Stripe patterns and a projection-valued formulation of the eikonal equation | Zendy

Mark A. Peletier | Zendy; Marco Veneroni | Zendy

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Stripe patterns and a projection-valued formulation of the eikonal equation

Author(s) -

Mark A. Peletier,

Marco Veneroni

Publication year - 2012

Publication title -

philosophical transactions of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.074

H-Index - 169

eISSN - 1471-2962

pISSN - 1364-503X

DOI - 10.1098/rsta.2011.0425

Subject(s) - eikonal equation , projection (relational algebra) , eikonal approximation , mathematics , field (mathematics) , unit vector , block (permutation group theory) , work (physics) , mathematical analysis , statistical physics , physics , pure mathematics , geometry , algorithm , quantum mechanics

We describe recent work on striped patterns in a system of block copolymers. A by-product of the characterization of such patterns is a new formulation of the eikonal equation. In this formulation, the unknown is a field of projection matrices of the form P=e⊗e, where e is a unit vector field. We describe how this formulation is better adapted to the description of striped patterns than the classical eikonal equation, and illustrate this with examples.

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