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International Conference on Parallel Computing Technologies

PaCT 2007: Parallel Computing Technologies pp 385–400Cite as

Cellular Automata Models for Complex Matter

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4671))

Abstract

Complex matter may lie in various forms from granular matter, soft matter, fluid-fluid or solid-fluid mixtures to compact heterogeneous material. Cellular automata models make a suitable and powerful tool to catch the influence of the microscopic scale onto the macroscopic behaviour of these complex systems. Rather than a survey, this paper will attempt to bring out the main concepts underlying these models and to give an insight for future work.

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References

  1. Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55, 601–644 (1983)

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

  3. Désérable, D.: Cellular automata for granular matter: what trends? In: Bainov, D., Nenov, S. (eds.) Second Int. Conf. on Applied Math. SICAM 2005, Plovdiv, p. 64 (2005)

    Google Scholar 

  4. Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38, 364–374 (1988)

    Article  MathSciNet  Google Scholar 

  5. Kadanoff, L.P., Nagel, S.R., Wu, L., Zhou, S.M.: Scaling and universality in avalanches. Phys. Rev. A 39, 6524–6537 (1989)

    Article  Google Scholar 

  6. Makse, H.A., Herrmann, H.J.: Microscopic model for granular stratification and segregation. Europhys. Lett. 43, 1–6 (1998)

    Article  Google Scholar 

  7. Cizeau, P., Makse, H.A., Stanley, H.E.: Mechanisms of granular spontaneous stratification and segregation in two-dimensional silos. Phys. Rev. E 59, 4408–4421 (1999)

    Article  Google Scholar 

  8. Makse, H.A.: Grain segregation mechanism in aeolian sand ripples. Eur. Phys. J. E 1, 127–135 (2000)

    Article  Google Scholar 

  9. Caps, H., Vandewalle, N.: Ripple and kink dynamics. Phys. Rev. E 64(041302), 1–6 (2001)

    Google Scholar 

  10. Bak, P., Tang, C.: Earthquakes as a self-organized critical phenomena. J. Geophys. Res. 94(B11), 15635–15637 (1989)

    Article  Google Scholar 

  11. Weatherley, D., Mora, P., Xia, M.: Long-range automaton models of earthquakes: power-law accelerations, correlation evolution, and mode-switching. Pure and Applied Geophys. 159(10), 2469–2490 (2002)

    Article  Google Scholar 

  12. Iovine, G., Di Gregorio, S., Lupiano, V.: Debris-flow susceptibility assessment through cellular automata modelling: an example from 15–16 December 1999 disaster at Cervinara and San Martino Valle Caudina (Campania, southern Italy). Natural Hazards Earth Syst. Sc. 3, 457–468 (2003)

    Google Scholar 

  13. Kronholm, K., Birkeland, K.W.: Integrating spatial patterns into a snow avalanche cellular automata model. Geophys. Res. Lett. 32(19), L19504 (2005)

    Article  Google Scholar 

  14. Wolf-Gladrow, D.A.: Lattice-gas cellular automata and lattice Boltzmann models. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  15. Boghosian, B.M.: Lattice gases and cellular automata. Fut. Gen. Comp. Sys. 16, 171–185 (1999)

    Article  Google Scholar 

  16. Chopard, B., Dupuis, A., Masselot, A., Luthi, P.: Cellular automata and lattice Boltzmann techniques: an approach to model and simulate complex systems. Advances in Complex Systems 5(2-3), 103–246 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  17. Frisch, U., d’Humières, D., Hasslacher, B., Lallemand, P., Pomeau, Y., Rivet, J.P.: Lattice-gas hydrodynamics in two and three dimensions. Complex Systems 1, 649–707 (1987)

    MATH  MathSciNet  Google Scholar 

  18. Rothman, D.H., Keller, J.M.: Immiscible cellular-automaton fluids. J. Stat. Phys. 52, 1119–1127 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  19. Stockman, H.W, Li, Ch., Wilson, J.L.: A lattice-gas and lattice Boltzmann study of mixing at continuous fracture junctions: importance of boundary conditions. Geophys. Res. Lett. 24(12), 1515–1518 (1997)

