用正交多项式最佳逼近调和生长团簇
Optimal approximation of harmonic growth clusters by orthogonal polynomials
摘要：
具有最大数量守恒律的二维系统中的界面动力学为许多物理过程提供了精确的理论模型，从不混溶粘性流的流体动力学（Hele-Shaw流的零表面张力极限，[1]）到硬球的颗粒动力学[2]，甚至是扩散限制的聚集[3]。虽然存在连续体情况的完整解[4，5]，但由于其实际应用，边界演化的有效近似非常有用[6]。在这篇文章中，讨论了基于变形高斯核正交多项式的近似方案[7]，以及与势理论的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
