The BCC lattice in a long range interaction system

2022/07/31 by Xiaofeng Ren, Juncheng Wei, Ren, Xiaofeng +1
Chemistry · Engineering · Materials Science · #82B20 82D60 92C15 11F20 #Advanced Polymer Synthesis and Characterization #Analysis of PDEs (math.AP) #Block Copolymer Self-Assembly #FOS: Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2208.00528

openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered lattice are both commonly observed in three dimensions. A geometric variational problem motivated by the diblock copolymer theory consists of a short range interaction energy and a long range interaction energy. In three dimensions, and when the long range interaction is given by the nonlocal operator (-Δ)^-3/2, it is proved that the body centered cubic lattice is the preferred structure.

Related

• Non-hexagonal lattices from a two species interacting system
• Microstructures and anti-phase boundaries in long-range lattice systems
• The hexagonal lattice is universally locally optimal
• Local optimality of cubic lattices for interaction energies
• Uniform bound on the number of partitions for optimal configurations of the Ohta-Kawasaki energy in 3D