    Article  Google Scholar 

  20. 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 

  21. Higuera, F.J., Succi, S., Benzi, R.: Lattice-gas dynamics with enhanced collisions. Europhys. Lett. 9, 345–349 (1989)

    Article  Google Scholar 

  22. Lallemand, P., Luo, L.-S.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E 61, 6546–6562 (2000)

    MathSciNet  Google Scholar 

  23. Chen, S., Doolen, G.D.: Lattice-Boltzmann method for fluid flow. Ann. Rev. Fluid Mech. 30, 329–364 (1998)

    Article  MathSciNet  Google Scholar 

  24. Flekkøy, E.G., Herrmann, H.J.: Lattice Boltzmann models for complex fluids. Physica A 199, 1–11 (1993)

    Article  Google Scholar 

  25. Ladd, A.J.C., Verberg, R.: Lattice Boltzmann simulations of particle-fluid suspensions. J. Stat. Phys. 104(5), 1191–1251 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  26. Chen, H., Succi, S., Orszag, S.: Analysis of subgrid scale turbulence using the Boltzmann Bhatnagar-Gross-Krook kinetic equation. Phys. Rev. E 59, R2527–2530 (1999)

    Article  Google Scholar 

  27. Xu, K., Prendergast, K.H.: Numerical Navier-Stokes solutions from gas kinetic theory. J. Comp. Phys. 114, 9–17 (1993)

    Article  MathSciNet  Google Scholar 

  28. Talia, D., Sloot, P. (eds.): Cellular automata: promise and prospects in computational science. Special issue of Fut. Gen. Comp. Sys. 16, 157–305 (1999)

    Google Scholar 

  29. Litwiniszyn, J.: Application of the equation of stochastic processes to mechanics of loose bodies. Archivuum Mechaniki Stosowanej 8(4), 393–411 (1956)

    MATH  MathSciNet  Google Scholar 

  30. Müllins, W.W.: Stochastic theory of particle flow under gravity. J. Appl. Phys. 43, 665–678 (1972)

    Article  Google Scholar 

  31. Baxter, G.W., Behringer, R.P.: Cellular automata models of granular flow. Phys. Rev. A 42, 1017–1020 (1990)

    Article  Google Scholar 

  32. Désérable, D.: A versatile two-dimensional cellular automata network for granular flow. SIAM J. Applied Math. 62(4), 1414–1436 (2002)

    Article  MATH  Google Scholar 

  33. Peng, G., Herrmann, H.J.: Density waves of granular flow in a pipe using lattice-gas automata. Phys. Rev. E 49, R1796–1799 (1994)

    Article  Google Scholar 

  34. 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 

  35. Coppersmith, S.N., Liu, C.H., Majumdar, S., Narayan, O., Witten, T.A.: Model for force fluctuations in bead packs. Phys. Rev. E 53, 4673–4685 (1996)

    Article  Google Scholar 

  36. Hemmingsson, J., Herrmann, H.J., Roux, S.: Vectorial cellular automaton for the stress in granular media. J. Phys. I 45, 853–872 (1997)

    Google Scholar 

  37. Masson, S., Désérable, D., Martinez, J.: Modélisation de matériaux granulaires par automate cellulaire. Revue Française de Génie Civil 5(5), 629–650 (2001)

    Google Scholar 

  38. Wolf, D.E., Schreckenberg, M., Bachem, A. (eds.): Traffic and Granular Flow’95, Jülich. World Scientific Publishing, Singapore (1996)

    Google Scholar 

  39. Schadschneider, A., Pöschel, T., Kühne, R., Schreckenberg, M., Wolf, D.E. (eds.): Traffic and Granular Flow’05. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  40. Nagel, K.: Particle hopping models and traffic flow theory. Phys. Rev. E 53, 4655–4672 (1996)

    Article  Google Scholar 

  41. Nagatani, T.: The physics of traffic jams. Rep. Prog. Phys 65, 1331–1386 (2002)

    Article  Google Scholar 

  42. Boon, J.-P., Dab, D., Kapral, R., Lawniczak, A.: Lattice gas automata for reactive systems. Phys. Rep. 273, 55–148 (1996)

    Article  MathSciNet  Google Scholar 

  43. Bandman, O.L.: Cellular-neural automaton: a hybrid model for reaction-diffusion simulation. Fut. Gen. Comp. Sys. 18(6), 737–745 (2002)

