TY - JOUR
T1 - Optimal periodic structures with general space group symmetries in the Ohta–Kawasaki problem
AU - van den Berg, Jan Bouwe
AU - Williams, J. F.
PY - 2021/1
Y1 - 2021/1
N2 - We consider the problem of rigorously computing periodic minimizers to the Ohta–Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the true infinite dimensional solution and also on the energy. We use a method with prescribed symmetries to explore the phase space, computing candidate minimizers both with and without experimentally observed symmetries. We find qualitative differences between the phase diagram of the Ohta–Kawasaki energy and self consistent field theory when well away from the weak segregation limit.
AB - We consider the problem of rigorously computing periodic minimizers to the Ohta–Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the true infinite dimensional solution and also on the energy. We use a method with prescribed symmetries to explore the phase space, computing candidate minimizers both with and without experimentally observed symmetries. We find qualitative differences between the phase diagram of the Ohta–Kawasaki energy and self consistent field theory when well away from the weak segregation limit.
KW - Ohta-Kawasaki
KW - Optimal structures
KW - Rigorous numerics
UR - http://www.scopus.com/inward/record.url?scp=85092051187&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85092051187&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2020.132732
DO - 10.1016/j.physd.2020.132732
M3 - Article
AN - SCOPUS:85092051187
SN - 0167-2789
VL - 415
SP - 1
EP - 23
JO - Physica D. Nonlinear Phenomena
JF - Physica D. Nonlinear Phenomena
M1 - 132732
ER -
