2007/10/17 by Yves van Gennip, van Gennip, Yves, Mark A. Peletier +1
Mathematics · Physics and Astronomy · #49N99 (Primary) #82D60 (Secundary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:49N99 #msc:82D60
paper · pdf · doi:10.48550/arxiv.0710.3298
40 pages, 34 Postscript figures; second version has some minor corrections; to appear in "Interfaces and Free Boundaries"
arxiv created 2009/09/07 · arxiv updated 2009/12/01
We study the stability of layered structures in a variational model for diblock copolymer-homopolymer blends. The main step consists of calculating the first and second derivative of a sharp-interface Ohta-Kawasaki energy for straight mono- and bilayers. By developing the interface perturbations in a Fourier series we fully characterise the stability of the structures in terms of the energy parameters. In the course of our computations we also give the Green's function for the Laplacian on a periodic strip and explain the heuristic method by which we found it.