Relativistic lattice gas hydrodynamics
Tóm tắt
Non-relativistic cellular automata can model non-relativistic hydrodynamical flows. In this article we show that if the hopping occurs on a space-time lattice which is generated by discrete subgroups of the Poincaré group and if the collision rules embody the relativistic conservation laws, we can modelrelativistic flows. The simplest version of the relativistic model is formally isomorphic with the non-relativistic Hardy, de Pazzis and Pomeau (HPP) lattice model, provided we reinterpret the various quantities that appear there. This observation explains the non-Galilean invariant results of HPP.
Tài liệu tham khảo
N.N. Bogoliubov, inStudies in Statistical Mechanics, eds J. de Boer and G.E. Uhlenbeck, Interscience, N.Y., 1962.
W. Israel inRelativistic Fluid Dynamics, eds A. Anile and Y. Choquet-Bruhat, Springer-Verlag, Lecture Notes in Mathematics No. 1385, 1989, pp. 152–210.
C. Eckart,Phys. Rev. 58 (1940) 919.
L.D. Landau,Izv. Akad. Nauk SSSR 17 (1953) 51; L.D. Landau and E.M. Lifshitz,Fluid Mechanics, Pergamon Press, Oxford, 1959.
W. A. Hiscock and L. Lindblom,Ann. Phys. 151 (1983) 466; W. A. Hiscock and L. Lindblom,Phys. Rev. D31 (1985) 725; W.A. Hiscock and L. Lindblom,Phys. Rev. D35 (1987) 3723.
B. Carter inRelativistic Fluid Dynamics, eds A. Anile and Y. Choquet-Bruhat, Springer, Berlin, 1989; T.S. Olson and W.A. Hiscock,Phys. Rev. D41 (1990) 3687.
W. Israel,Ann. Phys. (NY) 100 (1976) 310; W. Israel and J.M. Stewart,Proc. Roy. Soc. (London) A365 (1979) 43.
I. Müller,Z. Phys. 198 (1967) 329; I. Müller and T. Ruggeri,Extended Thermo-dynamics, Springer, Berlin, 1992.
W.A. Hiscock and T.S. Olson,Phys. Lett. A141 (1989) 125.
W.A. Hiscock and L. Lindblom,Phys. Lett. A131 (1988) 509.
Gary E. Doolen, ed.Lattice Gas Methods for Partial Differential Equations, Proc. Vol. IV, Santa Fe Institute Studies in the Sciences of Complexity, Addison Wesley, 1990.
M.S. Raghunathan,Subgroups of Lie Groups, Erg. Math. Bd.68, Springer-Verlag, 1972; A. Schild,Can. J. Math. 1 (1949) 29; P.A.M. Dirac, inProblems of Theoretical Physics, Memorial Volume to Igor E. Tamm, Nauka, Moscow, 1972, pp. 45–51.
S.R. de Groot, W.A. van Leeuwen and Ch.G. Van Weert,Relativistic Kinetic Theory, North Holland, Amsterdam, 1980.