106,318 research outputs found
Anisotropic Wavefronts and Laguerre Geometry
Motivated by the study of wave fronts in anisotropic media, we propose an
incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An
anisotropic version of the Laguerre functional is considered. In some
circumstances, this functional can be used to determine that two wavefronts
observed at distinct times in a homogeneous, anisotropic medium, do not
originate from the same source
Refractors in anisotropic media associated with norms
We show existence of interfaces between two anisotropic materials so that
light is refracted in accordance with a given pattern of energy. To do this we
formulate a vector Snell law for anisotropic media when the wave fronts are
given by norms for which the corresponding unit spheres are strictly convex.Comment: 26 pages, 2 figure
Helicoidal surfaces with constant anisotropic mean curvature
We study surfaces with constant anisotropic mean curvature which are
invariant under a helicoidal motion. For functionals with axially symmetric
Wulff shapes, we generalize the recently developed twizzler representation of
Perdomo to the anisotropic case and show how all helicoidal constant
anisotropic mean curvature surfaces can be obtained by quadratures
Nematic Films and Radially Anisotropic Delaunay Surfaces
We develop a theory of axisymmetric surfaces minimizing a combination of
surface tension and nematic elastic energies which may be suitable for
describing simple film and bubble shapes. As a function of the elastic constant
and the applied tension on the bubbles, we find the analogues of the unduloid,
sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure
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