arXiv subjects

Avinash Chand Yadav

Publications and source records attributed to Avinash Chand Yadav.

At least 19 recordsLinked to original sources

arXiv2026

Scaling features in the Olami-Feder-Christensen model

We consider the Olami-Feder-Christensen (OFC) model on a square lattice with open boundary conditions. The model exhibits self-organized criticality and explains the Gutenberg-Richter law observed for earthquakes. A parameter $α$ controls the level of local dissipation: $α<0.25$ corresponds to locally dissipative and $α= 0.25$ marks locally conservative dynamics. The avalanche size distribution follows a decaying power-law, with a non-universal critical exponent. Here, we examine the local and total stress fluctuations in the OFC model for both locally conservative and dissipative dynamics. The finite-size scaling analysis of the power spectra for the stress fluctuations reveals qualitatively the same but quantitatively significantly different behavior. The dynamic exponent describing the divergence of the correlation time with system size changes from nearly ballistic in the conservative to diffusive in the locally dissipative dynamics with $α= 0.21$. The local stress also exhibits a signature of nearly canonical $1/f$ noise in the intermediate regime, and $1/f^2$-type scaling dominates the high-frequency regime. We further examine the probability distribution of the difference between avalanche size and area. We find a power-law behavior with a scaling exponent close to one in the conservative OFC model. The scaling feature vanishes even for the physically relevant case $α= 0.21$. To examine the robustness of such features, we also examine the same quantity in the Bak-Tang-Wiesenfeld and Manna sandpile models on a square lattice. We find that the power-law behavior survives for these systems due to locally conservative dynamics.

cond-mat.stat-mech↗

arXiv2026

Stationary $1/f^α$ noise in discrete models of the Kardar-Parisi-Zhang class

In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible to reach the stationary state. We compute the two-time autocorrelation and power spectra independently. The correlation function remains non-exponential and vanishes after a correlation time that diverges with system size. As a result, the power spectra display a lower cutoff that maintains constant power. In the nontrivial frequency regime, we observe $1/f^α$-type scaling with the spectral exponent 5/3. Finite-size scaling reveals that the temporal correlation function follows a dynamic scaling. Our findings, supported by scaling-theoretical arguments, establish that the fluctuations are wide-sense stationary, implying applicability of the Wiener-Khinchin theorem.

cond-mat.stat-mech↗

arXiv2025

$1/f$ noise in extremal dynamics

The Bak-Sneppen (BS) evolution model remains a well-studied example of self-organized criticality (SOC). We propose a simple variant of the BS model, where the global fitness fluctuations show $1/f^α$ noise with a spectral exponent nearly equal to 1 (pink noise). To further corroborate, we compute the two-time autocorrelation function that decays logarithmically. The $1/f$ noise in the global fitness is robust and hyper-universal. We identify the dominance of non-trivial local fitness cross-power spectra.

cond-mat.stat-mech↗

arXiv2025

Avalanche activity noises in sandpile models

We consider the Bak-Tang-Wiesenfeld (BTW) and the Manna sandpile models of self-organized criticality. In the models, previous studies revealed a signature of long-range temporal correlations in the avalanche activity. We examine the power spectra of the noises with different system sizes and find that the power spectrum for a finite-size system exhibits three distinct frequency regimes: (i) a frequency-independent behavior below a lower cutoff frequency, (ii) a hump-type behavior in the intermediate-frequency regime, and (iii) a power-law scaling $1/f^α$ in the high-frequency regime. The power scales with the system size in all regimes, but with different exponents. Also, the lower cutoff and peak frequencies decay in a power-law manner with the system size. We apply finite-size scaling and obtain data collapse for the power spectra, corroborating the estimation of the scaling exponents. Our studies reveal subtle scaling features for the temporal correlation within the avalanches.

cond-mat.stat-mech↗

arXiv2025

$1/f$ noise in the Ising model

We simulate the $N$-spin critical Ising model on a square lattice using Glauber dynamics and consider the typical one-unit time equal to $N$ single-spin-flip attempts. The divergence of correlation time with the linear extent of the system results in critical slowing down, a challenge to equilibration because the spin configurations generated in such a way are temporally correlated. We examine temporal correlations in the number of accepted spin flips and show a signature of non-trivial long-time correlation of a logarithmically decaying form or the corresponding power spectral density follows canonical $1/f$ noise.

cond-mat.stat-mech↗

arXiv2025

Correlation time in extremal self-organized critical models

We investigate correlation time numerically in extremal self-organized critical models, namely, the Bak-Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of species over the entire spatial region in the critical state. We apply the methods of finite-size scaling and extreme value theory to understand the statistics of the correlation time. We find power-law system size scaling behaviors for the mean, the variance, the mode, and the peak probability of the correlation time. We obtain data collapse for the correlation time cumulative probability distribution, and the scaling function follows the generalized extreme value density close to the Gumbel function.

cond-mat.stat-mech↗

arXiv2024

Scaling behavior in the number theoretic division model of self-organized criticality

We revisit the number theoretic division model of self-organized criticality [Phys. Rev. Lett. 101, 158702 (2008)]. The model consists of a pool of $M-1$ ordered integers $\{2, 3, \cdots, M\}$, and the aim is to dynamically form a primitive set of integers, where no number can be divided or divisible by others. Using intensive simulation studies and finite-size scaling method, we find the primitive set size fluctuations in the division model to show power spectral density of the form $1/f^α$ in the frequency regime $1/M\ll f \ll 1/2$ with $α\approx 2$ (different from $α\approx 1.80(1)$ as reported previously) along with an additional scaling in terms of the system size $\sim M^b$. We also show similar power spectra properties for a class of random walks with a power-law distributed jump size (Lévy flights).

