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Log-optimal spherical configuration Musin, Oleg
Description
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two orthogonal to each other regular simplices of cardinality m and n, where m+n=d+2. The global minimum occurs when m=n if d is even and m=n+1 otherwise. This characterizes a new class of configurations that minimize the logarithmic energy on the (d-1)-sphere for all d. The other two classes known in the literature, the regular simplex and the cross polytope, are both universally optimal configurations. This is a joint work with Peter Dragnev.
Item Metadata
| Title |
Log-optimal spherical configuration
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| Creator | |
| Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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| Date Issued |
2019-10-03T09:05
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| Description |
We enumerate and classify all stationary logarithmic configurations of d+2 points on the unit (d-1)-sphere in d-dimensions. In particular, we show that the logarithmic energy attains its relative minima at configurations that consist of two orthogonal to each other regular simplices of cardinality m and n, where m+n=d+2. The global minimum occurs when m=n if d is even and m=n+1 otherwise. This characterizes a new class of configurations that minimize the logarithmic energy on the (d-1)-sphere for all d. The other two classes known in the literature, the regular simplex and the cross polytope, are both universally optimal configurations. This is a joint work with Peter Dragnev.
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| Extent |
42.0 minutes
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| Subject | |
| Type | |
| File Format |
video/mp4
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| Language |
eng
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| Notes |
Author affiliation: University of Texas Rio Grande Valley
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| Series | |
| Date Available |
2020-04-01
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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| DOI |
10.14288/1.0389708
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| URI | |
| Affiliation | |
| Peer Review Status |
Unreviewed
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| Scholarly Level |
Faculty
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| Rights URI | |
| Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International