A New Sandpile Model with Smoothness Assumptions

• Autorzy: Brocchi S. , Massazza P.

Identyfikatory

DOI

10.3233/FI-2016-1314

• Języki publikacji: EN

Abstrakty

EN

We consider two new granular dynamical systems obtained from the Sand Pile Model SPM(n) by adding a smoothness condition. First, we define the Smooth Sand Pile Model SmSPM(n) and we provide a characterization of the reachable states, together with some interesting properties of the resulting lattice. Then we extend it to SmSPM*(n), a related dynamical system with a more complex lattice structure.

Słowa kluczowe

EN

sand piles; discrete dynamical system

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 143, nr 3/4
• Strony: 261--286
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Brocchi S.

• Università degli Studi di Firenze, Dipartimento di Matematica e Informatica ’U. Dini’, Viale G. B. Morgagni 65, 50134 Florence, Italy

autor

Massazza P.

• Università degli Studi dell’Insubria, Dipartimento di Scienze Teoriche e Applicate, Via Mazzini 5, 21100 Varese, Italy

Bibliografia

• [1] Brylawski T. The lattice of integer partitions. Discrete Mathematics. 1973;6(3):201 – 219. doi:http://dx.doi.org/10.1016/0012-365X(73)90094-0.
• [2] Goles E, Kiwi MA. Games on line graphs and sand piles. Theoretical Computer Science. 1993;115(2):321 – 349. doi:http://dx.doi.org/10.1016/0304-3975(93)90122-A.
• [3] Brocchi S, Massazza P. Smooth Sand Piles. In: Proceedings of Reachability Problems - 6th International Workshop (RP 2012). vol. 7550 of Lecture Notes in Computer Science. Springer Berlin Heidelberg; 2012. p. 66–78.
• [4] Latapy M, Mantaci R, Morvan M, Phan HD. Structure of some sand piles model. Theoretical Computer Science. 2001;262(1-2):525 – 556. doi:http://dx.doi.org/10.1016/S0304-3975(00)00363-7.
• [5] Goles E, Morvan M, Phan HD. Sandpiles and order structure of integer partitions. Discrete Applied Mathematics. 2002;117(1-3):51 – 64. doi:http://dx.doi.org/10.1016/S0166-218X(01)00178-0.
• [6] Corteel S, Gouyou-Beauchamps D. Enumeration of sand piles. Discrete Mathematics. 2002;256(3):625 – 643. doi:http://dx.doi.org/10.1016/S0012-365X(02)00339-4.
• [7] Massazza P. A CAT algorithm for sand piles. PUMA Pure Mathematics and Applications. 2008;18(2-3):147–157.
• [8] Kadanoff LP, Nagel SR, Wu L, Zhou Sm. Scaling and universality in avalanches. Phys Rev A. 1989 Jun; 39:6524–6537. doi:10.1103/PhysRevA.39.6524.
• [9] Massazza P, Radicioni R. A CAT algorithm for the exhaustive generation of ice piles. RAIRO – Theoretical Informatics and Applications. 2011;44(4):525–543.
• [10] Formenti E, Masson B, Pisokas T. Advances in Symmetric Sandpiles. Fundamenta Informaticae. 2007;76(1-2):91–112.
• [11] Phan THD. Two sided Sand Piles Model and unimodal sequences. RAIRO - Theoretical Informatics and Applications. 2008 7;42:631–646. Available from: http://www.rairo-ita.org/article_S0988375408000192. doi:10.1051/ita:2008019.
• [12] Massazza P. On the exhaustive generation of symmetric sand piles. In: Proceedings of GASCom 2010. UQAM, Montr´eal; 2010. doi:10.13140/RG.2.1.1703.1122.
• [13] Formenti E, Pham TV, Phan THD, Tran TTH. Fixed-point forms of the parallel symmetric sandpile model. Theoretical Computer Science. 2014;533:1 – 14. doi:http://dx.doi.org/10.1016/j.tcs.2014.02.051.
• [14] Mantaci R, Massazza P, Yun´es JB. An efficient algorithm for generating symmetric ice piles. Theoretical Computer Science. 2015;doi:http://dx.doi.org/10.1016/j.tcs.2015.10.024.
• [15] Duchi E, Mantaci R, Phan HD, Rossin D. Bidimensional sand pile and ice pile models. PUMA Pure Mathematics and Applications. 2007;17(1-2):71–96.