A Pseudopolynomial Algorithm for Alexandrov's Theorem

Alexandrov's Theorem states that every metric with the global topology and local geometry required of a convex polyhedron is in fact the intrinsic metric of a unique convex polyhedron. Recent work by Bobenko and Izmestiev describes a differential equation whose solution leads to the polyhedron corresponding to a given metric. We describe an algorithm based on this differential equation to compute the polyhedron to arbitrary precision given the metric, and prove a pseudopolynomial bound on its running time. Along the way, we develop pseudopolynomial algorithms for computing shortest paths and weighted Delaunay triangulations on a polyhedral surface, even when the surface edges are not shortest paths.Comment: 25 pages; new Delaunay triangulation algorithm, minor other changes; an abbreviated v2 was at WADS 200

Partially incoherent gap solitons in Bose-Einstein condensates

We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite temperature, using the Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent condensate, and normal and anomalous densities of incoherent vapor co-trapped with the condensate. Both intragap and intergap solitons are constructed, with chemical potentials of the components falling in one or different bandgaps in the OL-induced spectrum. Solitons change gradually with temperature. Families of intragap solitons are completely stable (both in direct simulations, and in terms of eigenvalues of perturbation modes), while the intergap family may have a very small unstable eigenvalue (nevertheless, they feature no instability in direct simulations). Stable higher-order (multi-humped) solitons, and bound complexes of fundamental solitons are found too.Comment: 8 pages, 9 figures. Physical Review A, in pres

First-passage theory of exciton population loss in single-walled carbon nanotubes reveals micron-scale intrinsic diffusion lengths

One-dimensional crystals have long range translational invariance which manifests as long exciton diffusion lengths, but such intrinsic properties are often obscured by environmental perturbations. We use a first-passage approach to model single-walled carbon nanotube (SWCNT) exciton dynamics (including exciton-exciton annihilation and end effects) and compare it to results from both continuous-wave and multi-pulse ultrafast excitation experiments to extract intrinsic SWCNT properties. Excitons in suspended SWCNTs experience macroscopic diffusion lengths, on the order of the SWCNT length, (1.3-4.7 um) in sharp contrast to encapsulated samples. For these pristine samples, our model reveals intrinsic lifetimes (350-750 ps), diffusion constants (130-350 cm^2/s), and absorption cross-sections (2.1-3.6 X 10^-17 cm^2/atom) among the highest previously reported.and diffusion lengths for SWCNTs.Comment: 6 pages, 3 figure

Invariant manifolds and the geometry of front propagation in fluid flows

Recent theoretical and experimental work has demonstrated the existence of one-sided, invariant barriers to the propagation of reaction-diffusion fronts in quasi-two-dimensional periodically-driven fluid flows. These barriers were called burning invariant manifolds (BIMs). We provide a detailed theoretical analysis of BIMs, providing criteria for their existence, a classification of their stability, a formalization of their barrier property, and mechanisms by which the barriers can be circumvented. This analysis assumes the sharp front limit and negligible feedback of the front on the fluid velocity. A low-dimensional dynamical systems analysis provides the core of our results.Comment: 14 pages, 11 figures. To appear in Chaos Focus Issue: Chemo-Hydrodynamic Patterns and Instabilities (2012

A survey of thermodynamic properties of the compounds of the elements CHNOPS Eighth progress report, 1 Apr. - 30 Jun. 1966

Thermodynamic properties of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur compound

Ultra-short solitons and kinetic effects in nonlinear metamaterials

We present a stability analysis of a modified nonlinear Schroedinger equation describing the propagation of ultra-short pulses in negative refractive index media. Moreover, using methods of quantum statistics, we derive a kinetic equation for the pulses, making it possible to analyze and describe partial coherence in metamaterials. It is shown that a novel short pulse soliton, which is found analytically, can propagate in the medium.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Nematic-Isotropic Transition with Quenched Disorder

Nematic elastomers do not show the discontinuous, first-order, phase transition that the Landau-De Gennes mean field theory predicts for a quadrupolar ordering in 3D. We attribute this behavior to the presence of network crosslinks, which act as sources of quenched orientational disorder. We show that the addition of weak random anisotropy results in a singular renormalization of the Landau-De Gennes expression, adding an energy term proportional to the inverse quartic power of order parameter Q. This reduces the first-order discontinuity in Q. For sufficiently high disorder strength the jump disappears altogether and the phase transition becomes continuous, in some ways resembling the supercritical transitions in external field.Comment: 12 pages, 4 figures, to be published on PR