scholarly journals Cellular automaton fluids — A review

Sadhana ◽  
1989 ◽  
Vol 14 (3) ◽  
pp. 133-172 ◽  
Author(s):  
M Raj Lakshmi
Keyword(s):  
Cellular Automaton ◽  
Cellular Automaton Fluids

Immiscible cellular-automaton fluids

1988 ◽  
Vol 52 (3-4) ◽  
pp. 1119-1127 ◽  
Author(s):  
Daniel H. Rothman ◽  
Jeffrey M. Keller
Keyword(s):  
Cellular Automaton ◽  
Cellular Automaton Fluids

Cellular‐automaton fluids: A model for flow in porous media

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 509-518 ◽  
Author(s):  
Daniel H. Rothman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Numerical Methods ◽  
Boundary Conditions ◽  
Pressure Gradient ◽  
Cellular Automaton ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Cellular Automaton Fluids

Numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties. The large‐scale viewpoint is perhaps the most prevalent. Darcy’s law relates the chief macroscopic parameters of interest—flow rate, permeability, viscosity, and pressure gradient—and may be invoked to solve for any of these parameters when the others are known. In practical situations, however, this solution may not be possible. Attention is then typically focused on the estimation of permeability, and numerous numerical methods based on knowledge of the microscopic pore‐space geometry have been proposed. Because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult, microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores, throats, and cracks. I propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries. This new method solves the Navier‐Stokes equations numerically using the cellular‐automaton fluid model introduced by Frisch, Hasslacher, and Pomeau. The cellular‐ automaton fluid is extraordinarily simple—particles of unit mass traveling with unit velocity reside on a triangular lattice and obey elementary collision rules—but is capable of modeling much of the rich complexity of real fluid flow. Cellular‐automaton fluids are applicable to the study of porous media. In particular, numerical methods can be used to apply the appropriate boundary conditions, create a pressure gradient, and measure the permeability. Scale of the cellular‐automaton lattice is an important issue; the linear dimension of a void region must be approximately twice the mean free path of a lattice gas particle. Finally, an example of flow in a 2-D porous medium demonstrates not only the numerical solution of the Navier‐Stokes equations in a highly irregular geometry, but also numerical estimation of permeability and a verification of Darcy’s law.

scholarly journals Cellular Automaton Fluids: Basic Theory

2018 ◽  
pp. 359-408
Author(s):  
Stephen Wolfram
Keyword(s):  
Cellular Automaton ◽  
Basic Theory ◽  
Cellular Automaton Fluids

scholarly journals Cellular automaton fluids 1: Basic theory

1986 ◽  
Vol 45 (3-4) ◽  
pp. 471-526 ◽  
Author(s):  
Stephen Wolfram
Keyword(s):  
Cellular Automaton ◽  
Basic Theory ◽  
Cellular Automaton Fluids

A Probabilistic Cellular Automaton for Evolution

1995 ◽  
Vol 5 (9) ◽  
pp. 1129-1134 ◽  
Author(s):  
Nikolaus Rajewsky ◽  
Michael Schreckenberg
Keyword(s):  
Cellular Automaton ◽  
Probabilistic Cellular Automaton

Autómatas Celulares Aplicados al Comportamiento de Células de Cáncer Cervicouterino

2019 ◽  
Vol 6 (1) ◽  
pp. 44-49
Author(s):  
Tania Muñoz Jiménez ◽  
Aurora Torres Soto ◽  
María Dolores Torres Soto
Keyword(s):  
Cellular Automaton ◽  
Medical Model ◽  
Research Process ◽  
Simulation Algorithm ◽  
Stages Of Development ◽  
Literary Research ◽  
Migration Dynamics ◽  
Three Stages ◽  
And Migration ◽  
Best Parameters

En este documento se describe el desarrollo e implementación de un modelo para simular computacionalmente la dinámica del crecimiento y migración del cáncer cervicouterino, considerando sus principales características: proliferación, migración y necrosis, así como sus etapas de desarrollo. El modelo se desarrolló mediante un autómata celular con enfoques paralelo y secuencial. El autómata celular se basó en el modelo de Gompertz para simular las etapas de desarrollo de este cáncer, el cual se dividió en tres etapas cada una con diferentes comportamientos durante la simulación. Se realizó un diseño experimental con parámetros de entrada que se seleccionaron a partir de la investigación literaria y su discusión con médicos expertos. Al final del proceso de investigación, se logró obtener un algoritmo computacional de simulación muy bueno comparado con el modelo médico de Gompertz y se encontraron los mejores parámetros para su ejecución mediante un diseño factorial soportado estadísticamente. This paper describes the development and implementation of a model to computationally simulate the growth and migration dynamics of cervical cancer, considering its main characteristics: proliferation, migration and necrosis, as well as its stages of development. The model was developed by means of a cellular automaton with parallel and sequential approaches. The cellular automaton was based on the model of Gompertz to simulate the stages of development of this cancer, which was divided into three stages, each with different behaviors during the simulation. An experimental design was carried out with input parameters that were selected from literary research and its discussion with expert physicians. At the end of the research process, a very good simulation algorithm was obtained compared to the Gompertz medical model and the best parameters for its execution were found by means of a statistically supported factorial design.

Replication of a Binary Image on a One-Dimensional Cellular Automaton with Linear Rules

2018 ◽  
Vol 27 (4) ◽  
pp. 415-430
Author(s):  
U Srinivasa Rao ◽  
Jeganathan L ◽  
Keyword(s):  
Cellular Automaton ◽  
Binary Image ◽  
One Dimensional
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