Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Detection of Other Planetary Systems Using Photometry

Detection of extrasolar short-period planets, particularly if they are in the liquid-water zone, would be one of the most exciting discoveries of our lifetime. A well-planned space mission has the capability of making this discovery using the photometric method. An Earth-sized planet transiting a Sun-like star will cause a decrease in the apparent luminosity of the star by one part in 10,000 with a duration of about 12 hours and a period of about one year. Given a random orientation of orbital plane alignments with the line-of-sight to a star, and assuming our solar system to be typical, one would expect 1 percent of the stars monitored to exhibit planetary transits. A null result would also be significant and indicate that Earth-sized planets are rare. For the mission to be successful one needs a sensor system that can simultaneously monitor many thousands of stars with a photometric precision of one part in 30,000 per hour of integration. Confirmation of a detection will involve detection of a second transit that will yield a period and predict the time for a third and subsequent transits. The technology issues that need to be addressed are twofold: one is for an appropriate optical design; the other is for a detector system with the necessary photometric precision. Two candidates for the detector system are silicon diodes and CCD's

Orbit/attitude estimation for the GOES spacecraft using VAS landmark data

A software system is described which provides for batch least squares estimation of spacecraft orbit, attitude, and camera bias parameters using image data from the Geostationary Operational Environmental Satellites (GOES). The image data are obtained by the Visible and Infrared Spin Scan Radiometer (VISSR) Atmospheric Sounder (VAS). The resulting estimated parameters are used for absolute image registration. Operating in the Digital Equipment Corporation (DEC) PDP-11/70 computer, the FORTRAN system also includes the capabilities of image display and manipulations. An overview of the system is presented as well as some numerical results obtained from observations taken by the SMS-2 satellite over a 3 day interval in August 1975

State estimation and absolute image registration for geosynchronous satellites

Spacecraft state estimation and the absolute registration of Earth images acquired by cameras onboard geosynchronous satellites are described. The basic data type of the procedure consists of line and element numbers of image points called landmarks whose geodetic coordinates, relative to United States Geodetic Survey topographic maps, are known. A conventional least squares process is used to estimate navigational parameters and camera pointing biases from observed minus computed landmark line and element numbers. These estimated parameters along with orbit and attitude dynamic models are used to register images, using an automated grey level correlation technique, inside the span represented by the landmark data. In addition, the dynamic models can be employed to register images outside of the data span in a near real time mode. An important application of this mode is in support of meteorological studies where rapid data reduction is required for the rapid tracking and predicting of dynamic phenomena

Interacting multi-component exciton gases in a potential trap: phase separation and Bose-Einstein condensation

The system under consideration is a multi-component gas of interacting para- and orthoexcitons confined in a three dimensional potential trap. We calculate the spatially resolved optical emission spectrum due to interband transitions involving weak direct and phonon mediated exciton-photon interactions. For each component, the occurrence of a Bose-Einstein condensate changes the spectrum in a characteristic way so that it directly reflects the constant chemical potential of the excitons and the renormalization of the quasiparticle excitation spectrum. Moreover, the interaction between the components leads, in dependence on temperature and particle number, to modifications of the spectra indicating phase separation of the subsystems. Typical examples of density profiles and luminescence spectra of ground-state para- and orthoexcitons in cuprous oxide are given.Comment: 7 pages, 6 figure

Calculation of the static and dynamical correlation energy of pseudo-one-dimensional beryllium systems via a many-body expansion

Low-dimensional beryllium systems constitute interesting case studies for the test of correlation methods because of the importance of both static and dynamical correlation in the formation of the bond. Aiming to describe the whole dissociation curve of extended Be systems we chose to apply the method of increments (MoI) in its multireference (MR) formalism. However, in order to do so an insight into the wave function was necessary. Therefore we started by focusing on the description of small Be chains via standard quantum chemical methods and gave a brief analysis of the main characteristics of their wave functions. We then applied the MoI to larger beryllium systems, starting from the Be6 ring. First, the complete active space formalism (CAS-MoI) was employed and the results were used as reference for local MR calculations of the whole dissociation curve. Despite this approach is well established for the calculation of systems with limited multireference character, its application to the description of whole dissociation curves still requires further testing. After discussing the role of the basis set, the method was finally applied to larger rings and extrapolated to an infinite chain

Preliminary design study of advanced multistage axial flow core compressors

A preliminary design study was conducted to identify an advanced core compressor for use in new high-bypass-ratio turbofan engines to be introduced into commercial service in the 1980's. An evaluation of anticipated compressor and related component 1985 state-of-the-art technology was conducted. A parametric screening study covering a large number of compressor designs was conducted to determine the influence of the major compressor design features on efficiency, weight, cost, blade life, aircraft direct operating cost, and fuel usage. The trends observed in the parametric screening study were used to develop three high-efficiency, high-economic-payoff compressor designs. These three compressors were studied in greater detail to better evaluate their aerodynamic and mechanical feasibility

The Quantum Speed Limit of Optimal Controlled Phasegates for Trapped Neutral Atoms

We study controlled phasegates for ultracold atoms in an optical potential. A shaped laser pulse drives transitions between the ground and electronically excited states where the atoms are subject to a long-range 1/R^3 interaction. We fully account for this interaction and use optimal control theory to calculate the pulse shapes. This allows us to determine the minimum pulse duration, respectively, gate time T that is required to obtain high fidelity. We accurately analyze the speed limiting factors, and we find the gate time to be limited either by the interaction strength in the excited state or by the ground state vibrational motion in the trap. The latter needs to be resolved by the pulses in order to fully restore the motional state of the atoms at the end of the gate.Comment: 11 pages, 10 figures, 1 tabl

A Two-Parameter Recursion Formula For Scalar Field Theory

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($\zeta$) allows one to continuously extrapolate between Wilson's approximate recursion formula and the recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $\gamma$ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved recursion formulas.Comment: 7 pages, uses Revtex, one Postcript figur

Consciousness science : real progress and lingering misconceptions.

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