External Fields and Uniform Distribution in Squares and Cubes

Johann Brauchart

External Fields and Uniform Distribution in Squares and Cubes

Institute of Analysis and Number Theory (5010)

Research output: Contribution to conference › Poster

Abstract

Points in the unit cube in Rd that maximize, say, the sum of all mutual Euclidean distances, or minimize, say, their potential energy (harmonic kernel), are located at the boundary of the unit cube. This phenomenon is a consequence of classical potential theory. We introduce suitable external fields to obtain a uniform distribution over the unit cube of optimal configurations for
the corresponding "energy functional".

Original language	English
Number of pages	1
Publication status	Published - 11 Sept 2019
Event	HDA2019: 8th Workshop on High-Dimensional Approximation - ETH Zurich, Zurich, Switzerland Duration: 9 Sept 2019 → 13 Sept 2019 https://math.ethz.ch/sam/news-and-events/conferences-and-workshops/archive/8th-workshop-on-high-dimensional-approximation.html

Workshop

Workshop	HDA2019: 8th Workshop on High-Dimensional Approximation
Abbreviated title	HDA 2019
Country/Territory	Switzerland
City	Zurich
Period	9/09/19 → 13/09/19
Internet address	https://math.ethz.ch/sam/news-and-events/conferences-and-workshops/archive/8th-workshop-on-high-dimensional-approximation.html

Fields of Expertise

Information, Communication & Computing

Treatment code (Nähere Zuordnung)

Basic - Fundamental (Grundlagenforschung)

FWF - Self WW - Self organization by local interaction: minimal energy, external fields, and numerical integration
Brauchart, J.
1/10/16 → 28/02/19
Project: Research project
Special Research Area (SFB) F55 Quasi-Monte Carlo Methods: Theory and Applications
Grabner, P., Tichy, R., Kusner, W. B., Ziefle, J., Brauchart, J., Iaco, M. R. & Aistleitner, C.
1/02/14 → 31/01/23
Project: Research project

1 Workshop, seminar or course (Participation in/Organisation of)
1 Poster presentation

HDA2019: 8th Workshop on High-Dimensional Approximation
Johann Brauchart (Participant)
9 Sept 2019 → 13 Sept 2019
Activity: Participation in or organisation of › Workshop, seminar or course (Participation in/Organisation of)
External Fields and Uniform Distribution in Squares and Cubes
Johann Brauchart (Speaker)
11 Sept 2019 → 13 Sept 2019
Activity: Talk or presentation › Poster presentation › Science to science

Cite this

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title = "External Fields and Uniform Distribution in Squares and Cubes",

abstract = "Points in the unit cube in Rd that maximize, say, the sum of all mutual Euclidean distances, or minimize, say, their potential energy (harmonic kernel), are located at the boundary of the unit cube. This phenomenon is a consequence of classical potential theory. We introduce suitable external fields to obtain a uniform distribution over the unit cube of optimal configurations forthe corresponding {"}energy functional{"}.",

author = "Johann Brauchart",

year = "2019",

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language = "English",

note = "HDA2019: 8th Workshop on High-Dimensional Approximation, HDA 2019 ; Conference date: 09-09-2019 Through 13-09-2019",

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N2 - Points in the unit cube in Rd that maximize, say, the sum of all mutual Euclidean distances, or minimize, say, their potential energy (harmonic kernel), are located at the boundary of the unit cube. This phenomenon is a consequence of classical potential theory. We introduce suitable external fields to obtain a uniform distribution over the unit cube of optimal configurations forthe corresponding "energy functional".

AB - Points in the unit cube in Rd that maximize, say, the sum of all mutual Euclidean distances, or minimize, say, their potential energy (harmonic kernel), are located at the boundary of the unit cube. This phenomenon is a consequence of classical potential theory. We introduce suitable external fields to obtain a uniform distribution over the unit cube of optimal configurations forthe corresponding "energy functional".

M3 - Poster

T2 - HDA2019: 8th Workshop on High-Dimensional Approximation

Y2 - 9 September 2019 through 13 September 2019

ER -

External Fields and Uniform Distribution in Squares and Cubes

Abstract

Workshop

Fields of Expertise

Treatment code (Nähere Zuordnung)

Fingerprint

Projects

FWF - Self WW - Self organization by local interaction: minimal energy, external fields, and numerical integration

Special Research Area (SFB) F55 Quasi-Monte Carlo Methods: Theory and Applications

Activities

HDA2019: 8th Workshop on High-Dimensional Approximation

External Fields and Uniform Distribution in Squares and Cubes

Cite this