Hexagonal Patterns in a Simplified Model for Block Copolymers

DOI10.1137/130922732zbMath1309.49019arXiv1305.6540OpenAlexW2117411139MaRDI QIDQ5173228

Steven M. Roper, David P. Bourne, Mark Adriaan Peletier

Publication date: 9 February 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.6540

zbMATH Keywords

minimizersEuler-Lagrange equationVoronoi diagramscrystallizationenergy-driven pattern formationdi-block copolymerssmall volume fraction limit

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Statistical mechanics of polymers (82D60) Methods involving semicontinuity and convergence; relaxation (49J45) Discrete approximations in optimal control (49M25) Optimality conditions for problems involving relations other than differential equations (49K21)

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Centroidal Power Diagrams, Lloyd's Algorithm, and Applications to Optimal Location Problems ⋮ Pattern formation of a nonlocal, anisotropic interaction model ⋮ Asymptotic optimality of the triangular lattice for a class of optimal location problems ⋮ Optimality of the triangular lattice for a particle system with Wasserstein interaction ⋮ Geometric Self-Assembly of Rigid Shapes: A Simple Voronoi Approach ⋮ Semi-discrete optimal transport methods for the semi-geostrophic equations ⋮ Least Wasserstein distance between disjoint shapes with perimeter regularization

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