9,213 research outputs found
Supersymmetry Across Nanoscale Heterojunction
We argue that supersymmetric transformation could be applied across the
heterojunction formed by joining of two mixed semiconductors. A general
framework is described by specifying the structure of ladder operators at the
junction for making quantitative estimation of physical quantities. For a
particular heterojunction device, we show that an exponential grading inside a
nanoscale doped layer is amenable to exact analytical treatment for a class of
potentials distorted by the junctions through the solutions of transformed
Morse-Type potentials.Comment: 7 pages, 2 figure
New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials
We have generated, using an sl(2,R) formalism, several new classes of
quasi-solvable elliptic potentials, which in the appropriate limit go over to
the exactly solvable forms. We have obtained exact solutions of the
corresponding spectral problems for some real values of the potential
parameters. We have also given explicit expressions of the families of
associated orthogonal polynomials in the energy variable.Comment: 14 pages, 5 tables, LaTeX2
Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials
We obtain the exact nontopological soliton lattice solutions of the
Associated Lam\'e equation in different parameter regimes and compute the
corresponding energy for each of these solutions. We show that in specific
limits these solutions give rise to nontopological (pulse-like) single
solitons, as well as to different types of topological (kink-like) single
soliton solutions of the Associated Lam\'e equation. Following Manton, we also
compute, as an illustration, the asymptotic interaction energy between these
soliton solutions in one particular case. Finally, in specific limits, we
deduce the soliton lattices, as well as the topological single soliton
solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy
An algorithm for two-dimensional mesh generation based on the pinwheel tiling
We propose a new two-dimensional meshing algorithm called PINW able to
generate meshes that accurately approximate the distance between any two domain
points by paths composed only of cell edges. This technique is based on an
extension of pinwheel tilings proposed by Radin and Conway. We prove that the
algorithm produces triangles of bounded aspect ratio. This kind of mesh would
be useful in cohesive interface finite element modeling when the crack
propagation pathis an outcome of a simulation process.Comment: Short version appears in Proceedings of 2004 International Meshing
Roundtable at http://www.imr.sandia.go
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