Free access
Issue
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 1085 - 1105
DOI http://dx.doi.org/10.1051/m2an/2010053
Published online 26 August 2010
  1. F.J. Alexander and A.L. Garcia, The direct simulation Monte Carlo method. Comp. Phys. 11 (1997) 588–593. [CrossRef]
  2. R.D. Astumian and P. Hanggi, Brownian motors. Phys. Today 55 (2002) 33–39. [CrossRef]
  3. F. Baras, G. Nicolis, M.M. Mansour and J.W. Turner, Stochastic theory of adiabatic explosion. J. Statis. Phys. 32 (1983) 1–23. [CrossRef]
  4. J.B. Bell, A.L. Garcia and S.A. Williams, Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations. Phys. Rev. E 76 (2007) 016708. [CrossRef] [MathSciNet]
  5. I. Bena, M.M. Mansour and F. Baras, Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime. Phys. Rev. E 59 (1999) 5503–5510. [CrossRef] [MathSciNet]
  6. I. Bena, F. Baras and M.M. Mansour, Hydrodynamic fluctuations in the Kolmogorov flow: Nonlinear regime. Phys. Rev. E 62 (2000) 6560–6570. [CrossRef]
  7. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon, Oxford (1994).
  8. M. Bixon and R. Zwanzig, Boltzmann-Langevin equation and hydrodynamic fluctuations. Phys. Rev. 187 (1969) 267–272. [CrossRef] [MathSciNet]
  9. D. Blömker, S. Maier-Paape and T. Wanner, Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation. Trans. Amer. Math. Soc. 360 (2008) 449–489. [CrossRef] [MathSciNet]
  10. E. Calzetta, Relativistic fluctuating hydrodynamics. Class. Quantum Grav. 15 (1998) 653–667. [CrossRef]
  11. H.D. Ceniceros and G.O. Mohler, A practical splitting method for stiff SDEs with application to problems with small noise. Multiscale Model. Simul. 6 (2007) 212–227. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  12. C. Cohen, J.W.H. Sutherland and J.M. Deutch, Hydrodynamic correlation functions for binary mixtures. Phys. Chem. Liquids 2 (1971) 213–235. [CrossRef]
  13. G. De Fabritiis, R. Delgado-Buscalioni and P.V. Coveney, Multiscale modeling of liquids with molecular specificity. Phys. Rev. Lett. 97 (2006) 134501. [CrossRef] [PubMed]
  14. G. De Fabritiis, M. Serrano, R. Delgado-Buscalioni and P.V. Coveney, Fluctuating hydrodynamic modeling of fluids at the nanoscale. Phys. Rev. E 75 (2007) 026307. [CrossRef]
  15. J.M.O. de Zarate and J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier Science (2007).
  16. R. Delgado-Buscalioni and G. De Fabritiis, Embedding molecular dynamics within fluctuating hydrodynamics in multiscale simulations of liquids. Phys. Rev. E 76 (2007) 036709. [CrossRef]
  17. J. Eggers, Dynamics of liquid nanojets. Phys. Rev. Lett. 89 (2002) 084502. [CrossRef] [PubMed]
  18. P. Español, Stochastic differential equations for non-linear hydrodynamics. Physica A 248 (1998) 77. [CrossRef]
  19. R.F. Fox and G.E. Uhlenbeck, Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations. Phys. Fluids 13 (1970) 1893–1902. [CrossRef] [MathSciNet]
  20. A.L. Garcia, Nonequilibrium fluctuations studied by a rarefied gas simulation. Phys. Rev. A 34 (1986) 1454–1457. [CrossRef] [PubMed]
