arXiv subjects

Abdul Quadir

Publications and source records attributed to Abdul Quadir.

6 recordsLinked to original sources

arXiv2026

The Directed Abelian Sandpile Model on Cylinders

We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at one boundary. Recurrent configurations form a finite abelian group, and repeated grain addition at a specific site generates deterministic dynamics on this group. Using Dhar's formulation, the sandpile group is identified with the co-kernel of the reduced directed Laplacian. We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition. Our results establish a direct connection between the algebraic structure of the sandpile group and the periodicity of the driven dynamics, establishing the manner in which the underlying algebraic structure governs both deterministic and stochastic evolution in directed sandpile.

cond-mat.stat-mech↗

arXiv2026

Fitness Fluctuations and Correlation Time Scaling in the Barycentric Bak-Sneppen Model

We consider the barycentric version of the Bak-Sneppen model, a one-dimensional self-organized critical model that describes generalized Keynesian beauty contests with a local interaction rule. We numerically investigate the power spectral density of the fitness variable and correlation time. Through data collapse for both variables, we estimate the critical exponents. For global and local fitness variables, the power spectral density exhibits $1/f^{\alpha}$ with $0< \alpha < 2$, indicative of long-range correlations. We also investigate the cover time, defined as the duration required for the extinction or mutation of species across the entire system in the critical state of the barycentric BS model. Using finite-size scaling and extreme value theory, we analyze the statistical properties of the cover time. Our results show power-law scaling with system size for the mean, variance, mode, and peak probability. Furthermore, the cumulative probability distribution exhibits data collapse, and the associated scaling function is well described by the generalized extreme value density, closely approximating the Gumbel family.

cond-mat.stat-mech↗

arXiv2025

Extreme events scaling in self-organized critical models

We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of block maxima, the study numerically reveals that the distributions for extreme avalanche size and area follow the generalized extreme value (GEV) distribution. The extreme avalanche size follows the Gumbel distribution with shape parameter $\xi=0$ while in the case of the extreme avalanche area, we report $\xi>0$. We propose scaling functions for extreme avalanche activities that connect the activities on different length scales. With the help of data collapse, we estimate the precise values of these critical exponents. The scaling functions provide an understanding of the intricate dynamics for different variants of the sandpile model, shedding light on the relationship between system size and extreme event characteristics. Our findings give insight into the extreme behavior of SOC models and offer a framework to understand the statistical properties of extreme events.

cond-mat.stat-mech↗

arXiv2024

Scaling of Extreme Events in 2d BTW Sandpile

We study extreme events in a finite-size 2D Abelian sandpile model, specifically focusing on avalanche area and size. Employing the approach of Block Maxima, the study numerically reveals that the rescaled distributions for the largest avalanche size and area converge into the Gumbel and Weibull family of Generalized Extreme Value (GEV) distributions respectively. Numerically, we propose scaling functions for extreme avalanche activities that connect the activities on different length scales. With the help of data collapse, we estimate the precise values of these scaling exponents. The scaling function provides an understanding of the intricate dynamics within the sandpile model, shedding light on the relationship between system size and extreme event characteristics. The findings presented in this paper give valuable insights into the extreme behaviour of the Abelian sandpile model and offer a framework to understand the statistical properties of extreme events in complex systems.

cond-mat.stat-mech↗

arXiv2022

Critical neuronal avalanches in levels model under noisy drive

We consider a neuronal levels model that exhibits critical avalanches satisfying power-law distribution. The model has recently explained a change in the scaling exponent from 3/2 to 5/4, accounting for a change in the drive condition from no input to moderate strength, along with a relaxed separation of time-scale between drive and dissipation. To understand the robustness of the scaling features, we examine the effect of different noisy stimuli in the moderate input regime. Our tool of analysis is the scaling method. We compute scaling functions associated with the avalanche size distribution, revealing striking finite-size scaling. For a class of noisy drives, we find that the scaling exponent can take a value different from 5/4, with an explicit system size dependence of the distribution.

cond-mat.stat-mech↗

arXiv2022

Finite-size scaling of critical avalanches

We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it may decrease on increasing the system size at a fixed avalanche size. We implement the scaling method and identify scaling functions. The data collapse ensures a correct estimation of the critical exponents and distinguishes two exponents related to avalanche size and system size. Our simple analysis provides striking implications. While the exact value for avalanches size exponent remains elusive for the prototype sandpile on a square lattice, we suggest the exponent should be 1. The simulation results represent that the distribution shows a logarithmic system size dependence, consistent with the normalization condition. We also argue that for train or Oslo sandpile model with bulk drive, the avalanche size exponent is slightly less than 1 which is significantly different from the previous estimate 1.11.

cond-mat.stat-mech↗