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 https://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] [Google Scholar]
  2. R.D. Astumian and P. Hanggi, Brownian motors. Phys. Today 55 (2002) 33–39. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  7. G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon, Oxford (1994). [Google Scholar]
  8. M. Bixon and R. Zwanzig, Boltzmann-Langevin equation and hydrodynamic fluctuations. Phys. Rev. 187 (1969) 267–272. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  10. E. Calzetta, Relativistic fluctuating hydrodynamics. Class. Quantum Grav. 15 (1998) 653–667. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  15. J.M.O. de Zarate and J.V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures. Elsevier Science (2007). [Google Scholar]
  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] [Google Scholar]
  17. J. Eggers, Dynamics of liquid nanojets. Phys. Rev. Lett. 89 (2002) 084502. [CrossRef] [PubMed] [Google Scholar]
  18. P. Español, Stochastic differential equations for non-linear hydrodynamics. Physica A 248 (1998) 77. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  20. A.L. Garcia, Nonequilibrium fluctuations studied by a rarefied gas simulation. Phys. Rev. A 34 (1986) 1454–1457. [CrossRef] [PubMed] [Google Scholar]
  21. A.L. Garcia, Numerical Methods for Physics. Second edition, Prentice Hall (2000). [Google Scholar]
  22. A.L. Garcia, Estimating hydrodynamic quantities in the presence of microscopic fluctuations. Commun. Appl. Math. Comput. Sci. 1 (2006) 53–78. [CrossRef] [MathSciNet] [Google Scholar]
  23. A.L. Garcia and C. Penland, Fluctuating hydrodynamics and principal oscillation pattern analysis. J. Stat. Phys. 64 (1991) 1121–1132. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  27. J.O. Hirshfelder, C.F. Curtis and R.B. Bird, Molecular Theory of Gases and Liquids. John Wiley & Sons (1954). [Google Scholar]
  28. D.J. Horntrop, Mesoscopic simulation of Ostwald ripening. J. Comp. Phys. 218 (2006) 429–441. [CrossRef] [Google Scholar]
  29. D.J. Horntrop, Spectral method study of domain coarsening. Phys. Rev. E 75 (2007) 046703. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  35. G.E. Kelly and M.B. Lewis, Hydrodynamic fluctuations. Phys. Fluids 14 (1971) 1925–1931. [CrossRef] [Google Scholar]
  36. A.M. Lacasta, J.M. Sancho and F. Sagués, Phase separation dynamics under stirring. Phys. Rev. Lett. 75 (1995) 1791–1794. [CrossRef] [PubMed] [Google Scholar]
  37. L.D. Landau and E.M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics 6. Pergamon (1959). [Google Scholar]
  38. L.D. Landau and E.M. Lifshitz, Statistical Physics, Course of Theoretical Physics 5. Pergamon, 3rd edition, part 1st edition (1980). [Google Scholar]
  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] [Google Scholar]
  40. A. Lemarchand and B. Nowakowski, Fluctuation-induced and nonequilibrium-induced bifurcations in a thermochemical system. Mol. Simulat. 30 (2004) 773–780. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  46. E. Moro, Hybrid method for simulating front propagation in reaction-diffusion systems. Phys. Rev. E 69 (2004) 060101. [CrossRef] [Google Scholar]
  47. M. Moseler and U. Landman, Formation, stability, and breakup of nanojets. Science 289 (2000) 1165–1169. [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  49. B. Nowakowski and A. Lemarchand, Stochastic effects in a thermochemical system with newtonian heat exchange. Phys. Rev. E 64 (2001) 061108. [CrossRef] [Google Scholar]
  50. B. Nowakowski and A. Lemarchand, Sensitivity of explosion to departure from partial equilibrium. Phys. Rev. E 68 (2003) 031105. [CrossRef] [Google Scholar]
  51. G. Oster, Darwin's motors. Nature 417 (2002) 25. [CrossRef] [PubMed] [Google Scholar]
  52. R.K. Pathria, Statistical Mechanics. Butterworth-Heinemann, Oxford (1996). [Google Scholar]
  53. G. Quentin and I. Rehberg, Direct measurement of hydrodynamic fluctuations in a binary mixture. Phys. Rev. Lett. 74 (1995) 1578–1581. [CrossRef] [PubMed] [Google Scholar]
  54. L. Rayleigh, Scientific Papers II. Cambridge University Press, Cambridge (1900) 200–207. [Google Scholar]
  55. R. Schmitz, Fluctuations in nonequilibrium fluids. Phys. Rep. 171 (1988) 1–58. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  57. D.H. Sharp, An overview of Rayleigh-Taylor instability. Phys. D 12 (1984) 3–18. [NASA ADS] [CrossRef] [Google Scholar]
  58. Y. Sone, Kinetic Theory and Fluid Dynamics. Springer (2002). [Google Scholar]
  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] [Google Scholar]
  60. C. Van den Broeck, R. Kawai and P. Meurs, Exorcising a Maxwell demon. Phys. Rev. Lett. 93 (2004) 090601. [CrossRef] [PubMed] [Google Scholar]
  61. N. Vladimirova, A. Malagoli and R. Mauri, Diffusion-driven phase separation of deeply quenched mixtures. Phys. Rev. E 58 (1998) 7691–7699. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]

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