Minimal Surfaces with Only Horizontal Symmetries

Silva, Márcio Fabiano da; Lobos, Guillermo Antonio; Batista, Valério Ramos

doi:10.5402/2011/943462

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2020

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“…For instance, in [2] the authors show the importance of these surfaces in crystallography, and a still incomplete geometrical classification of crystal structures was later given in [3]. See a further contribution to this classification in [4].…”

Section: Introductionmentioning

confidence: 99%

An Evolver program for weighted Steiner trees

Botelho¹,

Zampirolli²,

Batista³

2020

Preprint

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We present an algorithm to find near-optimal weighted Steiner minimal trees in the plane. The algorithm is implemented in Evolver programming language, which already contains many built-in energy minimisation routines. Some are invoked in the program, which enable it to consist of only 183 lines of source code. Our algorithm reproduces the physical experiment of a soap film detaching from connected pins towards a stable configuration. In the non-weighted case comparisons with GeoSteiner are drawn for terminals that form a pattern.

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Section: Introductionmentioning

confidence: 99%