Stripe patterns and the eikonal equation

M.A. Peletier, M. Veneroni

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review


We study a new formulation for the Eikonal equation $|\nabla u|=1$ on a bounded subset of $\rm{R}^2$. Considering a field P of orthogonal projections onto 1-dimensional subspaces, with $\rm{div} P \in L^2$, we prove existence and uniqueness for solutions of the equation $P \rm{div} P = 0$. We give a geometric description, comparable with the classical case, and we prove that such solutions exist only if the domain is a tubular neighbourhood of a regular closed curve. This formulation provides a useful approach to the analysis of stripe patterns. It is specifically suited to systems where the physical properties of the pattern are invariant under rotation over 180 degrees, such as systems of block copolymers or liquid crystals.
Originele taal-2Engels
Pagina's (van-tot)183-189
TijdschriftDiscrete and Continuous Dynamical Systems - Series S
Nummer van het tijdschrift1
StatusGepubliceerd - 2012

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