A Variational Level Set Approach for Surface Area Minimization of Triply Periodic Surfaces

Abstract

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and computational formulation to study the optimality of the Schwartz P, Schwartz D, and Schoen G surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases not equal. Due to the computational cost of the fully, three-dimensional shape optimization problem, we implement our numerical simulations using a parallel level set method software package.

28 pages, 16 figures, 3 tables

References in corpus (4)

• Soap Froths and Crystal Structures
• Strong-Segregation Theory of Bicontinuous Phases in Block Copolymers
• A systematic approach to bicontinuous cubic phases in ternary amphiphilic systems
• A Topology-Preserving Level Set Method for Shape Optimization

Cited by in corpus (4)

• IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures
• Effect of Transport Mechanism on the Coarsening of Bicontinuous Structures: A Comparison between Bulk and Surface Diffusion
• Parametric polynomial minimal surfaces of arbitrary degree
• A level set topology optimization theory based on Hamilton's principle