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An Overview: Discretizing Manifolds via Particle Interactions

  • Sergiy V. BorodachovEmail author
  • Douglas P. Hardin
  • Edward B. Saff
Chapter
  • 289 Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The problem of distributing points on a manifold (or discretizing a manifold) arises in many contexts that are of interest to the scientific community as well as in applied fields—statistical sampling, quadrature rules, information theory, coding techniques, computer-aided design, interpolation schemes, finite element tessellations, ground states of matter—to name but a few. Our goal is to address this problem from the perspective of particle interactions; namely, starting from a given formula for the pairwise interactions of N particles (points) that are confined to a given manifold A in the Euclidean space \(\mathbb R^{p},\) we wish to describe the structure of those configurations that arise when the N particles reach an equilibrium state (a state of minimal energy).

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Sergiy V. Borodachov
    • 1
    Email author
  • Douglas P. Hardin
    • 2
  • Edward B. Saff
    • 2
  1. 1.Department of MathematicsTowson UniversityTowsonUSA
  2. 2.Center for Constructive Approximation, Department of MathematicsVanderbilt UniversityNashvilleUSA

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