arXiv subjects

Rahul Chhimpa

Publications and source records attributed to Rahul Chhimpa.

12 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 $\alpha$ controls the level of local dissipation: $\alpha<0.25$ corresponds to locally dissipative and $\alpha = 0.25$ 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 $\alpha = 0.21$. 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 $\alpha = 0.21$. 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.

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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.

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arXiv2025

Continuous sample space reducing stochastic process

We propose a simple model for sample space reducing (SSR) stochastic process, where the dynamical variable denoting the size of the state space is continuous. In general, one can view the model as a multiplicative stochastic process, with a constraint that the size of the state space cannot be smaller than a visibility parameter $ε$. We study the survival time statistics that reveal a subtle difference from the discrete version of the process. A straightforward generalization can explain the noisy SSR process, characterized by a tunable parameter $λ\in [0, 1]$. We also examine the statistics of the size of the state space that follows a power-law distributed probability $\mathbb{P}_ε(z\le ε) \sim z^{-α}$, with a nontrivial value of the exponent as a function of the tunable parameter $α= 1+λ$.

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.

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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.

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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.

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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.

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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.

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