Uniform semiclassical wave function for coherent 2D electron flow

We find a uniform semiclassical (SC) wave function describing coherent branched flow through a two-dimensional electron gas (2DEG), a phenomenon recently discovered by direct imaging of the current using scanned probed microscopy. The formation of branches has been explained by classical arguments, but the SC simulations necessary to account for the coherence are made difficult by the proliferation of catastrophes in the phase space. In this paper, expansion in terms of "replacement manifolds" is used to find a uniform SC wave function for a cusp singularity. The method is then generalized and applied to calculate uniform wave functions for a quantum-map model of coherent flow through a 2DEG. Finally, the quantum-map approximation is dropped and the method is shown to work for a continuous-time model as well.Comment: 9 pages, 7 figure

Effective constraint potential in lattice Weinberg - Salam model

We investigate lattice Weinberg - Salam model without fermions for the value of the Weinberg angle $\theta_W \sim 30^o$, and bare fine structure constant around $\alpha \sim 1/150$. We consider the value of the scalar self coupling corresponding to bare Higgs mass around 150 GeV. The effective constraint potential for the zero momentum scalar field is used in order to investigate phenomena existing in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model. This is the region of the phase diagram, where the continuum physics is to be approached. We compare the above mentioned effective potential (calculated in selected gauges) with the effective potential for the value of the scalar field at a fixed space - time point. We also calculate the renormalized fine structure constant using the correlator of Polyakov lines and compare it with the one - loop perturbative estimate.Comment: LATE

Geodesic Flow on the Normal Congruence of a Minimal Surface

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral K\"ahler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description of minimal surfaces in ${\Bbb{R}}^3$ and relate it to the classical Weierstrass representation.Comment: AMS-LATEX 8 pages 2, figure

High Resolution Low-Bandwidth Real-Time Reconnaissance using Structure from Motion with Planar Homography Estimation

Aerial real-time surveillance exists in a paradigm balancing the constraints of delivering high quality data and transporting data quickly. Typically, to have more of one, sacrifices must be made to the other. This is true of the environment in which an Unmanned Aerial Vehicle (UAV) operates, where real-time communication may be done through a low-bandwidth satellite connection resulting in low-resolution data, and serves as the primary limiting factor in all intelligence operations. Through the use of efficient computer vision techniques, we propose a new Structure from Motion (SfM) method capable of compressing high-resolution data, and delivering that data in real-time. Specifically demonstrating a 90 percent compression of original video imagery at 4 Hz which equates to an 80x computation time speed-up compared to traditional SfM methods, with an added benefit of presenting the original 2D intelligence data as a 3D virtual mode

Symplectic structures associated to Lie-Poisson groups

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Comment: 30 page

Developing Collaborative Relationships to Enhance Self-Employment Services for People with Disabilities

RTC: Rural researchers surveyed 571 U.S. Small Business Development Centers (SBDCs) to learn about linkages between Vocational Rehabilitation (VR) and SBDCs that could enhance self-employment outcomes for people with disabilities. 346 of 527 deliverable surveys were returned for a 64% response rate. The resulting data show a positive relationship between the presence of informal and/or formal agreements and SBDCs’ experience providing self-employment services for people with disabilities. VR-SBDC coordination could expand the outcomes of both agencies, reduce fragmentation between agencies, and capitalize on the strengths of each program

Lasing from single, stationary, dye-doped glycerol/water microdroplets located on a superhydrophobic surface

We report laser emission from single, stationary, Rhodamine B-doped glycerol/water microdroplets located on a superhydrophobic surface. In the experiments, a pulsed, frequency-doubled Nd:YAG laser operating at 532 nm was used as the excitation source. The microdroplets ranged in diameter from a few to 20 um. Lasing was achieved in the red-shifted portion of the dye emission spectrum with threshold fluences as low as 750 J/cm2. Photobleaching was observed when the microdroplets were pumped above threshold. In certain cases, multimode lasing was also observed and attributed to the simultaneous lasing of two modes belonging to different sets of whispering gallery modes.Comment: to appear in Optics Communication

Analytical solutions for two heteronuclear atoms in a ring trap

We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.Comment: 6 pages, 6 figure