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Title:
Lattice Hydrodynamics
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Abstract:
We construct a particular lattice model of 3D incompressible fluid motion with viscosity parameter. The construction follows the momentum derivation of the continuum model switching to combinatorial topology instead of taking the calculus limit. The lattice consists of two interpenetrating face centered cubic lattices which is the crystal structure of NaCl. The lattice defines sodium extreme point cubes with their faces, edges and vertices and chlorine extreme point cubes with their faces, edges and vertices. In this way the lattice of sites organizes a chain complex L of four vector spaces built from overlapping uniform cubes, faces, edges and sites giving a multi-layered covering of periodic three space. There are two nilpotent operators on L, a duality involution, each of odd degree, and a combinatorial Laplacian. The result of the momentum derivation is an ODE on one degree of L which is a combinatorial version of the continuum model.
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