Large Scale Monte Carlo Simulations of Fluids under Gravity
A multilevel Monte Carlo method for simulations of fluids under gravity is developed. The approach is based on the Conditional Probability of a state that can be treated as the stochastic equation for the simulated system. The method is illustrated for test cases of a perfect gas and hard-core fluids in one- and two-dimensions, by using model Conditional Probability functions.
N. Metropolis, A.W. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
D. Kandel, E. Domany, and A. Brandt, Phys. Rev. B 40, 330 (1989).
N.B. Wilding, Phys. Rev. E 52, 602 (1995).
A. Brandt, Nucl. Phys. B 26, 137 (1992).
A. Brandt, M. Galun, and D. Ron, J. Stat. Phys. 74, 313 (1993).
P.C. Hohenberg and M. Barmatz, Phys. Rev. A 6, 289 (1971).
M.R. Moldover, J.V. Sengers, and R.W. Ramon, Rev. of Mod. Phys. 51, 79 (1979).
L.A. Bulavin, Yu.M. Ostanevich, A.P. Simkina, and A.V. Strelkov, Ukr. Fiz. Zh. 16, 91 (1971).
L.A. Bulavin, Critical Properties of Liquids (ASMI, Kiev, 2002) (in Russian).
L.A. Bulavin, Neutron Diagnostics of Liquid State of Matter (Institute for Security of AES, Kiev, 2012)(in Russian).
V.Ya. Antonchenko, L.A. Bulavin, V.V. Ilyin, and L.M. Maksymuk, Ukr. Fiz. Zh. 7, 99 (2012).
P.T. Landsberg, J. Dunning-Davies, and D. Pollard, Am. J. Phys. 62, 712 (1994).
F.L. Roman, A. Gonzales, J.A. White, and S. Velasco, Z. Phys. B 104, 353 (1997).
T. Biben, J. Hansen, and J. Barrat, J. Chem. Phys. 98, 7330 (1993).
J. Ibsen, P. Cordero, and R. Tabensky, J. Chem. Phys. 107, 5515 (1997)
D.C. Hong, Phys. Rev. E 63, 051506-1 (2001).
H.M. Jaeger and S.R. Nagel, Rev. Mod. Phys. 68, 1259 (1996).
P.V. Quinn and D.C. Hong, Phys. Rev. E 62, 8295 (2000).
T.L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).
A. Brandt, in Multigrid Methods, edited by W. Hackbush and Trottenberg (Springer, Berlin, 1982).
A. Brandt and D. Ron, in Multiscale Computational Methods in Chemistry and Physics, edited by A. Brandt, J. Bernholc, and K. Binder (IOS Press, Amsterdam, 2000).
L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, Oxford, 1980).
Y. Levin, Physica A 287, 100 (2000).
A. Brandt and V. Ilyin, in Multiscale Computational Methods in Chemistry and Physics, edited by A. Brandt, J. Bernholc and K. Binder (IOS Press, Amsterdam, 2000).
Ya.I. Frenkel, Statistical Physics (Academy of Sciencies of the USSR, Moscow, 1948) (in Russian).
J. Guemes, S. Velasko, and A.C. Hernandez, Physica A 152, 226 (1988).
F.L. Roman, J.A. Whitee, and S. Velasko, Phys. Rev. E 3, 2360 (1996).
R. Piazza, T. Bellini, and V. Degiorgio, Phys. Rev. Let. 71, 4267 (1993).
M.A. Rutgeers, J.H. Dunsmuir, J.Z. Xue, W.B. Russel, and P.M. Chaikin, Phys. Rev. B 53, 5043 (1996).
L. Tonks, Phys. Rev. 50, 955 (1936).
M. Baus and L.J. Colot, Phys. Rev. A 36, 3912 (1987).
S. Warr and J.-P. Hansen, Europhys. Lett. 36, 589 (1996).