982 research outputs found
Geometry induced potential on a 2D-section of a wormhole: catenoid
We show that a two dimensional wormhole geometry is equivalent to a catenoid,
a minimal surface. We then obtain the curvature induced geometric potential and
show that the ground state with zero energy corresponds to a reflectionless
potential. By introducing an appropriate coordinate system we also obtain bound
states for different angular momentum channels. Our findings can be realized in
suitably bent bilayer graphene sheets with a neck or in a honeycomb lattice
with an array of dislocations or in nanoscale waveguides in the shape of a
catenoid.Comment: to appear in Phys.Rev.
Complete Embedded Self-Translating Surfaces under Mean Curvature Flow
We describe a construction of complete embedded self-translating surfaces
under mean curvature flow by desingularizing the intersection of a finite
family of grim reapers in general position.Comment: 42 pages, 8 figures. v2: typos correcte
Stability of bicontinuous cubic phases in ternary amphiphilic systems with spontaneous curvature
We study the phase behavior of ternary amphiphilic systems in the framework
of a curvature model with non-vanishing spontaneous curvature. The amphiphilic
monolayers can arrange in different ways to form micellar, hexagonal, lamellar
and various bicontinuous cubic phases. For the latter case we consider both
single structures (one monolayer) and double structures (two monolayers). Their
interfaces are modeled by the triply periodic surfaces of constant mean
curvature of the families G, D, P, C(P), I-WP and F-RD. The stability of the
different bicontinuous cubic phases can be explained by the way in which their
universal geometrical properties conspire with the concentration constraints.
For vanishing saddle-splay modulus , almost every phase considered
has some region of stability in the Gibbs triangle. Although bicontinuous cubic
phases are suppressed by sufficiently negative values of the saddle-splay
modulus , we find that they can exist for considerably lower
values than obtained previously. The most stable bicontinuous cubic phases with
decreasing are the single and double gyroid structures since
they combine favorable topological properties with extreme volume fractions.Comment: Revtex, 23 pages with 10 Postscript files included, to appear in J.
Chem. Phys. 112 (6) (February 2000
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