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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.05699 |
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| _version_ | 1866913537380581376 |
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| author | Chhimpa, Rahul Yadav, Avinash Chand |
| author_facet | Chhimpa, Rahul Yadav, Avinash Chand |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scaling behavior in the number theoretic division model of self-organized criticality Chhimpa, Rahul Yadav, Avinash Chand Statistical Mechanics 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). |
| title | Scaling behavior in the number theoretic division model of self-organized criticality |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2410.05699 |