scholarly journals On the set of Fixed Points of the Parallel Symmetric Sand Pile Model

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Kévin Perrot ◽  
Thi Ha Duong Phan ◽  
Trung Van Pham
Keyword(s):  
Fixed Points ◽  
Lexicographic Order ◽  
Sand Pile ◽  
Self Organized ◽  
Successor Relation ◽  
Self Organized Criticality ◽  
International Audience ◽  
Transition Rules ◽  
The Difference ◽  
Pile Model

International audience Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of $\textit{Self-Organized Criticality}$. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain moving transition rules. The transition rules permit one grain to fall to its right or left (symmetric) neighboring column if the difference of height between those columns is larger than 2. The model is nondeterministic and grains always fall downward. We propose a study of the set of fixed points reachable in the Parallel Symmetric Sand Pile Model (PSSPM). Using a comparison with the Symmetric Sand Pile Model (SSPM) on which rules are applied once at each iteration, we get a continuity property. This property states that within PSSPM we can't reach every fixed points of SSPM, but a continuous subset according to the lexicographic order. Moreover we define a successor relation to browse exhaustively the sets of fixed points of those models.

Crowd Evacuation Stability Based on Self-Organized Criticality Theory

2014 ◽  
Vol 501-504 ◽  
pp. 2403-2406 ◽  
Author(s):  
Rong Yong Zhao ◽  
Jian Wang ◽  
Wei Qing Ling
Keyword(s):  
Stability Analysis ◽  
Complex Problem ◽  
Unstable State ◽  
Sand Pile ◽  
Mapping Model ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Crowd Evacuation ◽  
Crowd Motion ◽  
The Stability

In emergency, the crowd evacuation from public buildings is the most important issue to save human lives. Panic generation and spread normally can lead to the unstable state -stampede during the crowd motion. The stability of crowd evacuation is a complex problem being researched for decades. This paper introduces self-organized criticality(SOC) theory to build the mapping model from a collective crowd into a sand pile with SOC. Therefore, the complex problem of stability analysis for crowd evacuation is converted into sandpiper stability analysis in a relatively simpler way.

THE FIXED SCALE TRANSFORMATION: STATUS AND PERSPECTIVES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 650-662 ◽  
Author(s):  
L. PIETRONERO
Keyword(s):  
Growth Models ◽  
Path Integrals ◽  
Coarse Grained ◽  
Scale Transformation ◽  
Scale Invariant ◽  
Simplified Models ◽  
Self Organized ◽  
Self Organized Criticality ◽  
New Type ◽  
Pile Model

Irreversible fractal growth models like DLA and DBM have confronted us with theoretical problems of a new type that cannot be described in terms of the standard concepts like field theory and the renormalization group. The Fixed Scale Transformation is a theoretical scheme of a new type that is able to treat these problems in a reasonably systematic way. The idea is to focus on the dynamics at a given scale and to compute accurately the correlations at this scale by suitable lattice path integrals. The use of scale invariant growth rules then allows the generalization of these correlations to coarse-grained cells of any size and therefore to obtain the fractal dimension. We summarize the present status of the FST approach by focusing on the most recent results about the scale invariant dynamics of DLA/DBM. The possible extensions to other problems like the sand pile model (self-organized-criticality) and simplified models of turbulence will also be considered.

A Day at the Beach: Human Agents Self-Organizing on the Sand Pile

1999 ◽  
Vol 02 (01) ◽  
pp. 37-63 ◽  
Author(s):  
Hiroshi Ishii ◽  
Scott E. Page ◽  
Niniane Wang
Keyword(s):  
Power Law ◽  
Critical State ◽  
Sand Pile ◽  
Self Organized ◽  
Ability To Act ◽  
Sand Land ◽  
Social Scientific ◽  
Pile Model ◽  
Power Law Distributions ◽  
Self Organizing

In this paper, we analyze the sand pile model of self-organized criticallity from a social scientific perspective. In the sand pile model, particles of sand land at random locations on a square table and self-organize into a critical state: a conical pile. Thereafter, the size of avalanches satisfies a power law. This empirical fact has led some to claim that self-organizing criticality explains power law distributions that occur in human systems. However, unlike grains of sand, people possess both preferences and the ability to act purposefully given those preferences. We find that by including purposive agents and allowing heterogeneity of purposes, the sand pile need not become critical. We also show that if we allow institutions to moderate actions that we can create any distribution of avalanches.

Black swans, extreme risks, and the e-pile model of self-organized criticality

2021 ◽  
Vol 144 ◽  
pp. 110665
Author(s):  
Alexander V. Milovanov ◽  
Jens Juul Rasmussen ◽  
Bertrand Groslambert
Keyword(s):  
Self Organized ◽  
Black Swans ◽  
Self Organized Criticality ◽  
Pile Model ◽  
Extreme Risks

scholarly journals SELF-ORGANIZED CRITICALITY IN A MODEL OF COLLECTIVE BANK BANKRUPTCIES

2002 ◽  
Vol 13 (03) ◽  
pp. 333-341 ◽  
Author(s):  
AGATA ALEKSIEJUK ◽  
JANUSZ A. HOŁYST ◽  
GUEORGI KOSSINETS
Keyword(s):  
Financial Market ◽  
Percolation Theory ◽  
Bank Failure ◽  
Directed Percolation ◽  
Power Law Distribution ◽  
Self Organized ◽  
Banking Networks ◽  
Self Organized Criticality ◽  
The Difference ◽  
2D And 3D

The question we address here is of whether phenomena of collective bankruptcies are related to self-organized criticality. In order to answer it we propose a simple model of banking networks based on the random directed percolation. We study effects of one bank failure on the nucleation of contagion phase in a financial market. We recognize the power law distribution of contagion sizes in 3d- and 4d-networks as an indicator of SOC behavior. The SOC dynamics was not detected in 2d-lattices. The difference between 2d- and 3d- or 4d-systems is explained due to the percolation theory.

scholarly journals Firing Patterns in the Parallel Chip-Firing Game

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Ziv Scully ◽  
Tian-Yi Jiang ◽  
Yan Zhang
Keyword(s):  
Simple Model ◽  
Complete Characterization ◽  
Local Behavior ◽  
Emergent Complexity ◽  
Self Organized ◽  
Chip Firing ◽  
Self Organized Criticality ◽  
International Audience ◽  
Sandpile Group

International audience The $\textit{parallel chip-firing game}$ is an automaton on graphs in which vertices "fire'' chips to their neighbors. This simple model, analogous to sandpiles forming and collapsing, contains much emergent complexity and has connections to different areas of mathematics including self-organized criticality and the study of the sandpile group. In this work, we study $\textit{firing sequences}$, which describe each vertex's interaction with its neighbors in this game. Our main contribution is a complete characterization of the periodic firing sequences that can occur in a game, which have a surprisingly simple combinatorial description. We also obtain other results about local behavior of the game after introducing the concept of $\textit{motors}$. Le $\textit{parallel chip-firing game}$, c’est une automate sur les graphiques, dans lequel les sommets “tirent” des jetons à leurs voisins. Ce modèle simple, semblable aux tas de sable qui forment et s’affaissent, contient beaucoup de complexité émergente et a des connections avec différents domaines de mathématiques, incluant le $\textit{self-organized criticality}$ et l’étude du $\textit{sandpile group}$. Dans ce projet, on étudie les $\textit{firing sequences}$, qui décrivent les interactions de chaque sommet avec ses voisins dans le jeu. Notre contribution principale est une caractérisation complète des séquences de tir qui peuvent arriver dans une jeu, qui ont une description combinatoire assez simple. Nous obtenonsaussi d'autres résultats sur le conduite locale du jeu après l’introduction du concept des $\textit{motors}$.

scholarly journals Self-organized criticality in a rice-pile model

1996 ◽  
Vol 54 (5) ◽  
pp. R4512-R4515 ◽  
Author(s):  
Luís A. Nunes Amaral ◽  
Kent Bækgaard Lauritsen
Keyword(s):  
Self Organized ◽  
Self Organized Criticality ◽  
Pile Model

scholarly journals On the Toppling of a Sand Pile

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jean-Christophe Novelli ◽  
Dominique Rossin
Keyword(s):  
Lower Bound ◽  
Young Tableaux ◽  
Sand Pile ◽  
International Audience ◽  
Pile Model ◽  
Sand Piles

International audience In this paper, we provide the first study of the sand pile model SPM(0) where we assume that all the grains are numbered with a distinct integer.We obtain a lower bound on the number of terminal sand piles by establishing a bijection between a subset of these sand piles and the set of shifted Young tableaux. We then prove that this number is at least factorial.

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