Highlight
Free Access
Issue
ESAIM: M2AN
Volume 47, Number 6, November-December 2013
Page(s) 1583 - 1626
DOI https://doi.org/10.1051/m2an/2013077
Published online 20 August 2013
  1. M.P. Allen and D.J. Tildesley, Computer simulation of liquids. Clarendon Press, New York, NY, USA (1989). [Google Scholar]
  2. P. Billingsley, Convergence of probability measures. Wiley Series in Probability and Statistics: Probability and Statistics. John Wiley and Sons Inc., New York, second edition (1999). [Google Scholar]
  3. P. Calderoni, D. Dürr and S. Kusuoka, A mechanical model of Brownian motion in half-space. J. Stat. Phys. 55 (1989) 649–693. [CrossRef] [Google Scholar]
  4. G. Ciccotti, R. Kapral and A. Sergi, Non-equilibrium molecular dynamics. In Handbook of Materials Modeling, edited by S. Yip (2005) 745–761. [Google Scholar]
  5. R. Cont and P. Tankov, Financial modelling with jump processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC, Boca Raton, FL (2004). [Google Scholar]
  6. D. Dürr, S. Goldstein and J. Lebowitz, A mechanical model for the Brownian motion of a convex body. Z. Wahrscheinlichkeit 62 (1983) 427–448. [CrossRef] [Google Scholar]
  7. D. Dürr, S. Goldstein and J.L. Lebowitz. A mechanical model of Brownian motion. Comm. Math. Phys. 78 (1981) 507–530. [CrossRef] [Google Scholar]
  8. B. Edwards, C. Baig and D. Keffer, A validation of the p-SLLOD equations of motion for homogeneous steady-state flows. J. Chem. Phys. 124 (2006). [Google Scholar]
  9. D.J. Evans and G.P. Morriss, Statistical mechanics of nonequilibrium liquids. ANU E Press, Canberra (2007). [Google Scholar]
  10. N.G. Hadjiconstantinou, Discussion of recent developments in hybrid atomistic-continuum methods for multiscale hydrodynamics. Bull. Pol. Acad. Sci-Te. 53 (2005) 335–342. [Google Scholar]
  11. J.H. Irving and J.G. Kirkwood, The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics. J. Chem. Phys. 18 (1950) 817–829. [CrossRef] [Google Scholar]
  12. R. Joubaud and G. Stoltz, Nonequilibrium shear viscosity computations with Langevin dynamics. Multiscale Model. Simul. 10 (2012) 191–216. [CrossRef] [Google Scholar]
  13. P. Kotelenez, Stochastic ordinary and stochastic partial differential equations. In vol. 58 of Stoch. Modell. Appl. Probab. (2008). [Google Scholar]
  14. T.G. Kurtz, Semigroups of conditioned shifts and approximation of Markov processes. Ann. Probab. 3 (1975) 618–642. [CrossRef] [Google Scholar]
  15. S. Kusuoka and S. Liang, A Classical Mechanical Model of Brownian Motion with Plural Particles. Rev. Math. Phys. 22 (2010) 733–838. [CrossRef] [MathSciNet] [Google Scholar]
  16. C. Le Bris and T. Lelièvre, Micro-macro models for viscoelastic fluids: modelling, mathematics and numerics. Sci. China Math. 55 (2012) 353–384. [CrossRef] [Google Scholar]
  17. F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of the Nosé-Hoover thermostatted harmonic oscillator. Arch. Ration. Mech. Anal. 184 (2007) 449–463. [CrossRef] [MathSciNet] [Google Scholar]
  18. F. Legoll, M. Luskin and R. Moeckel, Non-ergodicity of Nosé-Hoover dynamics. Nonlinearity 22 (2009) 1673–1694. [CrossRef] [Google Scholar]
  19. M. McPhie, P. Daivis, I. Snook, J. Ennis and D. Evans, Generalized Langevin equation for nonequilibrium systems. Phys. A 299 (2001) 412–426. [CrossRef] [Google Scholar]
  20. S.T. O’Connell and P.A. Thompson, Molecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows. Phys. Rev. E 52 (1995) R5792–R5795. [CrossRef] [Google Scholar]
  21. W. Ren and W. E, Heterogeneous multiscale method for the modeling of complex fluids and micro-fluidics. J. Comput. Phys. 204 (2005) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Rowley and M. Painter, Diffusion and viscosity equations of state for a Lennard-Jones fluid obtained from molecular dynamics simulations. Int. J. Thermophys. 18 (1997) 1109–1121. [CrossRef] [Google Scholar]
  23. A.V. Skorokhod, Limit theorems for Markov processes. Theor. Probab. Appl. 3 (1958) 202–246. [CrossRef] [Google Scholar]
  24. T. Soddemann, B. Dünweg and K. Kremer, Dissipative particle dynamics: A useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. Phys. Rev. E 68 (2003) 046702. [CrossRef] [Google Scholar]
  25. B. Todd and P.J. Daivis, A new algorithm for unrestricted duration nonequilibrium molecular dynamics simulations of planar elongational flow. Comput. Phys. Commun. 117 (1999) 191–199. [CrossRef] [Google Scholar]
  26. B.D. Todd and P.J. Daivis, Homogeneous non-equilibrium molecular dynamics simulations of viscous flow: techniques and applications. Mol. Simulat. 33 (2007) 189–229. [CrossRef] [Google Scholar]
  27. M.E. Tuckerman, C.J. Mundy, S. Balasubramanian and M.L. Klein, Modified nonequilibrium molecular dynamics for fluid flows with energy conservation. J. Chem. Phys. 106 (1997) 5615–5621. [CrossRef] [Google Scholar]
  28. T. Werder, J.H. Walther and P. Koumoutsakos, Hybrid atomistic-continuum method for the simulation of dense fluid flows. J. Comp. Phys. 205 (2005) 373–390. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you