Self Organized Critical Dynamic on the Sierpinski Carpet
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910743531618304 |
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| author | Gomez, Viviana Tellez, Gabriel |
| author_facet | Gomez, Viviana Tellez, Gabriel |
| contents | Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power-law with a non-integer exponent, i.e. a fractal. To achieve this, we proposed an Ising-BCP (bond-correlated percolation) model as the foundation for investigating critical dynamics. Within this framework, we outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice. This efficiency was attributed to the iterative construction of the lattice and the distribution of spins within it. The key outcome of our findings is a novel dependence of self-organized criticality on topology for this particular model, which may have several applications in fields regarding information transmission. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09771 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self Organized Critical Dynamic on the Sierpinski Carpet Gomez, Viviana Tellez, Gabriel Statistical Mechanics Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power-law with a non-integer exponent, i.e. a fractal. To achieve this, we proposed an Ising-BCP (bond-correlated percolation) model as the foundation for investigating critical dynamics. Within this framework, we outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice. This efficiency was attributed to the iterative construction of the lattice and the distribution of spins within it. The key outcome of our findings is a novel dependence of self-organized criticality on topology for this particular model, which may have several applications in fields regarding information transmission. |
| title | Self Organized Critical Dynamic on the Sierpinski Carpet |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2412.09771 |