STRONG EVENTS IN THE SAND-PILE MODEL

2004 ◽  
Vol 15 (02) ◽  
pp. 279-288 ◽  
Author(s):  
A. B. SHAPOVAL ◽  
M. G. SHNIRMAN
Keyword(s):  
Power Law ◽  
Sand Pile ◽  
System Length ◽  
Pile Model ◽  
Number Of Particles

Here is a sand-pile introduced by Bak et al. The system accumulates particles one by one. From time to time it topples. Every toppling initiates an event. The distribution of the events' size follows a power law for all the events except the strongest ones. The fraction of the strongest events does not depend on the system length. The number of particles and their clustering increase before the strongest events.

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.

scholarly journals IDEAL-MODIFIED BOSONIC GAS TRAPPED IN AN ARBITRARY THREE-DIMENSIONAL POWER-LAW POTENTIAL

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
E. CASTELLANOS ◽  
C. LÄMMERZAHL
Keyword(s):  
Dispersion Relation ◽  
Power Law ◽  
Three Dimensional ◽  
Particle Dispersion ◽  
Einstein Condensate ◽  
Gravity Models ◽  
Condensation Temperature ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

GROWTH OF COLLOIDAL CRYSTALS UNDER MICROGRAVITY

2002 ◽  
Vol 16 (01n02) ◽  
pp. 338-345 ◽  
Author(s):  
M. ISHIKAWA ◽  
H. MORIMOTO ◽  
T. OKUBO ◽  
T. MAEKAWA
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Brownian Dynamics ◽  
Normal Gravity ◽  
Colloidal Crystals ◽  
Growth Dynamics ◽  
Sounding Rocket ◽  
Microgravity Experiment ◽  
Colloidal Crystallization ◽  
Number Of Particles

The growth dynamics of colloidal crystallization was evaluated under sedimentation free conditions using sounding rocket and Brownian Dynamics (BD) simulation. The Bragg's reflections of colloidal crystals were measured during microgravity flight and average sizes of crystallites were obtained by the Sherrer's method. Results showed a power-law relationship between size and time, L ∝ tα where L is the size of crystallites and t is time. The obtained α s were 0.33 ± 0.03 in microgravity and 0.25 ± 0.02 in normal gravity, respectively. Browninan Dynamics (BD) simulation showed the time evolution of ordered domains that consisted of connected structures of crystalline clusters. The power law relationship n ∝ t0.5 in post-nucleation period was confirmed between the number of particles (n) in clusters and time. The calculated power was related to α using the fractal dimension of crystalline clusters and α = 0.31 was obtained. The value was matched well with that of the microgravity experiment.

SAND PILE AS A UNIVERSAL COMPUTER

1996 ◽  
Vol 07 (02) ◽  
pp. 113-122 ◽  
Author(s):  
ERIC GOLES ◽  
MAURICE MARGENSTERN
Keyword(s):  
Computer Program ◽  
Logic Gates ◽  
One Dimensional ◽  
Sand Pile ◽  
Pile Model

We show that the sand pile model is able to simulate, by specific configurations, logic gates and registers and, therefore any computer program. Further, we give its interpretation in terms of a set of several one-dimensional interacting avalanches.

Numerical Approaches of Cluster Statistics for Stochastic Manganese Deposits

2014 ◽  
Vol 69 (10-11) ◽  
pp. 581-588 ◽  
Author(s):  
Mehmet Bayirli
Keyword(s):  
Critical Exponent ◽  
Power Law ◽  
Distribution Functions ◽  
Scaling Properties ◽  
Manganese Clusters ◽  
Sedimentary Deposits ◽  
Manganese Deposits ◽  
The Subject ◽  
Numerical Approaches ◽  
Number Of Particles

AbstractIn terms of origin, the most important manganese deposits are sedimentary deposits which grow on the surface and/or fractures of the natural magnesite ore. They reveal various morphological characteristic according to their location in origin. Some of them may be fractal in appearance. Although several studies have been completed with regards to their growth mechanism, it may be safe to say that their cluster statistics and scaling properties have rarely been subject an academic scrutiny. Hence, the subject of this study has been designed to calculate cluster statistics of manganese deposits by first; transferring the images of manganese deposits into a computer and then scaling them with the help of software. Secondly, the root-mean square (rms) thickness (also called as expected value in systems), the number of particles, clusters and cluster sizes are computed by means of scaling method. In doing so it has been found that the rms thickness and the number of particles are in correlation, a result which is called as power-law behaviour, T~N-ε (the critical exponent is computed as ε = 1.743). It has also been found that the correlation between the number of clusters and their sizes are determined with the power-law behaviour n(s)~s-τ (the critical exponent t may vary between 1.054 and 1.321). Finally, the distribution functions of natural manganese clusters on the magnesite subtract have been determined. All that may point to the fact that the manganese deposits may be formed according to a Poisson distribution. The results found and the conclusion reached in this study may be used to compare various natural deposits in geophysics.

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