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
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Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| title |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| spellingShingle |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices Self-organized criticallity Fractal lattices Física |
| title_short |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| title_full |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| title_fullStr |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| title_full_unstemmed |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| title_sort |
Self Organized Critical Dynamics on Sierpinski Fractal Lattices |
| dc.creator.fl_str_mv |
Gómez Ramírez, Viviana |
| dc.contributor.advisor.none.fl_str_mv |
Téllez Acosta, Gabriel |
| dc.contributor.author.none.fl_str_mv |
Gómez Ramírez, Viviana |
| dc.contributor.jury.none.fl_str_mv |
Jiménez Rincón, Jose Julián |
| dc.subject.keyword.eng.fl_str_mv |
Self-organized criticallity Fractal lattices |
| topic |
Self-organized criticallity Fractal lattices Física |
| dc.subject.themes.spa.fl_str_mv |
Física |
| description |
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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2024 |
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2024-02-01T00:57:53Z |
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2024-02-01T00:57:53Z |
| dc.date.issued.none.fl_str_mv |
2024-12-07 |
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Trabajo de grado - Pregrado |
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info:eu-repo/semantics/bachelorThesis |
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http://purl.org/coar/resource_type/c_7a1f |
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eng |
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eng |
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Attribution-NonCommercial-NoDerivatives 4.0 International |
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http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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58 páginas |
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Universidad de los Andes |
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Física |
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Facultad de Ciencias |
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Departamento de Física |
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Universidad de los Andes |
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Téllez Acosta, Gabrielvirtual::209-1Gómez Ramírez, VivianaJiménez Rincón, Jose Julián2024-02-01T00:57:53Z2024-02-01T00:57:53Z2024-12-07https://hdl.handle.net/1992/73723instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/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.La criticalidad auto-organizada es una propiedad de sistemas dinámicos en los cuales, sin ajustes externos, un sistema evoluciona naturalmente hacia su estado crítico, caracterizado por patrones invariantes a escala y distribuciones de ley de potencias. Esta tesis explora la dinámica crítica auto-organizada en el retículo de la Alfombra de Sierpinski, una estructura que también sigue una ley de potencias en su dimensión, es decir, un fractal. Para lograr esto, se propone un modelo de Ising-percolación como escenario de estudio para la dinámica crítica. Dentro de este marco, se delinea un mecanismo de retroalimentación para la auto-organización crítica, junto con un algoritmo diseñado para implementarlo numéricamente. Los resultados obtenidos del algoritmo demuestran mayor eficiencia en la llegada a la auto-organización crítica en la Alfombra de Sierpinski. Esto es atribuido a la naturaleza iterativa de su construcción y a el impacto que esto tiene en la formación de clusters. El resultado clave de este estudio es una novedosa dependencia de la topología en la dinámica crítica auto-organizada, la cual puede tener diversas aplicaciones en campos relacionados con la transmisión de información.FísicoPregradoFísica estadística58 páginasapplication/pdfengUniversidad de los AndesFísicaFacultad de CienciasDepartamento de FísicaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Self Organized Critical Dynamics on Sierpinski Fractal LatticesTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_7a1fTexthttp://purl.org/redcol/resource_type/TPSelf-organized criticallityFractal 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