On the use of the computer models at study of autowave processes

Robert Mayer

Abstract


The article discusses various computer models of active media and autowave processes that arise in them, which can be used to teach students of physical and mathematical specialties the basics of computer modeling. Autowaves are self-sustaining waves in media with distributed sources of energy, they keep constant their speed, amplitude and shape. Waves occur in active media, elements of which may be in the rest state, excited state, and the state of refractoriness. Eight tasks associated with the creation of discrete and continuous models of the one-dimensional and two-dimensional active media are analyzed. These models allow to simulate the propagation of autowaves, their diffraction, annihilation, synchronization, formation of one-arm and two-arm autowaves, and to study the dependence of the autowave characteristics on the parameters of the active medium. We use the Wiener-Rosenbluth model, the cellular automata method, and numerical methods for differential equations solving. Two programs written in the Pascal language are presented; the results of computer modeling are discussed. The application of the considered models makes it possible to study the method of cellular automata, numerical methods for solving a system of differential equations, helps to formation of the programming skills, establishes the interdisciplinary connections, and increases interest in information technology.

Full Text:

PDF (Russian)

References


El'kin Ju.E. Avtovolnovye processy // Matematicheskaja biologija i bioinformatika. 2006. Tom 1. #1. – S. 27-40.

Boev V. D., Sypchenko R. P. Komp'juternoe modelirovanie. INTU – IT.RU, 2010. – 349 s.

Bulavin L. A., Vygornickij N. V., Lebovka N. I. Komp'juternoe modelirovanie fizicheskih sistem. Dolgoprudnyj: Izdatel'skij Dom "Intellekt", 2011. – 352 c.

Guld H., Tobochnik Ja. Komp'juternoe modelirovanie v fizike. V 2 ch. Ch. 2. M.: Mir, 1990. – 400 s.

Dul'nev G. N., Parfenov V. G., Sigalov A. V. Primenenie JeVM dlja reshenija zadach teploobmena: ucheb. posobie dlja teplofizich. i teplo-jenergetich. spec. vuzov. M.: Vyssh. shk., 1990. – 207 s.

Kunin S. Vychislitel'naja fizika. – M.: Mir, 1992. – 518 s.

Porshnev S. V. Komp'juternoe modelirovanie fizicheskih processov v pakete MATLAB. M.: Gorjachaja linija – Telekom, 2003. – 592 s.

Giordano N. J. Computational Physics. New Jersey: Prentice Hall, 1997. – 419 p.

Woolfson M. M., Pert G. J. An Introduction to Computer Simulation. – Oxford University Press, 1999. – 311 p.

Kalitkin N. N. Chislennye metody. – BHV-Peterburg, 2011. – 592 s.

Rashhikov V. I., Roshal' A. S. Chislennye metody reshenija fizicheskih zadach: ucheb. posobie. SPb.: Izdatel'stvo "Lan'", 2005. – 208 s.

Phillipson P. E., Schuster P. Modeling by Nonlinear Differential Equations: Dissipative and Conservative Processes. – World Scientific Publishing, 2009. – 225 p.

Vasil'ev V.A., Romanovskih Ju.M., Jahno V.G. Avtovolnovye processy. – M.: Nauka. Gl. red. fiz-mat. lit., 1987. – S. 240.

Zhabotinskij A.M. Koncentracionnye kolebanija. – M.: Nauka, 1974. – S. 178.

Osipov V.V. Prostejshie avtovolny // Sorosovskij obrazovatel'nyj zhurnal. 1999. # 7. – S. 115-121.

Berkovich S.Ja. Kletochnye avtomaty kak model' real'nosti: Poiski novyh predstavlenij fizicheskih i informacionnyh processov. - M.: Izd-vo MGU, 1993. – 112 s.

Toffoli T., Margolus N. Mashiny kletochnyh avtomatov. – M.: Mir, 1991. – 280 s.

Majer R.V. Komp'juternoe modelirovanie avtovolnovyh processov. – Potencial. – 2009. – # 7. – C. 34 – 41.

Majer R.V. Ob ispol'zovanii metoda kompleksnyh amplitud dlja rascheta difrakcionnyh kartin na komp'jutere // Distancionnoe i virtual'noe obuchenie. – 2015. # 7. – S. 13 – 21.


Refbacks

  • There are currently no refbacks.


Abava  Кибербезопасность IT Congress 2024

ISSN: 2307-8162