Sphere packings centered at S-units of algebraic tori

Diverse densest binary sphere packings and phase diagram

Physical Review E ◽

10.1103/physreve.103.023307 ◽

2021 ◽

Vol 103 (2) ◽

Author(s):

Ryotaro Koshoji ◽

Mitsuaki Kawamura ◽

Masahiro Fukuda ◽

Taisuke Ozaki

Keyword(s):

Phase Diagram ◽

Sphere Packings

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Coarse- and fine-grid numerical behavior of MRT/TRT lattice-Boltzmann schemes in regular and random sphere packings

Journal of Computational Physics ◽

10.1016/j.jcp.2014.10.038 ◽

2015 ◽

Vol 281 ◽

pp. 708-742 ◽

Cited By ~ 63

Author(s):

Siarhei Khirevich ◽

Irina Ginzburg ◽

Ulrich Tallarek

Keyword(s):

Lattice Boltzmann ◽

Sphere Packings ◽

Fine Grid

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Properties of disordered sphere packings I. Geometric structure: Statistical model, numerical simulations and experimental results

Powder Technology ◽

10.1016/0032-5910(86)80018-3 ◽

1986 ◽

Vol 46 (2-3) ◽

pp. 121-131 ◽

Cited By ~ 50

Author(s):

L. Oger ◽

J.P. Troadec ◽

D. Bideau ◽

J.A. Dodds ◽

M.J. Powell

Keyword(s):

Statistical Model ◽

Numerical Simulations ◽

Geometric Structure ◽

Experimental Results ◽

Sphere Packings

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On S-class number relations of algebraic tori in Galois extensions of global fields

Nagoya Mathematical Journal ◽

10.1017/s0027763000003809 ◽

1991 ◽

Vol 124 ◽

pp. 133-144 ◽

Cited By ~ 5

Author(s):

Masanori Morishita

Keyword(s):

Class Number ◽

Quadratic Forms ◽

Euler Number ◽

Number Fields ◽

Binary Quadratic Forms ◽

Algebraic Number Fields ◽

Algebraic Tori ◽

Genus Theory ◽

Class Number Formula ◽

Number Formula

As an interpretation and a generalization of Gauss’ genus theory on binary quadratic forms in the language of arithmetic of algebraic tori, Ono [02] established an equality between a kind of “Euler number E(K/k)” for a finite Galois extension K/k of algebraic number fields and other arithmetical invariants associated to K/k. His proof depended on his Tamagawa number formula [01] and Shyr’s formula [Sh] which follows from the analytic class number formula of a torus. Later, two direct proofs were given by Katayama [K] and Sasaki [Sa].

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