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Annealed and quenched disorder in sand-pile models with local violation of conservation
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 92, Issue 2 , August , 2015 ; 15393755 (ISSN) ; Sebtosheikh, M ; Sharif University of Technology
American Physical Society
2015
Abstract
In this paper we consider the Bak, Tang, and Wiesenfeld (BTW) sand-pile model with local violation of conservation through annealed and quenched disorder. We have observed that the probability distribution functions of avalanches have two distinct exponents, one of which is associated with the usual BTW model and another one which we propose to belong to a new fixed point; that is, a crossover from the original BTW fixed point to a new fixed point is observed. Through field theoretic calculations, we show that such a perturbation is relevant and takes the system to a new fixed point
Effect of Dissipation and Perturbation in Sandpile Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Sandpile models are the simplest models to study self organized criticality (SOC). In these phenomena, system reaches its critical state and shows power law behavior without fine tuning of any external parameters. In nature, many examples of such phenomena has been observed such as earthquakes, rainfalls and heights of mountains. In SOC systems, always there is an input and an out put of energy. In sandpile models the dissipative sites that play the role of energy dissipation, are usualy put on the boundary. In this study we have considered sandpile models which have dissipative site in the bulk. We have controled the ratio of the dissipative sites to the number of whole sites and have shown...
Patterned and disordered continuous abelian sandpile model
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 80, Issue 4 , 2009 ; 15393755 (ISSN) ; Moghimi Araghi, S ; Sharif University of Technology
2009
Abstract
We study critical properties of the continuous Abelian sandpile model with anisotropies in toppling rules that produce ordered patterns on it. Also, we consider the continuous directed sandpile model perturbed by a weak quenched randomness, study critical behavior of the model using perturbative conformal field theory, and show that the model has a random fixed point. © 2009 The American Physical Society
Sandpile Model on Height Parameters
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Many statistical systems such as earthquakes, road trafcs, forest fres, neurocortical avalanches etc. exhibit self-organized criticality (SOC). In such systems without tuning extrenal parameters, the system arrives at criticality. During recent decades, a number of models are introduced which show the same charactristics. These models have made a platform to investigate the physics of self-organized criticality. Among them, sandpile models are the best known models. They exhibit critical behaviour such as scaling laws. Also in some of them conformal invariance is checked nummerically.Most of sandpile models deal with slope parameters, that is, the main dynamical parameters are the local...
Simulation of the Self-organized Critical Models on the
Human’s Brain Network
,
M.Sc. Thesis
Sharif University of Technology
;
Moghimi Araghi, Saman
(Supervisor)
Abstract
Self-organized critical phenomena are interesting phenomena which are ubiquitous in nature. Examples include mountain ranges , coastlines and also activities in the hu-man's brain. In these processes, without fine-tuning of any external parameter such as the temperature, the system exhibits critical behavior. In other words, the dynamics of the system, drives it towards an state in which long range correlations in space and scaling behaviors can be seen.The first successful model which could characterize such systems was BTW model, introduced by Bak , Tang and Wiesenfeld in 1987. This model, later named Abelian sandpile model, was very simple and because of this simplicity, a large amount of...
Continuous Transition from Self-organized Criticality to Self-organized Bistability
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
”Self-organized criticality” is a conceptual term that has helped us describe cer- tain critical behaviors in nature over the past approximately thirty years. In systems exhibiting this characteristic, critical behavior emerges without the need for external parameter adjustments. The necessary mechanism to observe such phenomena is for the critical point to be a dynamical attractor. Based on this, other phenomena have been proposed in which the critical point is not an attractor; instead, a stable cycle forms around it. This mechanism has led to the emergence of a new concept known as ”self- organized bistability.” The primary model proposed for such a phenomenon is based on a sandpile...
Continuous transforming the BTW to the Manna model
, Article Physica A: Statistical Mechanics and its Applications ; Volume 419 , 2015 , Pages 196-202 ; 03784371 (ISSN) ; Moghimi Araghi, S ; Najafi, M. N ; Sharif University of Technology
Abstract
In this paper we define some stochastic perturbations of the BTW model which make it into Manna model. These models have a continuous parameter p, where p = 0 and 1 correspond to the BTW and Manna models respectively. We have investigated the properties of the statistical observables of the waves of avalanches for various values of p. Our data supports the expectation of a crossover in such systems; at large scales Manna model is dominant. Therefore we find strong evidence in favor of the universality classes being distinct. Also it is observed that the BTW fixed point is unstable when Manna-type perturbation is added to the model
Direct evidence for conformal invariance of avalanche frontiers in sandpile models
, Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 79, Issue 3 , Volume 79, Issue 3 , 2009 ; 15393755 (ISSN) ; Moghimi-Araghi, S ; Dashti-Naserabadi, H ; Rouhani, S ; Sharif University of Technology
2009
Abstract
Appreciation of stochastic Loewner evolution (SLEκ), as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model are numerically shown to be conformally invariant and can be described by SLE with diffusivity κ=2. This value is the same as value obtained for loop-erased random walks. The fractal dimension and Schramm's formula for left passage probability also suggest the same result. We also check the same properties for Zhang's sandpile model. © 2009 The American Physical Society
Controlling cost in sandpile models through local adjustment of drive
, Article Physica A: Statistical Mechanics and its Applications ; Volume 534 , 2019 ; 03784371 (ISSN) ; Moghimi Araghi, S ; Sharif University of Technology
Elsevier B.V
2019
Abstract
In this paper we consider sandpile models and modify the drive mechanisms to control the size of avalanches. The modification to the drive mechanism is local. We have studied the scaling behavior of the BTW and Manna models. We have found that the BTW model is more sensitive to the modification than the Manna model. Furthermore we have assigned a cost function to each avalanche and have found an optimum value for the modification to arrive at the lowest cost © 2019
Fluctuations in the order of System Size in the Avalanche-Size Distribution of Sandpiles Model
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Since the concept of Self-Organized Criticality was introduced in terms of BTW Sandpiles model, its major features have been known as broad power law distributions without any tuning parameters. In some selforganized critical systems like brain and neural networks, some evidences and experiments show a periodic or non-power law distribution of avalanches in addition to the power-law distributions of avalanches. In this thesis we try to observe the same phenomenon in the well-known SOC models, namely the BTW and Manna sandpile models. We have considered small lattice sizes with periodic boundary conditions and a small amount of dissipation. Within such conditions we observe a periodic-like...
Synaptic Plasticity in Brain Networks Based on Sandpile Models
, M.Sc. Thesis Sharif University of Technology ; Moghimi Araghi, Saman (Supervisor)
Abstract
Based on the large number of interacting cells and their abundant connections, human brain is a complex system able to produce interesting collective behaviors. Studying these collective behaviors needs special tools that potentially could be found in the context of the statistical physics of critical phenomena, as these tools are specifically developed for understanding the large-scale properties of physical systems. Starting with the introduction of the self-organized criticality in the late 80s, a number of physicists have tried to utilize this concept for explaining some aspects of the brain properties, such as memory and learnig. The observation of the neuronal avalanches in the early...