    Article  MATH  Google Scholar 

  44. Pudov, S.: First order 2d cellular neural networks investigation and learning. In: Malyshkin, V. (ed.) PaCT 2001. LNCS, vol. 2127, pp. 94–97. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  45. Malinetski, G.G., Stepantsov, M.E.: Modelling diffusive processes by cellular automata with Margolus neighborhood. Zh. Vych. Mat.Mat. Phys. 36(6), 1017–1021 (1998)

    Google Scholar 

  46. Haecker, C.J., Bentz, D.P., Feng, X.P., Stutzman, P.E.: Prediction of cement physical properties by virtual testing. Cement International 1(3), 86–92 (2003)

    Google Scholar 

  47. Bentz, D.P., Garboczi, E.J.: Modelling the leaching of calcium hydroxide from cement paste: effects on pore space percolation and diffusivity. J. Mat. Struct. 25(9), 523–533 (1992)

    Article  Google Scholar 

  48. Kamali, S., Moranville, M., Garboczi, E., Prené, S., Gérard, B.: Hydrate dissolution influence on the Young’s modulus of cement pastes. In: FraMCos 2004, Vail, Colorado, pp. 631–638 (2004)

    Google Scholar 

  49. Bernard, F., Kamali-Bernard, S., Prince, W., Hjaj, M.: 3D multi-scale modeling of mortar mechanical behavior and effect of changes in the microstructure. In: FraMCos 2007, Catania, Italy (in press)

    Google Scholar 

  50. Psakhie, S.G., Horie, Y., Ostermeyer, G.P., Korostelev, S.Y., Smolin, A.Y., Shilko, E.V., Dmitriev, A.I., Blatnik, S., Spegel, M., Zavsek, S.: Movable cellular automata method for simulating materials with mesostructure. Theor. Appl. Fract. Mech. 37, 311–334 (2001)

    Article  Google Scholar 

  51. Popov, V.L., Filippov, A.E.: Method of movable lattice particles. Tribol. Int. 40(6), 930–936 (2007)

    Article  Google Scholar 

  52. Popov, V.L., Psakhie, S.G.: Theoretical principles of modelling elastoplastic media by movable cellular automata method. I. Homogeneous media. Phys. Mesomech. 4(1), 15–25 (2001)

    Google Scholar 

  53. Dmitriev, A.I., Popov, V.L., Psakhie, S.G.: Simulation of surface topography with the method of movable cellular automata. Tribol. Int. 39(5), 444–449 (2006)

    Article  Google Scholar 

  54. Mazoyer, J.: An overview of the firing squad synchronization problem. In: Choffrut, C. (ed.) Automata Networks. LNCS, vol. 316, pp. 82–94. Springer, Heidelberg (1988)

    Google Scholar 

  55. Kadanoff, L.P.: Scaling laws for Ising models near T c . Physics 2(6), 263–272 (1966)

    MathSciNet  Google Scholar 

  56. Désérable, D.: A framework for scaling and renormalization in the triangular lattice. In: Fourteenth Int. Symp. on Math. Theory of Networks & Systems MTNS 2000, Perpignan, p. 109 (2000)

    Google Scholar 

  57. Toffoli, T.: Programmable matter methods. Fut. Gen. Comp. Sys. 16, 187–201 (1999)

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire de Génie Civil & Génie Mécanique, Institut National des Sciences Appliquées, INSA, 20 Avenue des Buttes de Coësmes, 35043 Rennes, France

    Dominique Désérable, Pascal Dupont, Mustapha Hellou & Siham Kamali-Bernard

Authors
  1. Dominique Désérable
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  2. Pascal Dupont
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  3. Mustapha Hellou
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  4. Siham Kamali-Bernard
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Victor Malyshkin

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Désérable, D., Dupont, P., Hellou, M., Kamali-Bernard, S. (2007). Cellular Automata Models for Complex Matter. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2007. Lecture Notes in Computer Science, vol 4671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73940-1_39

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  • DOI: https://doi.org/10.1007/978-3-540-73940-1_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73939-5

  • Online ISBN: 978-3-540-73940-1

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