TY - GEN
T1 - Some remarks on free energy and coarse-graining
AU - Legoll, Frédéric
AU - Lelièvre, Tony
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.
PY - 2012/1/1
Y1 - 2012/1/1
N2 - We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from (Blanc et al. Journal of Nonlinear Science 20(2):241–275, 2010; Legoll and Lelièvre Nonlinearity 23(9):2131–2163, 2010.), concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation.
AB - We present recent results on coarse-graining techniques for thermodynamic quantities (canonical averages) and dynamical quantities (averages of path functionals over solutions of overdamped Langevin equations). The question is how to obtain reduced models to compute such quantities, in the specific case when the functional to be averaged only depends on a few degrees of freedom. We mainly review, numerically illustrate and extend results from (Blanc et al. Journal of Nonlinear Science 20(2):241–275, 2010; Legoll and Lelièvre Nonlinearity 23(9):2131–2163, 2010.), concerning the computation of the stress-strain relation for one-dimensional chains of atoms, and the construction of an effective dynamics for a scalar coarse-grained variable when the complete system evolves according to the overdamped Langevin equation.
UR - https://www.scopus.com/pages/publications/84870643135
U2 - 10.1007/978-3-642-21943-6_13
DO - 10.1007/978-3-642-21943-6_13
M3 - Conference contribution
AN - SCOPUS:84870643135
SN - 9783642219429
T3 - Lecture Notes in Computational Science and Engineering
SP - 279
EP - 329
BT - Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009
A2 - Runborg, Olof
A2 - Engquist, Bjorn
A2 - Tsai, Yen-Hsi R.
PB - Springer Verlag
T2 - Workshop on Numerical Analysis and Multiscale Computations, 2009
Y2 - 6 December 2009 through 11 December 2009
ER -