festschrift in honor of frank spitzer Durrett, Rick ; Kesten, Harry | Birkhäuser 1991 Nouveau

Path integral approach to quantum physics :
an introduction Roepstorff, G. | Springer-Verlag 1994 Nouveau

Computer simulation methods :
In theoretical physics Heermann, Dieter w. | Springer-Verlag 1990 Nouveau

Statistical mechanics of disordered systems :
a mathematical perspective Bovier, Anton | Cambridge University Press 2006 Nouveau

Collected papers I:
limit theorems, review articles Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau

Collected papers II:
PDE, SDE, diffusions, random media Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau

Collected papers III:
large deviations Varadhan, S. R. S. ; Bhatia, Rajendra ; Bhatt, Abhay ; Parthasarathy, K. R. | Springer;Hindustan Book Agency 2012 Nouveau