Influence of curvature on pattern formation: Turing mechanism in the circle
In this work, we study the influence of the curvature of the medium on the formation of patterns through the Turing mechanism of instability guided by diffusion. To analyze the effect of the curvature, we consider the simplest closed curve variety, a circumference. We present the Laplace-Beltrami op...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | México |
| Institución: | UNIVERSIDAD AUTÓNOMA DEL ESTADO DE HIDALGO |
| Repositorio: | PÄDI Boletín Científico de Ciencias Básicas e Ingeniería del ICBI |
| Idioma: | español |
| OAI Identifier: | oai:repository.uaeh.edu.mx:article/8411 |
| Acceso en línea: | https://repository.uaeh.edu.mx/revistas/index.php/icbi/article/view/8411 |
| Access Level: | acceso abierto |
| Palabra clave: | Turing patterns reaction-diffusion curve manifolds Patrones de Turing reacción-difusión variedades de curvas |
| Sumario: | In this work, we study the influence of the curvature of the medium on the formation of patterns through the Turing mechanism of instability guided by diffusion. To analyze the effect of the curvature, we consider the simplest closed curve variety, a circumference. We present the Laplace-Beltrami operator, which is the generalization of the Laplacian on manifolds, to solve the diffusion equation and describe the modifications that the curvature induces on the distribution function and the mean square displacement. As a particular case of study, we use the Gierer-Meinhardt model. It is shown that the range of unstable modes where it will be possible to find the spatio-temporal patterns depends on the radius and, therefore, on the specific circle’s curvature. |
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