Laplace equations, conformal superintegrability and B\^ocher contractions

Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation to define quadratic algebras, a generalization of Lie algebras. Distinct systems and their algebras are related by geometric limits, induced by generalized In\"on\"u-Wigner Lie algebra contractions of the symmetry algebras of the underlying spaces. These have physical/geometric implications, such as the Askey scheme for hypergeometric orthogonal polynomials. The systems can be best understood by transforming them to Laplace conformally superintegrable systems and using ideas introduced in the 1894 thesis of B\^ocher to study separable solutions of the wave equation. The contractions can be subsumed into contractions of the conformal algebra $so(4,C)$ to itself. Here we announce main findings, with detailed classifications in papers under preparation.Comment: 10 pages, 2 figure

The Halo Formation Rate and its link to the Global Star Formation Rate

The star formation history of the universe shows strong evolution with cosmological epoch. Although we know mergers between galaxies can cause luminous bursts of star formation, the relative importance of such mergers to the global star formation rate (SFR) is unknown. We present a simple analytic formula for the rate at which halos merge to form higher-mass systems, derived from Press-Schechter theory and confirmed by numerical simulations (for high halo masses). A comparison of the evolution in halo formation rate with the observed evolution in the global SFR indicates that the latter is largely driven by halo mergers at z>1. Recent numerical simulations by Kolatt et al. (1999) and Knebe & Muller (1999) show how merging systems are strongly biased tracers of mass fluctuations, thereby explaining the strong clustering observed for Lyman-break galaxies without any need to assume that Lyman-break galaxies are associated only with the most massive systems at z~3.Comment: 4 pages, 2 figures. To appear in `The Hy-redshift universe: Galaxy formation and evolution at high redshift' eds. A.J. Bunker and W.J.M. van Breuge

An analysis of bi-directional use of frequencies for satellite communications

The bi-directional use of frequencies allocated for space communications has the potential to double the orbit/spectrum capacity available. The technical feasibility of reverse band use (RBU) at C-band (4 GHz uplinks and 6 GHz downlinks) is studied. The analysis identifies the constraints under which both forward and reverse band use satellite systems can share the same frequencies with terrestrial, line of sight transmission systems. The results of the analysis show that RBU satellite systems can be similarly sized to forward band use (FBU) satellite systems. In addition, the orbital separation requirements between RBU and FBU satellite systems are examined. The analysis shows that a carrier to interference ratio of 45 dB can be maintianed between RBU and FBU satellites separated by less than 0.5 deg., and that a carrier to interference ratio of 42 dB can be maintained in the antipodal case. Rain scatter propagation analysis shows that RBU and FBU Earth stations require separation distances fo less than 10 km at a rain rate of 13.5 mm/hr escalating to less than 100 km at a rain rate of 178 mm/hr for Earth station antennas in the 3 to 10 m range

Observations on pulsating auroras

Photometric observations of pulsating aurora

Ultrasonic dispersion (delta V/V) determined from mechanical resonance frequency shifts

With standing wave ultrasonic techniques, small changes in phase velocity which result from changes in some external parameter (e.g., temperature or magnetic field) have traditionally been determined by observing shifts in the mechanical resonance frequency of a composite resonator. Some previous investigators have assumed that the fractional change in velocity is equal to the fractional change in frequency. Substantially improved formulas for determining the dispersion are presented and one of these is shown to be much more accurate than all previous approximations. The results of simulated and actual experiments over wide ranges of dispersion, transducer loading parameter, and frequency are analyzed in order to compare the errors inherent in the various approximations

Flutter Investigation of 60 Degree to 80 Degree Delta-Planform Surfaces at a Mach Number of 7.0

The flutter characteristics of a series of half-span delta surfaces which had leading-edge sweep angles ranging from 60 degrees to 80 degrees were investigated in helium flaw at a Mach number of 7.0 in the Langley hypersonic aeroelasticity tunnel. For each value of sweep angle both wedge and double-wedge airfoil sections were tested at two pitch-axis positions, The models were mounted so that a rigid-body flapping-pitching type of flutter was encountered. Analysis of the results and comparison with theory show that the wedge models are more stable than the corresponding double-wedge models; the pitch-axis location at or near the center of gravity is more stable than the more forward location; the effects of leading-edge sweep angle on the flutter characteristics appear to be small; and an uncoupled-mode piston-theory analysis gave the best agreement with the experimental results

Your Lawn

PDF pages: 3