- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
11
2009
3
Uniform energy and density distribution: diblock copolymers’ functional
Emanuele
Nunzio Spadaro
Universität Zürich, ZÜRICH, SWITZERLAND
We study a nonlocal variational problem arising in diblock copolymers models, whose energy is given by the Cahn–Hilliard functional plus a long-range interaction term. We prove that minimizers develop uniform energy and density distributions, thus justifying partially the highly regular microphase separation observed in diblock copolymers’ melts. We also give a new proof of the scaling law for the minimum energy. This work extends the techniques introduced in [1] where analogous results are proved for the sharp interface limit of the functional considered.
Partial differential equations
Mechanics of particles and systems
Calculus of variations and optimal control; optimization
General
447
474
10.4171/IFB/218
http://www.ems-ph.org/doi/10.4171/IFB/218