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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 60H10 | enregistrements trouvés : 119

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

Mathematical psychology and psychophysiologyproceedings of the symposium in applied mathematics of the a.m.s. and the s.i.a.m. held in philadelphia,april 15-16,1981 Grossberg, Stephen | American Mathematical Society 1981 Nouveau

Stochastic differential systems proceedings of the IFIP-WG. 7-1 working conferenceLithuaniaAug. 28 - Sept. 2 Grigelionis, B. | Springer-Verlag 1980 Nouveau

Stochastic analysis and applications :proceedings of the international conference held in swansea#April 11-15 Truman, A. ; Williams, D. | Springer-Verlag 1984 Nouveau

Ecole d'été de probabilités de Saint-Flour IX - 1979 :IXème école d'été de probabilités de Saint-Flour#Aout 19 - Sept. 5 Bickel, Peter J. ; El Karoui, Nicole ; Yor, Marc ; Hennequin, P. L. | Springer-Verlag 1981 Nouveau

Ecole d'été de probabilités de Saint-Flour X - 1980 :école d'été de probabilités de Saint-Flour#Juin 29 - Juil. 5 Bismut, J. M. ; Gross, L. ; Krickeberg , K. ; Hennequin, P. L. | Springer-Verlag 1982 Nouveau

Stochastic partial differential equations and applications :proceedings of a conference held in trento#Sept. 30 - Oct. 5 Da Prato, G. ; Tubaro, L. | Springer-Verlag 1987 Nouveau

Stability of stochastic dynamical systemsproceedings of the international symposium organized by the Control Theory CentreJuly 10-14 Curtain, Ruth F. | Springer-Verlag 1972 Nouveau

Mathematics of random media :proceedings of the AMS-SIAM summer seminar held at Virginia Polytechnic Institute and State University#May 29 - June 9 Kohler, Werner E. ; White, Benjamin S. | American Mathematical Society 1991 Nouveau

Statistics and control of random processes Novikov, A. A. ; Shiryaev, A. N. | American Mathematical Society 1994 Nouveau

Mathematical financeproceedings of the period of a workshop of the 1992-93 IMA program on control theory Davis, Mark H. A. ; Duffie, Darrell ; Fleming, Wendell H. ; Shreve, Steven E. | Springer 1995 Nouveau

Stochastic analysis and related topics Vthe Silivri workshop 1994Oslo-Silivri workshop on... at the Nazim Terzioglu Graduate Research Center of Istanbul UniversityJuly 18-29 Korezlioglu, H. ; Oksendal, B. ; Ustunel, A. S. | Birkhäuser 1996 Nouveau

Stochastic PDE's and Kolmogorov equations in infinite dimensions :lectures given at the 2nd session of the Centro Internazionale Matematico Estivo#(C.I.M.E.)#Aug. 24 - Sept. 1 Krylov, N. V. ; Rockner, Michael ; Zabczyk, Jerzy ; Da Prato, G. | Springer 1999 Nouveau

Stochastic models :seventh symposium on probability and stochastic processes held at Mexico City#June 23-28 Gonzales-Barrios, José M. ; Leon, Jorge A. ; Meda, Ana | American Mathematical Society 2003 Nouveau

Stochastic methods in finance :lectures given at the C.I.M.E.-E.M.S. summer school held in Bressanone#July 6-12 Back, K. ; Bielecki, T. R. ; Hippel, Arthur ; Peng, S. ; Schachermayer, W. ; Frittelli, Marco ; Runggaldier, Wolfgang | Springer 2004 Nouveau

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Mathematical psychology and psychophysiology
proceedings of the symposium in applied mathematics of the a.m.s. and the s.i.a.m. held in philadelphia,april 15-16,1981 Grossberg, Stephen | American Mathematical Society 1981 Nouveau

Stochastic differential systems
proceedings of the IFIP-WG. 7-1 working conference

Lithuania
Aug. 28 - Sept. 2 Grigelionis, B. | Springer-Verlag 1980 Nouveau

Stochastic analysis and applications :
proceedings of the international conference held in swansea#April 11-15 Truman, A. ; Williams, D. | Springer-Verlag 1984 Nouveau

Ecole d'été de probabilités de Saint-Flour IX - 1979 :
IXème école d'été de probabilités de Saint-Flour#Aout 19 - Sept. 5 Bickel, Peter J. ; El Karoui, Nicole ; Yor, Marc ; Hennequin, P. L. | Springer-Verlag 1981 Nouveau

Ecole d'été de probabilités de Saint-Flour X - 1980 :
école d'été de probabilités de Saint-Flour#Juin 29 - Juil. 5 Bismut, J. M. ; Gross, L. ; Krickeberg , K. ; Hennequin, P. L. | Springer-Verlag 1982 Nouveau

Stochastic partial differential equations and applications :
proceedings of a conference held in trento#Sept. 30 - Oct. 5 Da Prato, G. ; Tubaro, L. | Springer-Verlag 1987 Nouveau

Stability of stochastic dynamical systems
proceedings of the international symposium organized by the Control Theory Centre
July 10-14 Curtain, Ruth F. | Springer-Verlag 1972 Nouveau

Mathematics of random media :
proceedings of the AMS-SIAM summer seminar held at Virginia Polytechnic Institute and State University#May 29 - June 9 Kohler, Werner E. ; White, Benjamin S. | American Mathematical Society 1991 Nouveau

Mathematical finance
proceedings of the period of a workshop of the 1992-93 IMA program on control theory Davis, Mark H. A. ; Duffie, Darrell ; Fleming, Wendell H. ; Shreve, Steven E. | Springer 1995 Nouveau

Stochastic analysis and related topics V
the Silivri workshop 1994
Oslo-Silivri workshop on... at the Nazim Terzioglu Graduate Research Center of Istanbul University
July 18-29 Korezlioglu, H. ; Oksendal, B. ; Ustunel, A. S. | Birkhäuser 1996 Nouveau

Stochastic PDE's and Kolmogorov equations in infinite dimensions :
lectures given at the 2nd session of the Centro Internazionale Matematico Estivo#(C.I.M.E.)#Aug. 24 - Sept. 1 Krylov, N. V. ; Rockner, Michael ; Zabczyk, Jerzy ; Da Prato, G. | Springer 1999 Nouveau

Stochastic models :
seventh symposium on probability and stochastic processes held at Mexico City#June 23-28 Gonzales-Barrios, José M. ; Leon, Jorge A. ; Meda, Ana | American Mathematical Society 2003 Nouveau

Stochastic methods in finance :
lectures given at the C.I.M.E.-E.M.S. summer school held in Bressanone#July 6-12 Back, K. ; Bielecki, T. R. ; Hippel, Arthur ; Peng, S. ; Schachermayer, W. ; Frittelli, Marco ; Runggaldier, Wolfgang | Springer 2004 Nouveau