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Title: The BCC Lattice in a Long-Range Interaction System
While the hexagonal lattice is ubiquitous in two dimensions, the body centered cubic lattice and the face centered cubic 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 $$(-\Delta)^{-3/2}$$, it is proved that the body centered cubic lattice is the preferred structure.  more » « less
Award ID(s):
2307068
PAR ID:
10510793
Author(s) / Creator(s):
;
Publisher / Repository:
SIAM
Date Published:
Journal Name:
SIAM Journal on Applied Mathematics
Volume:
83
Issue:
5
ISSN:
0036-1399
Page Range / eLocation ID:
1854 to 1871
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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