scholarly journals Energy Minimization, Periodic Sets and Spherical Designs

2011 ◽  
Vol 2012 (4) ◽  
pp. 829-848 ◽  
Author(s):  
Renaud Coulangeon ◽  
Achill Schürmann
Keyword(s):  
Energy Minimization ◽  
Spherical Designs ◽  
Periodic Sets

Erratum: Energy Minimization, Periodic Sets, and Spherical Designs

2020 ◽  
Author(s):  
Renaud Coulangeon ◽  
Achill Schürmann
Keyword(s):  
Energy Minimization ◽  
Hexagonal Lattice ◽  
Sufficient Conditions ◽  
Local Version ◽  
Local Optimum ◽  
Leech Lattice ◽  
Pair Potentials ◽  
Periodic Sets ◽  
Universally Optimal ◽  
Point Lattice

Abstract In [ 3] we considered energy minimization of pair potentials among periodic sets of a fixed-point density. For a large class of potentials we presented sufficient conditions for a point lattice to give a local optimum among periodic sets. We hereby, in particular, derived a local version of Cohn and Kumar’s conjecture [ 1, Conjecture 9.4] by which the hexagonal lattice $\textsf{A}_2$, the root lattice $\textsf{E}_8$, and the Leech lattice are globally universally optimal. Latter conjecture has recently been proved for $\textsf{E}_8$ and the Leech lattice by Cohn et al. [ 2].

Comments on the Antonow and interfacial interaction rules

1990 ◽  
Vol 55 (5) ◽  
pp. 1143-1148 ◽  
Author(s):  
Jan Kloubek
Keyword(s):  
Free Energy ◽  
Energy Minimization ◽  
Interfacial Interaction ◽  
Aliphatic Hydrocarbon ◽  
Theoretical Base ◽  
Water Interface ◽  
Free Energy Minimization ◽  
Interaction Rule

Results presented for the aliphatic hydrocarbon-water interface show that the recent hypothesis of the free energy minimization called interfacial interaction rule, which was suggested as a theoretical base of the Antonow rule, cannot be generally valid.

scholarly journals Improve concentration of frequency and time (ConceFT) by novel complex spherical designs

2021 ◽  
Vol 54 ◽  
pp. 137-144
Author(s):  
Matt Sourisseau ◽  
Yu Guang Wang ◽  
Robert S. Womersley ◽  
Hau-Tieng Wu ◽  
Wei-Hsuan Yu
Keyword(s):  
Spherical Designs ◽  
Novel Complex
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