  21. A.L. Garcia, Numerical Methods for Physics. Second edition, Prentice Hall (2000).
  22. A.L. Garcia, Estimating hydrodynamic quantities in the presence of microscopic fluctuations. Commun. Appl. Math. Comput. Sci. 1 (2006) 53–78. [CrossRef] [MathSciNet]
  23. A.L. Garcia and C. Penland, Fluctuating hydrodynamics and principal oscillation pattern analysis. J. Stat. Phys. 64 (1991) 1121–1132. [CrossRef]
  24. A.L. Garcia, M.M. Mansour, G. Lie and E. Clementi, Numerical integration of the fluctuating hydrodynamic equations. J. Stat. Phys. 47 (1987) 209–228. [CrossRef]
  25. A.L. Garcia, M.M. Mansour, G.C. Lie, M. Mareschal and E. Clementi, Hydrodynamic fluctuations in a dilute gas under shear. Phys. Rev. A 36 (1987) 4348–4355. [CrossRef] [PubMed]
  26. G. Giupponi, G. De Fabritiis and P.V. Coveney, Hybrid method coupling fluctuating hydrodynamics and molecular dynamics for the simulation of macromolecules. J. Chem. Phys. 126 (2007) 154903. [CrossRef] [PubMed]
  27. J.O. Hirshfelder, C.F. Curtis and R.B. Bird, Molecular Theory of Gases and Liquids. John Wiley & Sons (1954).
  28. D.J. Horntrop, Mesoscopic simulation of Ostwald ripening. J. Comp. Phys. 218 (2006) 429–441. [CrossRef]
  29. D.J. Horntrop, Spectral method study of domain coarsening. Phys. Rev. E 75 (2007) 046703. [CrossRef]
  30. M. Ibañes, J García-Ojalvo, R. Toral and J.M. Sancho, Dynamics and scaling of noise-induced domain growth. Eur. Phys. J. B 18 (2000) 663–673. [CrossRef] [EDP Sciences]
  31. K. Kadau, T.C. Germann, N.G. Hadjiconstantinou, P.S. Lomdahl, G. Dimonte, B.L. Holian and B.J. Alder, Nanohydrodynamics simulations: An atomistic view of the Rayleigh-Taylor instability. PNAS 101 (2004) 5851–5855. [CrossRef]
  32. K. Kadau, C. Rosenblatt, J. Barber, T. Germann, Z. Huang, P. Carlès and B. Alder, The importance of fluctuations in fluid mixing. PNAS 104 (2007) 7741–7745. [CrossRef]
  33. W. Kang and U. Landman, Universality crossover of the pinch-off shape profiles of collapsing liquid nanobridges in vacuum and gaseous environments. Phys. Rev. Lett. 98 (2007) 064504. [CrossRef] [PubMed]
  34. A.L. Kawczynski and B. Nowakowski, Stochastic transitions through unstable limit cycles in a model of bistable thermochemical system. Phys. Chem. Chem. Phys. 10 (2008) 289–296. [CrossRef] [PubMed]
  35. G.E. Kelly and M.B. Lewis, Hydrodynamic fluctuations. Phys. Fluids 14 (1971) 1925–1931. [CrossRef]
  36. A.M. Lacasta, J.M. Sancho and F. Sagués, Phase separation dynamics under stirring. Phys. Rev. Lett. 75 (1995) 1791–1794. [CrossRef] [PubMed]
  37. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics 6. Pergamon (1959).
  38. L.D. Landau and E.M. Lifshitz, Statistical Physics, Course of Theoretical Physics 5. Pergamon, 3rd edition, part 1st edition (1980).
