Theory of multicolor lattice gas: A cellular automaton poisson solver

Chen, H.; Matthaeus, W. H.; Klein, Lawrence S.

doi:10.1016/0021-9991(90)90188-7

Cited by 25 publications

(9 citation statements)

References 6 publications

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“…On the other hand, PDEs are used to compute values of physical quantities at points, whereas CAs are used to compute values of physical quantities over finite volumes (CA cells). Several well-known partial differential equations have been solved on CA lattices, like the Diffusion equation [Chopard & Droz, 1991], the Laplace equation [Danikas et al, 1996], the Poisson equation [Chen et al, 1990], and the Weyl, Dirac, and Maxwell equations [Bialynicki-Birula, 1994], just to name a few.…”

Section: Computation With Cellular Automatamentioning

confidence: 99%

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

Dourvas

Sirakoulis

Adamatzky

2017

Int. J. Bifurcation Chaos

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The continuous increment in the performance of classical computers has been driven to its limit. New ways are studied to avoid this oncoming bottleneck and many answers can be found. An example is the Belousov–Zhabotinsky (BZ) reaction which includes some fundamental and essential characteristics that attract chemists, biologists, and computer scientists. Interaction of excitation wave-fronts in BZ system, can be interpreted in terms of logical gates and applied in the design of unconventional hardware components. Logic gates and other more complicated components have been already proposed using different topologies and particular characteristics. In this study, the inherent parallelism and simplicity of Cellular Automata (CAs) modeling is combined with an Oregonator model of light-sensitive version of BZ reaction. The resulting parallel and computationally-inexpensive model has the ability to simulate a topology that can be considered as a one-bit full adder digital component towards the design of an Arithmetic Logic Unit (ALU).

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Section: Computation With Cellular Automatamentioning

confidence: 99%

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

Dourvas

Sirakoulis

Adamatzky

2017

Int. J. Bifurcation Chaos

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“…This work will present an alternative solution for the nonlinear PBE in non-periodic domains by a lattice evolution method (LEM), based on the spirit of the lattice Boltzmann method solving Navier-Stokes equation [25,26]. Chen et al [27] were the first ones to solve Poisson equation by a lattice evolution method. They introduced the multicolor cellular automaton (CA) model into the lattice gas algorithm.…”

Section: Introductionmentioning

confidence: 99%

Lattice evolution solution for the nonlinear Poisson–Boltzmann equation in confined domains

Wang

2008

Communications in Nonlinear Science and Numerical Simulation

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“…Cellular automata have been extensively used to model complex systems including traffic flow, disease epidemics, stochastic growth, predator-prey dynamics, invasion of populations, earthquakes, forest fire spreading, image processing algorithms, among others (Boulter and Miller 2005;Ferreri and Venturino 2013;Quan-Xing and Zhen 2005). Furthermore, a substantial number of problems relating to differential equations have been solved by the cellular automata approach which includes diffusion equation (Chopard and Droz 1991), Poisson equation (Chen et al 1990), Laplace equation (Danikas et al 1996), among others.…”

Section: Introductionmentioning

confidence: 99%

The NERA model incorporating cellular automata approach and the analysis of the resulting induced stochastic mean field

Ruhomally

Dauhoo

2020

Comp. Appl. Math.

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A stochastic process depicting the spreading dynamics of illicit drug consumption in a given population forms the crux of this work. A probabilistic cellular automaton (PCA) model is developed to examine the effects of the social interactions between nonusers and drug users. The model, called NERA, comprises four classes of individuals, namely, nonuser (N), experimental user (E), recreational user (R), and addict user (A). The stochastic process evolves in time by local transition rules. By means of dynamical simple mean field approximation, a nonlinear system of differential equations illustrating the dynamics of the PCA is obtained. The existence and uniqueness of a positive solution of the model is established, and the fixed points of the system are sought to perform the stability analysis. Furthermore, a stochastic mean field (SMF) approach to the NERA system is introduced. SMF extends the latter model to integrate the stochastic behaviour of drug consumers in a given environment. The SMF system is shown to exhibit a unique global solution which is stochastically ultimately bounded. Simulations of the cellular automaton and mean field analysis are used to study the evolution of the model. Verification and validation are carried out using data available on the consumption of cannabis in the state of Washington (Darnell and Bitney in I − 502 evaluation and benefit-cost analysis: second required report, Washington state institute for public policy. Technical Report, 2017). These numerical experiments confirm that the NERA model can help in the analysis and quantification of the spatial dynamics of illicit drug usage in a given society and eventually provide insight to policy-makers on different steps to be taken to curb this social epidemic.

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Theory of multicolor lattice gas: A cellular automaton poisson solver

Cited by 25 publications

References 6 publications

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

Cellular Automaton Belousov–Zhabotinsky Model for Binary Full Adder

Lattice evolution solution for the nonlinear Poisson–Boltzmann equation in confined domains

The NERA model incorporating cellular automata approach and the analysis of the resulting induced stochastic mean field

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