Lattice Gas Hydrodynamics
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 that capture the essentials of actual fluctuations in real fluids.
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Chapter 4 Equilibrium statistical mechanics
Chapter 6 Linearized hydrodynamics
Chapter 7 Hydrodynamic fluctuations
Chapter 9 Hydrodynamic regimes
automaton average Boltzmann approximation Boltzmann equation Boolean ﬁeld Boon Bravais lattice cellular automata channels per node Chapter coefﬁcients collision operator collision phase collision rules collisional invariants components computed conﬁguration conserved correlation function d’Humieres deﬁned deﬁnition density ﬂuctuations detailed balance diﬂerent discrete dynamic structure factor effective energy eﬂicient eigenvalues ensemble-averaged entropy equilibrium Ernst evolution expression FHP models ﬁnite ﬁrst order ﬂow ﬂuid dynamics ﬂux G-invariant Galilean invariance global HPP model hydrodynamic hydrodynamic regime isometries kinetic energy Lallemand lattice Boltzmann equation lattice gas automata lattice gas model lattice gas simulations lattice gases linear Liouville equation macroscopic macroscopic variables macrostates mass matrix microdynamical equation Microscopic properties modes momentum node rt observable obtain Phys physical post-collision propagation phase quantities real ﬂuids reﬂection rest particles satisﬁed scale second order Section solvability condition space spectrum statistical mechanics symmetry tensor theory thermal thermodynamic three-dimensional transport coeﬂicients two-dimensional velocity vectors wavelength zero