  39. B.M. Law and J.C. Nieuwoudt, Noncritical liquid mixtures far from equilibrium: the Rayleigh line. Phys. Rev. A 40 (1989) 3880–3885. [CrossRef] [PubMed]
  40. A. Lemarchand and B. Nowakowski, Fluctuation-induced and nonequilibrium-induced bifurcations in a thermochemical system. Mol. Simulat. 30 (2004) 773–780. [CrossRef]
  41. M.M. Mansour, A.L. Garcia, G.C. Lie and E. Clementi, Fluctuating hydrodynamics in a dilute gas. Phys. Rev. Lett. 58 (1987) 874–877. [CrossRef] [PubMed]
  42. M.M. Mansour, A.L. Garcia, J.W. Turner and M. Mareschal, On the scattering function of simple fluids in finite systems. J. Stat. Phys. 52 (1988) 295–309. [CrossRef]
  43. M.M. Mansour, C. Van den Broeck, I. Bena and F. Baras, Spurious diffusion in particle simulations of the Kolmogorov flow. Europhys. Lett. 47 (1999) 8–13. [CrossRef]
  44. M. Mareschal, M.M. Mansour, G. Sonnino and E. Kestemont, Dynamic structure factor in a nonequilibrium fluid: a molecular-dynamics approach. Phys. Rev. A 45 (1992) 7180–7183. [CrossRef] [PubMed]
  45. P. Meurs, C. Van den Broeck and A.L. Garcia, Rectification of thermal fluctuations in ideal gases. Phys. Rev. E 70 (2004) 051109. [CrossRef]
  46. E. Moro, Hybrid method for simulating front propagation in reaction-diffusion systems. Phys. Rev. E 69 (2004) 060101. [CrossRef]
  47. M. Moseler and U. Landman, Formation, stability, and breakup of nanojets. Science 289 (2000) 1165–1169. [CrossRef] [PubMed]
  48. J.C. Nieuwoudt and B.M. Law, Theory of light scattering by a nonequilibrium binary mixture. Phys. Rev. A 42 (1989) 2003–2014. [CrossRef]
  49. B. Nowakowski and A. Lemarchand, Stochastic effects in a thermochemical system with newtonian heat exchange. Phys. Rev. E 64 (2001) 061108. [CrossRef]
  50. B. Nowakowski and A. Lemarchand, Sensitivity of explosion to departure from partial equilibrium. Phys. Rev. E 68 (2003) 031105. [CrossRef]
  51. G. Oster, Darwin's motors. Nature 417 (2002) 25. [CrossRef] [PubMed]
  52. R.K. Pathria, Statistical Mechanics. Butterworth-Heinemann, Oxford (1996).
  53. G. Quentin and I. Rehberg, Direct measurement of hydrodynamic fluctuations in a binary mixture. Phys. Rev. Lett. 74 (1995) 1578–1581. [CrossRef] [PubMed]
  54. L. Rayleigh, Scientific Papers II. Cambridge University Press, Cambridge (1900) 200–207.
  55. R. Schmitz, Fluctuations in nonequilibrium fluids. Phys. Rep. 171 (1988) 1–58. [CrossRef]
  56. J.V. Sengers and J.M.O. de Zárate, Thermal fluctuations in non-equilibrium thermodynamics. J. Non-Equilib. Thermodyn. 32 (2007) 319–329. [CrossRef]
  57. D.H. Sharp, An overview of Rayleigh-Taylor instability. Phys. D 12 (1984) 3–18. [NASA ADS] [CrossRef]
  58. Y. Sone, Kinetic Theory and Fluid Dynamics. Springer (2002).
  59. G.I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. London Ser. A 201 (1950) 192–196. [NASA ADS] [CrossRef]
  60. C. Van den Broeck, R. Kawai and P. Meurs, Exorcising a Maxwell demon. Phys. Rev. Lett. 93 (2004) 090601. [CrossRef] [PubMed]
  61. N. Vladimirova, A. Malagoli and R. Mauri, Diffusion-driven phase separation of deeply quenched mixtures. Phys. Rev. E 58 (1998) 7691–7699. [CrossRef]
  62. S.A. Williams, J.B. Bell and A.L. Garcia, Algorithm refinement for fluctuating hydrodynamics. Multiscale Model. Simul. 6 (2008) 1256–1280. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  63. M. Wu, G. Ahlers and D.S. Cannell, Thermally induced fluctuations below the onset of Rayleigh-Bénard convection. Phys. Rev. Lett. 75 (1995) 1743–1746. [CrossRef] [PubMed]

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