Journal
MULTISCALE MODELING & SIMULATION
Volume 10, Issue 1, Pages 191-216Publisher
SIAM PUBLICATIONS
DOI: 10.1137/110836237
Keywords
nonequilibrium molecular dynamics; hypocoercivity; linear response theory; shear viscosity
Funding
- ANDRA (the French National Radioactive Waste Management Agency)
- French Ministry of Research [ANR-09-BLAN-0216-01]
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We study the mathematical properties of a nonequilibrium Langevin dynamics which can be used to estimate the shear viscosity of a system. More precisely, we prove a linear response result which allows us to relate averages over the nonequilibrium stationary state of the system to equilibrium canonical expectations. We then write a local conservation law for the average longitudinal velocity of the fluid and show how, under some closure approximation, the viscosity can be extracted from this profile. We finally characterize the asymptotic behavior of the velocity profile, in the limit where either the transverse or the longitudinal friction goes to infinity. Some numerical illustrations of the theoretical results are also presented.
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