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Open Environment for 2d Lattice-Grain CA

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6350))

Abstract

An open cellular automata (CA) environment applied to the simulation of two-dimensional granular flows is presented herein. The CA belongs to the family of so-called “lattice-grain” (cellular) automata (LGrA) with one particle per cell. The time evolution is governed by a “request-exchange” synchronous mode which simulates a two-stage interaction-advection process. The transition rule follows a simple logic including three physical components: an external field, a set of kinematical exclusion rules and an inertial effect. After a short presentation of the CA logic, this paper describes the open user interface structured onto and emphasizes the versatility of the model.

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References

  1. Wolfram, S.: Statistical Mechanics of Cellular Automata. Rev. Mod. Phys. 55, 601–644 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kirkpatrick, S., Swendsen, R.H.: Statistical Mechanics and Disordered Systems. Comm. ACM 28(4), 363–373 (1985)

    Article  MathSciNet  Google Scholar 

  3. Frisch, U., Hasslacher, B., Pomeau, Y.: Lattice-Gas Automata for the Navier-Stokes Equation. Phys. Rev. Lett. 56(14), 1505–1508 (1986)

    Article  Google Scholar 

  4. Wolfram, S.: Cellular Automata Fluids 1: Basic Theory. J. Stat. Phys. 45, 471–526 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  5. McNamara, G.R., Zanetti, G.: Use of the Boltzmann Equation to Simulate Lattice-Gas Automata. Phys. Rev. Lett. 61(20), 2332–2335 (1988)

    Article  Google Scholar 

  6. Rothman, D.H., Zaleski, S.: Lattice Gas Cellular Automata. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  7. Chopard, B., Droz, M.: Cellular Automata Modeling of Physical Systems. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  8. Talia, D., Sloot, P.: Cellular Automata: Promise and Prospects in Computational Science. Special issue of Fut. Gen. Comp. Sys. 16, 157–305 (1999)

    Article  Google Scholar 

  9. Baxter, G.W., Behringer, R.P.: Cellular Automata Models of Granular Flow. Phys. Rev. A 42, 1017–1020 (1990)

    Article  Google Scholar 

  10. Peng, G., Herrmann, H.J.: Density Waves of Granular Flow in a Pipe Using Lattice-Gas Automata. Phys. Rev. E 49, R1796–R1799 (1994)

    Article  Google Scholar 

  11. Károlyi, A., Kertész, J., Havlin, S., Makse, H.A., Stanley, H.E.: Filling a Silo with a Mixture of Grains: Friction-Induced Segregation. Europhys. Lett. 44(3), 386–392 (1998)

    Article  Google Scholar 

  12. Ktitarev, D.V., Wolf, D.E.: Stratification of Granular Matter in a Rotating Drum: Cellular Automaton Modelling. Granular Matter 1, 141–144 (1998)

    Article  Google Scholar 

  13. Désérable, D., Masson, S., Martinez, J.: Influence of Exclusion Rules on Flow Patterns in a Lattice-Grain Model. In: Kishino, Y. (ed.) Powders and Grains 2001, Balkema, pp. 421–424 (2001)

    Google Scholar 

  14. Cisar, S.E., Ottino, J.M., Lueptow, R.M.: Geometric Effects of Mixing in 2D Granular Tumblers Using Discrete Models. AIChE Journal 53(5), 1151–1158 (2007)

    Article  Google Scholar 

  15. Désérable, D., Dupont, P., Hellou, M., Kamali-Bernard, S.: Cellular Automata Models for Complex Matter. In: Malyshkin, V.E. (ed.) PaCT 2007. LNCS, vol. 4671, pp. 385–400. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Désérable, D.: A Versatile Two-Dimensional Cellular Automata Network for Granular Flow. SIAM J. Applied Math. 62(4), 1414–1436 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Cottenceau, G., Crunchant, S., Garcia, P., Le Guelvouit, G., Michard, X., Padioleau, Y., Zemali, Y.: Grany–3 Project: Design of a Cellular Automaton Simulator Dedicated to Granular Media. Technical Report, INSA Computer Science Department, Supervisors: Désérable, D., Rozé, L (1999)

    Google Scholar 

  18. Cottenceau, G.: Grany–3, http://freshmeat.net/projects/grany3

  19. Litwiniszyn, J.: Application of the Equation of Stochastic Processes to Mechanics of Loose Bodies. Archivuum Mechaniki Stosowanej 8(4), 393–411 (1956)

    MathSciNet  MATH  Google Scholar 

  20. Müllins, W.W.: Stochastic Theory of Particle Flow under Gravity. J. Appl. Phys. 43, 665–678 (1972)

    Article  Google Scholar 

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Cottenceau, G., Désérable, D. (2010). Open Environment for 2d Lattice-Grain CA. In: Bandini, S., Manzoni, S., Umeo, H., Vizzari, G. (eds) Cellular Automata. ACRI 2010. Lecture Notes in Computer Science, vol 6350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15979-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-15979-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15978-7

  • Online ISBN: 978-3-642-15979-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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