Abstract
In this paper a new cellular automata model suitable for granular systems simulation is presented. The proposed model is shown to be equivalent to a particularization of the well known BCRE model of granular systems and a correspondence between the parameters of the presented model and the BCRE model is also set, allowing to fit these parameters for a given system. The model has the advantage over other cellular automata models of being more realistic in the behavior of the surface of heaps and slopes. The dynamics of the CA is analyzed in order to confirm that it also has one of the most important features of these systems, 1/f noise.
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References
Chen, C.C., den Nijs, M.: Directed avalanche processes with underlaying interface dynamics. Physical Review E 66 (2002)
Prado, C., Olami, Z.: Inertia and break of self-organized criticality in sandpile cellular-automata models. Phys. Rev. A 45, 6665–6669 (1992)
Nerone, N., Gabbanelli, S.: Surface fluctuations and the inertia effect in sandpiles. Granular Matter 3, 117–120 (2001)
Müller, M., Charypar, D., Gross, M.: Procedural modeling and animation: Particle-based fluid simulation for interactive applications. In: ACM SIGGRAPH/ Eurographics Symposium on Computer Animation, pp. 154–159 (2003)
Pla-Castells, M.: Nuevos modelos de sistemas granulares basados en autómatas celulares para simulación en tiempo real. MSc Thesis. Escuela de Ingenierías, Universidad de Valencia (2003)
Pla-Castells, M., García, I., Martínez, R.J.: Visual Representation Of Enhanced Sand Pile Models. In: Industrial Simulation Conference, Universidad Politécnica de Valencia, Valencia, Spain, pp. 141–146 (2003)
Christensen, K., Olami, Z., Bak, P.: Deterministic 1/f noise in nonconservative models of self-organized criticality. Phys. Rev. Letters 68, 2417–2420 (1992)
Bouchaud, J.P., Cates, M.E., Prakash, J.R., Edwards, S.F.: A Model for the Dynamics of Sandpile Surfaces. J. Phys. I France 4, 1383–1410 (1994)
Aradian, A., Raphael, E., de Gennes, P.G.: Surface flows of granular materials: a short introduction to some recent models. Comptes Rendus Physique 3, 187–196 (2002)
Hadeler, K.P., Kuttler, C.: Dynamical models for granular matter. Granular Matter 2, 9–18 (1999)
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality. Phys. Rev. A 38, 364–374 (1988)
Kadanoff, L.P., Nagel, S.R., Wu, L., Zhou, S.: Scaling and universality in avalanches. Phys. Rev. A 39, 6524–6537 (1989)
Dorso, C.O., Dadamia, D.: Avalanche prediction in Abelian sandpile model. Physica A: Statistical Mechanics and its Applications 308, 179–191 (2002)
Kertesz, J., Torok, J., Krishnamurthy, S., Roux, S.: Slow dynamics in selforganizing systems. Physica A: Statistical Mechanics and its Applications 314, 567–574 (2002)
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© 2004 Springer-Verlag Berlin Heidelberg
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Pla-Castells, M., García, I., Martínez, R.J. (2004). Approximation of Continuous Media Models for Granular Systems Using Cellular Automata. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_24
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DOI: https://doi.org/10.1007/978-3-540-30479-1_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23596-5
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