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Applied Mathematics Research eXpress (2009) Vol. 2008 : article ID abn004, 36 pages, doi:10.1093/amrx/abn004 published on January 6, 2009
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Sampling Constraints in Average: The Example of Hugoniot Curves

Jean-Bernard Maillet1 and Gabriel Stoltz

1 CEA/DAM, BP 12, 91680 Bruyères-le-Châtel, France
2 Université Paris Est, CERMICS, Projet MICMAC ENPC-INRIA, 6 & 8 Av. Pascal, 77455 Marne-la-Vallée Cedex 2, France

Correspondence: Correspondence to be sent to: stoltz{at}cermics.enpc.fr

We present a method for sampling microscopic configurations of a physical system distributed according to a canonical (Boltzmann–Gibbs) measure, with a constraint holding in average. Assuming that the constraint can be controlled by the volume and/or the temperature of the system, and considering the control parameter as a dynamical variable, a sampling strategy based on a nonlinear stochastic process is proposed. Convergence results for this dynamics are proved using entropy estimates. As an application, we consider the computation of points along the Hugoniot curve, which are equilibrium states obtained after equilibration of a material heated and compressed by a shock wave.


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