Optimal approximation of harmonic growth clusters by orthogonal polynomials

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Interface dynamics in two-dimensional systems with a maximal number of conservation laws gives an accurate theoretical model for many physical processes, from the hydrodynamics of immiscible, viscous flows (zero surface-tension limit of Hele-Shaw flows, [1]), to the granular dynamics of hard spheres [2], and even diffusion-limited aggregation [3]. Although a complete solution for the continuum case exists [4, 5], efficient approximations of the boundary evolution are very useful due to their practical applications [6]. In this article, the approximation scheme based on orthogonal polynomials with a deformed Gaussian kernel [7] is discussed, as well as relations to potential theory.

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Mathematical Physics, Statistical Mechanics, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/165007

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.1700
 http://arxiv.org/abs/0807.1700

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arXiv