cond-mat.stat-mech↗

arXiv2024

Fitness noise in the Bak-Sneppen evolution model in high dimensions

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)] has shown the emergence of the $1/f^α$ noise for the ``fitness'' observable with $α\approx 1.2$ in one-dimension (1D) and $α\approx 2$ for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, and 4 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension ${\rm D}_u = 4$, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into return time statistics and the avalanche dimension.

cond-mat.stat-mech↗

arXiv2024

$1/f^α$ noise in the Robin Hood model

We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the evolution of low-temperature creep. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the $1/f^α$ noise for the local force with a nontrivial value of the spectral exponent $0< α< 2$. We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.

cond-mat.stat-mech↗

arXiv2023

Finite-time scaling for kinetic rough interfaces

We consider discrete models of kinetic rough interfaces that exhibit space-time scale-invariance in height-height correlation. A generic scaling theory implies that the dynamical structure factor of the height profile can uniquely characterize the underlying dynamics. We provide a finite-time scaling that systematically allows an estimation of the critical exponents and the scaling functions, eventually establishing the universality class accurately. As an illustration, we investigate a class of self-organized interface models in random media with extremal dynamics. The isotropic version shows a faceted pattern and belongs to the same universality class (as shown numerically) as the Sneppen (model A). We also introduce an anisotropic version of the Sneppen (model A) and suggest that the model belongs to the universality class of the tensionless one-dimensional Kardar-Parisi-Zhang equation.

cond-mat.stat-mech↗

arXiv2023

Fitness fluctuations in Bak-Sneppen model

We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in the fitness variables. We numerically compute the power spectral density and apply the finite-size scaling method to get data collapse. A clear signature of $1/f^α$ noise with $α\approx 1.2$ (long-time correlations) emerges for both local and global (or average) fitness noises. The limiting value 0 or 2 for the spectral exponent corresponds to the no interaction or random neighbors version model, respectively. The local power spectra are spatially uncorrelated and also show an additional scaling $\sim 1/L$ in the frequency regime $L^{-λ}\ll f\ll 1/2$, where $L$ is the linear extent of the system.

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

Energy fluctuations in one dimensional Zhang sandpile model

We consider the Zhang sandpile model in one-dimension (1D) with locally conservative (or dissipative) dynamics and examine its total energy fluctuations at the external drive time scale. The bulk-driven system leads to Lorentzian spectra, with a cutoff time $T$ growing linearly with the system size $L$. The fluctuations show $1/f^α$ behavior with $α\sim 1$ for the boundary drive, and the cutoff time varies non-linearly. For conservative local dynamics, the cutoff time shows a power-law growth $T \sim L^λ$ that differs from an exponential form $ \sim \exp(μL)$ observed for the nonconservative case. We suggest that the local dissipation is not a necessary ingredient of the system in 1D to get the $1/f$ noise, and the cutoff time can reveal the distinct nature of the local dynamics. We also discuss the energy fluctuations for locally nonconservative dynamics with random dissipation.

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↗

arXiv2021

Linking space-time correlations for a class of self-organized critical systems

The hypothesis of self-organized criticality explains the existence of long-range `space-time' correlations, observed inseparably in many natural dynamical systems. A simple link between these correlations is yet unclear, particularly in fluctuations at `external drive' time scales. As an example, we consider a class of sandpile models displaying non-trivial correlations. Employing the scaling methods, we demonstrate the computation of spatial correlation by establishing a link between local and global temporal correlations.

cond-mat.stat-mech↗

arXiv2021

Scaling theory for the $1/f$ noise

We show that in a broad class of processes that show a $1/f^α$ spectrum, the power also explicitly depends on the characteristic time scale. Despite an enormous amount of work, this generic behavior remains so far overlooked and poorly understood. An intriguing example is how the power spectrum of a simple random walk on a ring with $L$ sites shows $1/f^{3/2}$ not $1/f^2$ behavior in the frequency range $1/L^2 \ll f \ll 1/2$. We address the fundamental issue by a scaling method and discuss a class of solvable processes covering physically relevant applications.

cond-mat.stat-mech↗

arXiv2019

Scaling in simple continued fraction

We consider a class of real numbers, a subset of irrational numbers and certain mathematical constants, for which the elements in the simple continued fraction appears to be random. As an illustrative example, one can consider $π= \{x_0, x_1, x_2, \dots x_n\}$, where $x$'s are the continued fraction elements computed with an exact value of $π$ up to $N$ precision. We numerically compute probability distribution for the elements and observe a striking power-law behavior $P(x)\sim x^{-2}$. The statistical analysis indicates that the elements are uncorrelated and the scaling is robust with respect to the precision. Our arguments reveal that the underlying mechanism generating such a scaling may be sample space reducing process.

cond-mat.stat-mech↗

arXiv2018

Critical Pólya urn

We propose a variant model of P{ó}lya urn process, where the dynamics consist of two competing elements namely, suppression of growth and enhancement of dormant character. Here the level of such features are controlled by an internal parameter in a random manner, so as the system self-organizes and characteristic observables exhibit scale invariance suggesting the existence of criticality. Varying the internal control parameter, one can explain interesting universality classes for avalanche-type events. We also discuss different versions of the model. It is pointed that such an underlying mechanism has earlier been noted to operate in a neural network.

cond-mat.stat-mech↗