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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

Luan Carlos de SM Ozelim, André Luís B Cavalcante and Jan Baetens UGent (2017) JOURNAL OF SUPERCOMPUTING. 73(2). p.700-712
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Cellular automata, Advection-dispersion iota delta function, Advection, Diffusion, LATTICE-GAS AUTOMATA
journal title
JOURNAL OF SUPERCOMPUTING
J. Supercomput.
volume
73
issue
2
pages
700 - 712
Web of Science type
Article
Web of Science id
000395014100010
ISSN
0920-8542
1573-0484
DOI
10.1007/s11227-016-1795-7
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
8517554
handle
http://hdl.handle.net/1854/LU-8517554
date created
2017-04-12 14:18:21
date last changed
2017-08-02 12:58:44
@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},
}

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.