ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Anfinogentov V. G., Koronovskii A. A., Hramov A. E. Some models of lattice-gas class related with population number description. Izvestiya VUZ. Applied Nonlinear Dynamics, 2000, vol. 8, iss. 4, pp. 74-84. DOI: 10.18500/0869-6632-2000-8-4-74-84

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2000no4p074.pdf
(downloads: 0)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
517.39
DOI: 
10.18500/0869-6632-2000-8-4-74-84

Some models of lattice-gas class related with population number description

Autors: 
Anfinogentov Vasilij Gennadievich, Saratov State University
Koronovskii Aleksei Aleksandrovich, Saratov State University
Hramov Aleksandr Evgenevich, Immanuel Kant Baltic Federal University
Abstract: 

In this work we have proposed the model for population dynamics problems analysis. This model belongs is lattice—gas class models. The results of investigations are compared with the logistic equation solution, the nonlinear diffusion equation one and real demographic statistical data of USA.

Key words: 
-
Acknowledgments: 
The work was supported by the RFBR “Leading Scientific Schools” (00-15-96673) and Federal Target Program “Integration” project А0057/2000.
Reference: 
  1. Agraval H. Construction of molecular dynamics like cellular automata models for simulation оf compressible fluid dynamic systems. arXiv: comp—gas/9905002v1. arXiv Preprint; 1999. 275 p.
  2. Toffoli T, Margolus H. Cellular automata machines. Cambridge: MIT Press; 1987. 200p. DOI: 10.7551/mitpress/1763.001.0001.
  3. Wolfram S. Cellular automation fluids 1: Basic Theory. Journal оf Statistical Physics. 1986;45(3-4):471-526. DOI: 10.1007/BF01021083.
  4. Frish U, d’Humieres D, Hasslacher B, Lallemand Р, Pomeau Y, Rivet J—P. Lattice gas hydrodinamics in two and three dimensions. Complex Systems. 1987;1:649-707.
  5. Huang K. Statistical Mechanics. New York: Wiley; 1963. 493 p.
  6. Koronovsky AA, Khramov AE, Anfinogentov VG. Phenomenological model of electron flow with virtual cathode. Bulletin of the Russian Academy of Sciences: Physics. 1999;63(12):2355-2362. (in Russian).
  7. Csahok Z, Vicsek Т. Lattice-gas model for collective biological motion. Phys. Rev. Е. 1995;52(5):5297-5303. DOI: 10.1103/PhysRevE.52.5297.
  8. Schonfish В. Propagation оf fronts in cellular automata. Physica D. 1995;80:433-450. DOI: 10.1016/0167-2789(94)00192-S.
  9. Clavin Р, Lallemand Р, Рomeau Y, Searby С. Simulation оf free boundaries in flow system by lattice-gas models. J. оf Fluid Mechanics. 1988;188:437-464.
  10. Chopard B, Droz M. Cellular automata model for heat conduction in а fluid. Phys. Lett. A. 1988;126(8-9):476-480. DOI: 10.1016/0375-9601(88)90042-4.
  11. Chan KC, Liang NY. Critical phenomena in аn immiscible lattice-gas cellular automata. Europhys. Lett. 1990;13(6):495-500.
  12. Gerhardt M, Schuster H, Tyson JJ. A cellular automation model of excitable media III. Fitting the Belousov — Zhabotinskii reaction. Physica D. 1990;46:416-426.
  13. Aizawa Y, Nishikawa I, Kaneko K. Solution turbulence in one—dimensional cellular automata. Physica D. 1990;45(1-3):307-327. DOI: 10.1016/0167-2789(90)90191-Q.
  14. Qian YH, d'Himieres Р, Lallemand P. Diffusion simulation with а deterministic one—dimensional lattice—gas model. J. оf Stat. Phys. 1992;68(3-4):563-573. DOI: 10.1007/BF01341763.
  15. Jacobs DJ, Masters AJ. Domain growth in one—dimensional diffusive lattice gas with short-range attraction. Phys. Rev. В. 1994;49(4):2700-2710. DOI: 10.1103/physreve.49.2700.
  16. Рар M, Gouyet J—E. Dendritic growth in а mean—field lattice gas model. Phys. Rev. E. 1997;55(1):45-57. DOI: 10.1103/PhysRevE.55.45.
  17. Malinetsky GG, Stepantsov ME. Modelling the movement of the crowd using cellular automata. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(5):75-79. (in Russian).
  18. Malinetsky GG, Stepantsov ME. Construction of models of the grating gas class to solve gas dynamics problems. Izvestiya VUZ. Applied Nonlinear Dynamics. 1996;4(4-5):59-64. (in Russian).
  19. Hardy J, Рomeau Y, de Pazzis О. Time evolution of а two—dimensional model system. J. of Mat. Phys. 1973;14(12):1746-1759. DOI: 10.1063/1.1666248. Hardy J, Рomeau Y, de Pazzis О. Molecular dynamics оf а classical lattice gas: Transport properties and time correlation functions. Phys. Rev. А. 1976;13(5):1949-1961. DOI: 10.1103/PhysRevA.13.1949.
  20. Frish U, Hasslacher B, Pomeau Y. Lattice—gas automata for Navier — Stokes equation. Phys. Rev. Lett. 1986;56(14):1505-1508. DOI: 10.1103/PhysRevLett.56.1505.
  21. Koronovsky AA, Trubetskov DI. Nonlinear Dynamics in Action. Saratov: College; 1996. 324 p. (in Russian).
  22. Smith JM. Models in Ecology. London: Cambridge University Press; 1974. 160 p. Allee WC, Emerson AE, Park O, Park T, Shmidt KP. Principles оf animal ecology. Philadelphia. W.B. Saunders, 1949.
  23. Trubetskov DI. Kolmogorov, Petrovsky, Piskunov, Fisher and nonlinear diffusion equation. Izvestiya VUZ. Applied Nonlinear Dynamics. 1997;5(6):85-94. (in Russian).
  24. Kolmogorov AN, Petrovsky IG, Piskunov NS. Study of the diffusion equation associated with an increase in the amount of substance and its application to one biological problem. М.: ONTI; 1937. 25 p.
  25. Fisher RA.The wave оf advance оf advantageous genes. Ann. Eugenics. 1937;7(4):355-369. DOI: 10.1111/j.1469-1809.1937.tb02153.x.
  26. Koronovsky AA, Trubetskov DI, Hramov  г AE. Population dynamics as a process obeying the nonlinear diffusion equation. DOKLADY EARTH SCIENCES. 2000;372(3):755-758.
Received: 
07.03.2000
Accepted: 
28.06.2000
Published: 
23.10.2000
  • 272 reads