Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

I. Huerta-Trujillo; J. C. Chimal-Eguía; L. Muñoz-Salazar; J. A. Martinez-Nuño

doi:10.1155/2015/542507

Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

I. Huerta-Trujillo, J. C. Chimal-Eguía, L. Muñoz-Salazar, J. A. Martinez-Nuño

Centro de Investigación en Computación (CIC)

Research output: Contribution to journal › Article › peer-review

Abstract

This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.

Original language	English
Article number	542507
Journal	Discrete Dynamics in Nature and Society
Volume	2015
DOIs	https://doi.org/10.1155/2015/542507
State	Published - 2015

Access to Document

10.1155/2015/542507

Cite this

@article{3fcc4622c3df40d3b6c82dc498517e6e,

title = "Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton",

abstract = "This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.",

author = "I. Huerta-Trujillo and Chimal-Egu{\'i}a, {J. C.} and L. Mu{\~n}oz-Salazar and Martinez-Nu{\~n}o, {J. A.}",

note = "Publisher Copyright: {\textcopyright} 2015 I. Huerta-Trujillo et al.",

year = "2015",

doi = "10.1155/2015/542507",

language = "Ingl{\'e}s",

volume = "2015",

journal = "Discrete Dynamics in Nature and Society",

issn = "1026-0226",

}

TY - JOUR

T1 - Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

AU - Huerta-Trujillo, I.

AU - Chimal-Eguía, J. C.

AU - Muñoz-Salazar, L.

AU - Martinez-Nuño, J. A.

PY - 2015

Y1 - 2015

N2 - This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.

AB - This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency.

UR - http://www.scopus.com/inward/record.url?scp=84934324427&partnerID=8YFLogxK

U2 - 10.1155/2015/542507

DO - 10.1155/2015/542507

M3 - Artículo

SN - 1026-0226

VL - 2015

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

M1 - 542507

ER -

Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton

Abstract

Access to Document

Other files and links

Fingerprint

Cite this