Self Organized Critical Dynamics on Sierpinski Fractal Lattices
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. This thesis explores the self-organized critical dynamics on the Sierpinski Carpet l...
- Autores:
-
Gómez Ramírez, Viviana
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2024
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/73723
- Acceso en línea:
- https://hdl.handle.net/1992/73723
- Palabra clave:
- Self-organized criticallity
Fractal lattices
Física
- Rights
- openAccess
- License
- Attribution-NonCommercial-NoDerivatives 4.0 International
| Summary: | 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. This thesis explores the self-organized critical dynamics on the Sierpinski Carpet lattice, a structure which also follows a power-law on its dimension i.e. a fractal. To achieve this, we propose an Ising-percolation model as the foundation for investigating critical dynamics. Within this framework, we delineate a feedback mechanism for critical self-organization and design an algorithm for its numerical implementation. The results obtained from the algorithm demonstrate enhanced efficiency when driving the Sierpinski Carpet towards critical self-organization. This efficiency is linked to the iterative nature of its construction, which significantly influences the formation of clusters. The key outcome of our findings is a novel dependence of self-organized critical dynamics on topology, which may have several applications in fields regarding information transmission. |
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