Hyperuniformity in the compact setting: measuring the fine structure of a sequence of point sets on the sphere

Brauchart, J. (Speaker)

Activity: Talk or presentationInvited talk at conference or symposiumScience to science

Description

Hyperuniformity was introduced by Torquato and Stillinger as a concept to measure the occurrence of “intermediate” order between crystalline order and total disorder. Such configurations X

occur in jammed packings, in colloids, as well as in quasi–crystals. The main feature of hyperuniformity is the fact that local density fluctuations (“number variance”) are of smaller order than for an i.i.d. random (“Poissonian”) point configuration.

In recent work with Peter Grabner (Graz University of Technology), Woden Kusner (Vanderbilt University) and Jonas Ziefle (University of Tűbingen), we introduced the notion of hyperuniformity for sequences of finite point sets on the sphere. We identified three regimes of hyperuniformity. Several deterministically given point sets such as designs, QMC–designs, and certain energy minimising point sets exhibit hyperuniform behaviour.

We also considered hyperuniformity on the sphere for samples of point processes on the sphere.
Period6 Oct 2018
Held atMidwestern Workshop on Asymptotic Analysis
Event typeConference
LocationBloomington, United States, Indiana
Degree of RecognitionInternational

Keywords

  • Information, Communication & Computing
  • Basic - Fundamental (Grundlagenforschung)