Distribution of Points on the Sphere

Please enable javascript in your browser.

Bakhshizadeh, Milad | 2014

803 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46649 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Alishahi, Kasra; Shahshahani, Mehrdad; Kamalinejad, Ali
Abstract:
The focus of this thesis is the computation of the discrepancy for any given distribution of points on S2. The problem of the distribution of points on the sphere has a long history and Thomson’s Problem, inspired by early atomic theory dating back to 1904, was a landmark. While Thomson’s Problem is based on the Coulomb potential, the discrepancy measures the deviation of the number of points in a set from the expected one. The Polar Coordinates method was introduced in the context of Thomson’s problem. In this thesis the order of the growth of the discrepancy for this method is investigated and a modification of it is shown to lead to the best known results. In addition a new algorithm is introduced that enables one to determine whether discrepancy of a given distribution is greater than any given number d 2 R+, and in which case it specifies the location where high discrepancy occurs
Keywords:
Inhomogeneity ; Polar Coordinate ; Discrepancy ; Points on the Sphere Distribution ; Uniform Distribution ; Thomson's Problem

No TOC