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One-dimensional lattices topologically equivalent to three-dimensional lattices within the context of the lattice gas model

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  • Costanza, E.F.
  • Costanza, G.

Abstract

Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion on a cubic lattice within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to a cubic three-dimensional lattice is described in detail using a successive “unfolding” process. This example shows some new features that possess the procedure and extensions are also suggested in order to provide some another uses of the present approach.

Suggested Citation

  • Costanza, E.F. & Costanza, G., 2017. "One-dimensional lattices topologically equivalent to three-dimensional lattices within the context of the lattice gas model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 41-51.
    • Handle: RePEc:eee:phsmap:v:481:y:2017:i:c:p:41-51
    DOI: 10.1016/j.physa.2017.04.010
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    1. Costa Júnior, Manoel Pedro da & Khan, Ahmad Saeed & Sousa, Eliane Pinheiro de & Lima, Patrícia Verônica Pinheiro Sales, 2015. "53," Revista de Economia e Sociologia Rural (RESR), Sociedade Brasileira de Economia e Sociologia Rural, vol. 53(2), January.
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