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On the iota-delta function : a link between cellular automata and partial differential equations for modeling advection–dispersion from a constant source

(2017) JOURNAL OF SUPERCOMPUTING. 73(2). p.700-712
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Abstract
Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow and both share features with two-dimensional CAs. One-dimensional CAs, on the other hand, seem to have been neglected for modeling physical phenomena. In the present paper, we demonstrate that some one-dimensional CAs are equivalent to a stable linear finite difference scheme used to solve advection-diffusion partial differential equations (PDEs) by relying on the so-called iota-delta representation. Consequently, this work shows an important link between continuous and discrete models in general, and PDEs and CAs more in particular.
Keywords
Cellular automata, Advection-dispersion iota delta function, Advection, Diffusion, LATTICE-GAS AUTOMATA

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Chicago
Ozelim, Luan Carlos de SM, André Luís B Cavalcante, and Jan Baetens. 2017. “On the Iota-delta Function : a Link Between Cellular Automata and Partial Differential Equations for Modeling Advection–dispersion from a Constant Source.” Journal of Supercomputing 73 (2): 700–712.
APA
Ozelim, L. C. de S., Cavalcante, A. L. B., & Baetens, J. (2017). On the iota-delta function : a link between cellular automata and partial differential equations for modeling advection–dispersion from a constant source. JOURNAL OF SUPERCOMPUTING, 73(2), 700–712.
Vancouver
1.
Ozelim LC de S, Cavalcante ALB, Baetens J. On the iota-delta function : a link between cellular automata and partial differential equations for modeling advection–dispersion from a constant source. JOURNAL OF SUPERCOMPUTING. 2017;73(2):700–12.
MLA
Ozelim, Luan Carlos de SM, André Luís B Cavalcante, and Jan Baetens. “On the Iota-delta Function : a Link Between Cellular Automata and Partial Differential Equations for Modeling Advection–dispersion from a Constant Source.” JOURNAL OF SUPERCOMPUTING 73.2 (2017): 700–712. Print.
@article{8517554,
  abstract     = {Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow and both share features with two-dimensional CAs. One-dimensional CAs, on the other hand, seem to have been neglected for modeling physical phenomena. In the present paper, we demonstrate that some one-dimensional CAs are equivalent to a stable linear finite difference scheme used to solve advection-diffusion partial differential equations (PDEs) by relying on the so-called iota-delta representation. Consequently, this work shows an important link between continuous and discrete models in general, and PDEs and CAs more in particular.},
  author       = {Ozelim, Luan Carlos de SM and Cavalcante, Andr{\'e} Lu{\'i}s B and Baetens, Jan},
  issn         = {0920-8542},
  journal      = {JOURNAL OF SUPERCOMPUTING},
  keyword      = {Cellular automata,Advection-dispersion iota delta function,Advection,Diffusion,LATTICE-GAS AUTOMATA},
  language     = {eng},
  number       = {2},
  pages        = {700--712},
  title        = {On the iota-delta function : a link between cellular automata and partial differential equations for modeling advection--dispersion from a constant source},
  url          = {http://dx.doi.org/10.1007/s11227-016-1795-7},
  volume       = {73},
  year         = {2017},
}

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