Sparsity and Parallel Acquisition: Optimal Uniform and Nonuniform Recovery Guarantees

The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor measurements using compressed sensing. In the first half of the paper, we present both uniform and nonuniform recovery guarantees for the conventional sparse signal model in a so-called distinct sensing scenario. In the second half, using the so-called sparse and distributed signal model, we present nonuniform recovery guarantees which effectively broaden the class of sensing scenarios for which optimal recovery is possible, including to the so-called identical sampling scenario. To verify our recovery guarantees we provide several numerical results including phase transition curves and numerically-computed bounds.Comment: 13 pages and 3 figure

Dynamics of Order Parameter in Photoexcited Peierls Chain

The photoexcited dynamics of order parameter in Peierls chain is investigated by using a microscopic quantum theory in the limit where the hot electrons may establish themselves into a quasi-equilibrium state described by an effective temperature. The optical phonon mode responsible for the Peierls instability is coupled to the electron subsystem, and its dynamic equation is derived in terms of the density matrix technique. Recovery dynamics of the order parameter is obtained, which reveals a number of interesting features including the change of oscillation frequency and amplitude at phase transition temperature and the photo-induced switching of order parameter.Comment: 5 pages, 3 figure

Synthesis of octa-tailed calix[4]resorcinarenes and characterization of Langmuir-Blodgett films on these compounds.

This project was focused on synthesis of octa-tailed calix[4]resorcinarenes functionalized with pendant alpha-(diethyl acetamide) or alpha-(methyl acetate), preparation of Langmuir films and Langmuir-Blodgett films of the calix[4]resorcinarenes, and characterization of these compounds in solution and the Langmuir-Blodgett films. The octa-tailed calix[4]resorcinarene was synthesized by the cyclooligomerization of resorcinol and alpha,alpha-dihexyl acetaldehyde under acid-catalyzed conditions. The functionalized octa-tailed calix[4]resorcinarenes were obtained by substitution reaction with 2-bromo-NN-diethylacetamide or methyl bromoacetate under basic conditions. Langmuir films of the octa-tailed resorcin[4]arenes and their amide and ester derivatives were fabricated at the air/water interface. (Abstract shortened by UMI.)Dept. of Chemistry and Biochemistry. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1999 .C44. Source: Masters Abstracts International, Volume: 39-02, page: 0513. Adviser: P. Datton. Thesis (M.Sc.)--University of Windsor (Canada), 1999

An hourglass model for the flare of HST-1 in M87

To explain the multi-wavelength light curves (from radio to X-ray) of HST-1 in the M87 jet, we propose an hourglass model that is a modified two-zone system of Tavecchio & Ghisellini (hereafter TG08): a slow hourglass-shaped or Laval nozzle-shaped layer connected by two revolving exponential surfaces surrounding a fast spine, through which plasma blobs flow. Based on the conservation of magnetic flux, the magnetic field changes along the axis of the hourglass. We adopt the result of TG08---the high-energy emission from GeV to TeV can be produced through inverse Compton by the two-zone system, and the photons from radio to X-ray are mainly radiated by the fast inner zone system. Here, we only discuss the light curves of the fast inner blob from radio to X-ray. When a compressible blob travels down the axis of the first bulb in the hourglass, because of magnetic flux conservation, its cross section experiences an adiabatic compression process, which results in particle acceleration and the brightening of HST-1. When the blob moves into the second bulb of the hourglass, because of magnetic flux conservation, the dimming of the knot occurs along with an adiabatic expansion of its cross section. A similar broken exponential function could fit the TeV peaks in M87, which may imply a correlation between the TeV flares of M87 and the light curves from radio to X-ray in HST-1. The Very Large Array (VLA) 22 GHz radio light curve of HST-1 verifies our prediction based on the model fit to the main peak of the VLA 15 GHz radio light curve.Comment: 14 pages, 2 figures, accepted for publication in A

Magnetization Dynamics driven by Non-equilibrium Spin-Orbit Coupled Electron Gas

The dynamics of magnetization coupled to an electron gas via s-d exchange interaction is investigated by using density matrix technique. Our theory shows that non-equilibrium spin accumulation induces a spin torque and the electron bath leads to a damping of the magnetization. For the two-dimensional magnetization thin film coupled to the electron gas with Rashba spin-orbit coupling, the result for the spin-orbit torques is consistent with the previous semi-classical theory. Our theory predicts a damping of the magnetization, which is absent in the semi-classical theory. The magnitude of the damping due to the electron bath is comparable to the intrinsic Gilbert damping and may be important in describing the magnetization dynamics of the system.Comment: 7 pages, 2 figure

Anderson Impurity in Helical Metal

We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.Comment: The published versio