Skip to main content
Springer Nature Link
Log in

A Hybrid Approach to Reaction-Diffusion Processes Simulation

  • Conference paper
  • First Online:
Parallel Computing Technologies (PaCT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2127))

Included in the following conference series:

Abstract

A hybrid approach for simulating reaction-diffusion processes is proposed. It combines into a single iterative procedure Boolean operations of Cellular Automata Diffusion with real number computation of nonlinear reaction function. The kernel of the proposed approach is in constructing methods for transforming reals into spatial distribution of Boolean values. Two algorithms are proposed and illustrated by the simulation of some well studied typical reaction-diffusion phenomena. Computational features of the methods are discussed and problems for future research are outlined.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Toffoli T., Margolus M.: Cellular Automata Machines. MIT Press (1987) 280 p.

    Google Scholar 

  2. Malinetski G.G., Stepantsov M.E.: Modelling diffusive processes by cellular automata with Margolus neighborhood. Zhurnal Vychislitelnoy Matematiki i Matematicheskoy Physiki, vol. 36, N 6, (1998) 1017–1021 (in Russian).

    Google Scholar 

  3. Bandman O.L.: Comparative Study of Cellular-Automata Diffusion Models. In: Malyshkin V.(ed.): Lecture Notes in Computer Science. Vol. 1662. Springer-Verlag, berlin (1999) 395–409.

    Google Scholar 

  4. Toffoli T.: Cellular Automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Physica. 10D (1984) 117–127.

    MathSciNet  Google Scholar 

  5. Adamatsky A.: Reaction-Diffusion and Excitable processors: a sense of the unconventional. Parallel and Distributed Computing Practices. N1 (1999).

    Google Scholar 

  6. Latkin E.: SCAM: a chemical computer. Vychislitelnye systemy. Vol. 152. Institute of Mathematics, Novosibirsk (1995) 140–152 (in Russian).

    Google Scholar 

  7. Allouche J.P., Reder C.: Oscillations Spatio-Temporelles Engendrees par un Automate Cellullaire. Disc.Appl.Math.(1984) 215–254.

    Google Scholar 

  8. Bandini S., Illy E., Simone C., F.S. Liverani F.S.: A Computational Model Based on the Reaction-Diffusion Machine to Simulate Transportation Phenomena: the case of Coffee Percolation. In: Bandini S., Serra R., Liverani F.S. (eds): Cellular Automata: Research Towards Industry. Springer-Verlag (1998) 157–164.

    Google Scholar 

  9. Bandini S., Mauri G., Pavesi G., Simone C.: A Parallel Model Based on Cellular Automata for the Simulation of Pesticide Percolation in the Soil. In: Malyshkin V.(ed.): Lecture Notes in Computer Science. Vol. 1662. Springer-Verlag (1999) 382–394.

    Google Scholar 

  10. Rothman D.H., Zaleski S.: Lattice-Gas Cellular Automata. Simple Models of Complex Hydrodynamics. Cambridge University Press (1997) 293 pp.

    Google Scholar 

  11. Kolmogorov A.N., Petrovski I.N., Piskunov N.S.: A study of diffusion equation combined with the increase of substance, and its implementation to a biological problem. Bulletin of Moscow State University. Vol. 1, series A, issue B.(1937) (in Russian)

    Google Scholar 

  12. Madore B.F., Freedman W.L..: Computer Simulation of the Belousov-Zhabotinsky Reaction. In.: S. Wolfram (ed.). Theory and Application of Cellular Automata. Singapore, World Scientific (1986), 311–312.

    Google Scholar 

  13. Young D.A.. A Local Activator-Inhibitor model of Vertebrate Skin Patterns. In: S. Wolfram (ed.). Theory and Application of Cellular Automata. Singapore, World Scientific (1986), 320–327.

    Google Scholar 

  14. Achasova S., Bandman O., Markova V., Piskunov S.: Parallel Substitution Algorithm. Theory and Application. World Scientific, Singapore (1994) 240 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Supercomputer Software Department ICMMG, Siberian Branch, Russian Academy of Science, Pr. Lavrentieva, 6, Novosibirsk, 630090, Russia

    Olga Bandman

Authors
  1. Olga Bandman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Supercomputer Software Department, ICMand MG SB RAS, pr. Lavrentiev 6, 630090, Novosibirsk, Russia

    Victor Malyshkin

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bandman, O. (2001). A Hybrid Approach to Reaction-Diffusion Processes Simulation. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2001. Lecture Notes in Computer Science, vol 2127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44743-1_1

Download citation

  • DOI: https://doi.org/10.1007/3-540-44743-1_1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42522-9

  • Online ISBN: 978-3-540-44743-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics