Correlations in the sand pile model: From the log-normal distribution to self-organized criticality

1998 ◽  
Vol 250 (4-6) ◽  
pp. 275-280 ◽  
Author(s):  
Horacio Ceva ◽  
Javier Luzuriaga
Keyword(s):  
Normal Distribution ◽  
Sand Pile ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Log Normal ◽  
Pile Model ◽  
Log Normal Distribution

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.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

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