Lattice Gas Hydrodynamics describes the approach to fluid dynamics using a micro-world constructed as an automaton universe, where the microscopic dynamics is based not on a description of interacting particles, but on the laws of symmetry and invariance of macroscopic physics. We imagine point-like particles residing on a regular lattice, where they move from node to node and undergo collisions when their trajectories meet. If the collisions occur according to some simple logical rules, and if the lattice has the proper symmetry, then the automaton shows global behavior very similar to that of real fluids. This book carries two important messages. First, it shows how an automaton universe with simple microscopic dynamics - the lattice gas - can exhibit macroscopic behavior in accordance with the phenomenological laws of classical physics. Second, it demonstrates that lattice gases have spontaneous microscopic fluctuations which capture the essentials of actual fluctuations in real fluids.
In this paper we develop a formalism for calculating the autocorrélation function of a dynamical in terms of a well-defined memory function. Guided by simple physical arguments, an ansatz is ado the functional form of the memory function. This ansatz asserts that the raemory of dynamical cohér decays exponentially. It is f ound that : (a) Despite the monotonie exponential decay of the memory function, the autocorrélation function deduced can display négative régions in some circumstances and decay monotonically in other circumstan (b) The form of the autocorrélation function deduced is identical with that obtained from two ot différent analyses, suggesting that the major properties of the function are of gênerai validity. (c) The computed linear momentum autocorrélation function and power spectrum for liquid Ar are good agreement with the computer e.xperiments of Rahman. (d) The computed dipolar autocorrélation function reproduces ail the features of the experimentally determined autocorrélation function, though at présent insufficient data are available to provide a quanti tive test of the theory. (e) The ansatz used, although obviously not exact, is consistent with the theory of linear régressi (Appendix B). I. * Taken in part from a thesis presented by B.J.B. to The University of Chicago, July 1964. t NATO Postdoctoral Fellow.
to appear in PHYSICS REPORTS) Reactive lattice gas automata provide a microscopic approach to the dynamics of spatially-distributed reacting systems. An important virtue of this approach is that it o ers a method for the investigation of reactive systems at a mesoscopic level that goes beyond phenomenological reaction-di usion equations. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a simple physical picture to show how an automaton can be constructed to capture the essentials of a reactive molecular dynamics scheme. The statistical mechanical theory of the automaton is then developed for di usive transport and for reactive processes, and a general algorithm is presented for reactive LGA. The method is illustrated by considering applications to bistable and excitable media, oscillatory behavior in reactive systems, chemical chaos and pattern formation triggered by Turing bifurcations. The reactive lattice gas scheme is contrasted with related cellular automaton methods and the paper concludes with a discussion of future perspectives.
We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with H = T + V where T is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational method for maximizing the entropy subject to the average energy and normalization constraints. The analytical results show (i) that the nonextensive thermodynamics formalism should be called into question to explain experimental results described by extended exponential distributions exhibiting long tails, i.e. q-exponentials with q > 1, and (ii) that in the thermodynamic limit the theory is only consistent in the range 0 ≤ q ≤ 1 where the distribution has finite support, thus implying that configurations with e.g. energy above some limit have zero probability, which is at variance with the physics of systems in contact with a heat reservoir. We also discuss the (q-dependent) thermodynamic temperature and the generalized specific heat.(a)
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