Second order conditions of optimality for constrained optimization problems in finite dimensional spaces

Conditions of optimality for constrained optimization proble

Adaptive Horizon Model Predictive Control and Al'brekht's Method

A standard way of finding a feedback law that stabilizes a control system to an operating point is to recast the problem as an infinite horizon optimal control problem. If the optimal cost and the optmal feedback can be found on a large domain around the operating point then a Lyapunov argument can be used to verify the asymptotic stability of the closed loop dynamics. The problem with this approach is that is usually very difficult to find the optimal cost and the optmal feedback on a large domain for nonlinear problems with or without constraints. Hence the increasing interest in Model Predictive Control (MPC). In standard MPC a finite horizon optimal control problem is solved in real time but just at the current state, the first control action is implimented, the system evolves one time step and the process is repeated. A terminal cost and terminal feedback found by Al'brekht's methoddefined in a neighborhood of the operating point is used to shorten the horizon and thereby make the nonlinear programs easier to solve because they have less decision variables. Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying the horizon length of Model Predictive Control (MPC) as needed. Its goal is to achieve stabilization with horizons as small as possible so that MPC methods can be used on faster and/or more complicated dynamic processes.Comment: arXiv admin note: text overlap with arXiv:1602.0861

A unified evaluation of iterative projection algorithms for phase retrieval

Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and the possibility of using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational ``instruments'' developed for the phase retrieval problem, and discuss acceleration strategies.Comment: 12 pages, 9 figures, revte

Crosses with Amut Bmut homokaryons of Coprinus cinereus

In this paper we describe the initial genetic analysis of some developmental REMI and UV mutants of the self-compatible homokaryon Amut Bmut. We show that such homokaryons can mate with each other although in fruitbodies we often found spores of only one parent. Crosses with monokaryons of different mating types gave some indications about numbers of mutations and linkage of genetic markers. In most cases, however, we observed an uneven distribution of markers, most likely because of loss of certain progeny. Our results necessitate the construction of monokaryons as closely related to homokaryon AmutBmut as possible but with different mating type loci

Measuring Fundamental Galactic Parameters with Stellar Tidal Streams and SIM PlanetQuest

Extended halo tidal streams from disrupting Milky Way satellites offer new opportunities for gauging fundamental Galactic parameters without challenging observations of the Galactic center. In the roughly spherical Galactic potential tidal debris from a satellite system is largely confined to a single plane containing the Galactic center, so accurate distances to stars in the tidal stream can be used to gauge the Galactic center distance, R_0, given reasonable projection of the stream orbital pole on the X_GC axis. Alternatively, a tidal stream with orbital pole near the Y_GC axis, like the Sagittarius stream, can be used to derive the speed of the Local Standard of Rest (\Theta_LSR). Modest improvements in current astrometric catalogues might allow this measurement to be made, but NASA's Space Interferometry Mission (SIM PlanetQuest) can definitively obtain both R_0 and \Theta_LSR using tidal streams.Comment: 8 pages, 4 figures, accepted for publication in ApJ Letters (minor text revisions). Version with high resolution figures available at http://www.astro.caltech.edu/~drlaw/Papers/GalaxyParameters.pd

Local dissipation effects in two-dimensional quantum Josephson junction arrays with magnetic field

We study the quantum phase transitions in two-dimensional arrays of Josephson-couples junctions with short range Josephson couplings (given by the Josephson energy) and the charging energy. We map the problem onto the solvable quantum generalization of the spherical model that improves over the mean-field theory method. The arrays are placed on the top of a two-dimensional electron gas separated by an insulator. We include effects of the local dissipation in the presence of an external magnetic flux f in square lattice for several rational fluxes f=0,1/2,1/3,1/4 and 1/6. We also have examined the T=0 superconducting-insulator phase boundary as function of a dissipation alpha for two different geometry of the lattice: square and triangular. We have found critical value of the dissipation parameter independent on geometry of the lattice and presence magnetic field.Comment: accepted to PR

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

Exploring Halo Substructure with Giant Stars III: First Results from the Grid Giant Star Survey and Discovery of a Possible Nearby Sagittarius Tidal Structure in Virgo

We describe first results of a spectroscopic probe of selected fields from the Grid Giant Star Survey. Multifiber spectroscopy of several hundred stars in a strip of eleven fields along delta approximately -17^{circ}, in the range 12 <~ alpha <~ 17 hours, reveals a group of 8 giants that have kinematical characteristics differing from the main field population, but that as a group maintain coherent, smoothly varying distances and radial velocities with position across the fields. Moreover, these stars have roughly the same abundance, according to their MgH+Mgb absorption line strengths. Photometric parallaxes place these stars in a semi-loop structure, arcing in a contiguous distribution between 5.7 and 7.9 kpc from the Galactic center. The spatial, kinematical, and abundance coherence of these stars suggests that they are part of a diffuse stream of tidal debris, and one roughly consistent with a wrapped, leading tidal arm of the Sagittarius dwarf spheroidal galaxy.Comment: 8 pages including 4 figures. Accepted for publication in ApJ

Experimental evidence of a fractal dissipative regime in high-T_c superconductors

We report on our experimental evidence of a substantial geometrical ingredient characterizing the problem of incipient dissipation in high-T_c superconductors(HTS): high-resolution studies of differential resistance-current characteristics in absence of magnetic field enabled us to identify and quantify the fractal dissipative regime inside which the actual current-carrying medium is an object of fractal geometry. The discovery of a fractal regime proves the reality and consistency of critical-phenomena scenario as a model for dissipation in inhomogeneous and disordered HTS, gives the experimentally-based value of the relevant finite-size scaling exponent and offers some interesting new guidelines to the problem of pairing mechanisms in HTS.Comment: 5 pages, 3 figures, RevTex; Accepted for publication in Physical Review B; (figures enlarged