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Triply periodic minimal and constant mean curvature surfaces [PDF]
Interface Focus, 2012 We want to summarize some established results on periodic surfaces which are minimal or have constant mean curvature, along with some recent results. We will do this from a mathematical point of view with a general readership in mind.
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Two new embedded triply periodic minimal surfaces of genus 4 [PDF]
manuscripta mathematica, 2020 We add two new 1-parameter families to the short list of known embedded triply periodic minimal surfaces of genus 4 in $\mathbb{R}^3$. Both surfaces can be tiled by minimal pentagons with two straight segments and three planar symmetry curves as boundary.
Daniel Freese +3 more
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Triply-Periodic Smectics [PDF]
, 2006 Twist-grain-boundary phases in smectics are the geometrical analogs of the Abrikosov flux lattice in superconductors. At large twist angles, the nonlinear elasticity is important in evaluating their energetics.
Kamien, Randall D. +1 more
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, 2002 A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears that many (but not all) of them can be relaxed to smooth minimal surfaces (under an
Goodman-Strauss, Chaim, Sullivan, John M
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Bicontinuous minimal surface nanostructures for polymer blend solar cells [PDF]
, 2010 This paper presents the first examination of the potential for bicontinuous structures such as the gyroid structure to produce high efficiency solar cells based on conjugated polymers.
Alison B. Walker +63 more
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Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature [PDF]
, 1999 We study the phase behavior of ternary amphiphilic systems in the framework of a curvature model with non-vanishing spontaneous curvature. The amphiphilic monolayers can arrange in different ways to form micellar, hexagonal, lamellar and various ...
Anderson D. M. +15 more
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Materials & Design, 2019 Triply Periodic Minimal Surface (TPMS) structures fabricated via Additive Manufacturing (AM) have recently emerged as being appropriate candidates for high-value engineered structures, including porous bio-implants and energy absorbing structures.
Eric Yang +13 more
doaj +1 more source
Electronic structure of an electron on the gyroid surface, a helical labyrinth
, 2005 Previously reported formulation for electrons on curved periodic surfaces is used to analyze the band structure of an electron bound on the gyroid surface (the only triply-periodic minimal surface that has screw axes).
A. Carlsson +6 more
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Mean survival times of absorbing triply periodic minimal surfaces
Physical Review E, 2009 14 pages, 5 figures, 1 ...
Gevertz, J., Torquato, S.
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Evaluation of Cellular Solids Derived From Triply Periodic Minimal Surfaces [PDF]
Volume 2: Materials; Biomanufacturing; Properties, Applications and Systems; Sustainable Manufacturing, 2016 Cellular solids are a class of materials that have many interesting engineering applications, including ultralight structural materials [1]. The traditional method for analyzing these solids uses convex uniform polyhedral honeycombs to represent the geometry of the material [2], and this approach has carried over into the design of digital cellular ...
Cellucci, Daniel, Cheung, Kenneth C.
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