Equivalence classes of augmentations and Morse complex sequences of Legendrian knots

Let L be a Legendrian knot in R^3 with the standard contact structure. In [10], a map was constructed from equivalence classes of Morse complex sequences for L, which are combinatorial objects motivated by generating families, to homotopy classes of augmentations of the Legendrian contact homology algebra of L. Moreover, this map was shown to be a surjection. We show that this correspondence is, in fact, a bijection. As a corollary, homotopic augmentations determine the same graded normal ruling of L and have isomorphic linearized contact homology groups. A second corollary states that the count of equivalence classes of Morse complex sequences of a Legendrian knot is a Legendrian isotopy invariant.Comment: 28 pages, 17 figure

Flight investigation of the effect of tail boom strakes on helicopter directional control

A joint U.S. Army/NASA flight investigation was conducted utilizing a single-rotor helicopter to determine the effectiveness of horizontally mounted tail boom strakes on directional controllability and tail rotor power during low-speed, crosswind operating conditions. Three configurations were investigated: (1) baseline (strakes off), (2) single strake (strake at upper shoulder on port side of boom), and (3) double strake (upper strake plus a lower strake on same side of boom). The strakes were employed as a means to separate airflow over the tail boom and change fuselage yawing moments in a direction to improve the yaw control margin and reduce tail rotor power. Crosswind data were obtained in 5-knot increments of airspeed from 0 to 35 knots and in 30 deg increments of wind azimuth from 0 deg to 330 deg. At the most critical wind azimuth and airspeed in terms of tail rotor power, the strakes improved the pedal margin by 6 percent of total travel and reduced tail rotor power required by 17 percent. The increase in yaw control and reduction in tail rotor power offered by the strakes can expand the helicopter operating envelope in terms of gross weight and altitude capability. The strakes did not affect the flying qualities of the vehicle at airspeeds between 35 and 100 knots

G3-RAD and G3X-RAD: Modified Gaussian-3 (G3) and Gaussian-3X (G3X) procedures for radical thermochemistry

The G3-RAD, G3X-RAD, G3(MP2)-RAD, and G3X(MP2)-RAD, procedures, designed particularly for the prediction of reliable thermochemistry for free radicals, are formulated and their performance assessed using the G2/97 test set. The principal features of the RAD procedures include (a) the use of B3-LYP geometries and vibrational frequencies (in place of UHF and UMP2), including the scaling of vibrational frequencies so as to reproduce ZPVEs, (b) the use of URCCSD(T) [in place of UQCISD(T)] as the highest-level correlation procedure, and (c) the use of RMP (in place of UMP) to approximate basis-set-extension effects. G3-RAD and G3X-RAD are found to perform well overall with mean absolute deviations (MADs) from experiment of 3.96 and 3.65 kJ mol⁻¹, respectively, compared with 4.26 and 4.02 kJ mol⁻¹ for standard G3 and G3X. G3-RAD and G3X-RAD successfully predict heats of formation with MADs of 3.68 and 3.11 kJ mol⁻¹, respectively (compared with 3.93 and 3.60 kJ mol⁻¹ for standard G3 and G3X), and perform particularly well for radicals with MADs of 2.59 and 2.50 kJ mol⁻¹, respectively (compared with 3.51 and 3.18 kJ mol⁻¹ for standard G3 and G3X). The G3(MP2)-RAD and G3X(MP2)-RAD procedures give acceptable overall performance with mean absolute deviations from experiment of 5.17 and 4.92 kJ mol⁻¹, respectively, compared with 5.44 and 5.23 kJ mol⁻¹ for standard G3(MP2) and G3X(MP2). G3(MP2)-RAD and G3X(MP2)-RAD give improved performance over their standard counterparts for heats of formation (MADs=4.73 and 4.44 kJ mol⁻¹, respectively, versus 4.94 and 4.64 kJ mol⁻¹). G3(MP2)-RAD shows similar performance to G3(MP2) for radical heats of formation (MAD=5.10 versus 5.15 kJ mol⁻¹) while G3X(MP2)-RAD performs significantly better than G3X(MP2) (MAD=4.67 versus 5.19 kJ mol⁻¹).The authors gratefully acknowledge generous allocations of computing time on the Compaq Alphaserver of the National Facility of the Australian Partnership for Advanced Computing, Australian National University Supercomputer Facility, and the support of the Australian Research Council

Multi-color pyrometer for materials processing in space

The design, construction and calibration of a computer-linked multicolor pyrometer is described. The device was constructed for ready adaptation to a spacecraft and for use in the control of thermal processes for manufacturing materials in space. The pyrometer actually uses only one color at a time, and is relatively insensitive to uncertainties in the heated object's emissivity because the product of the color and the temperature has been selected to be within a regime where the radiant energy emitted from the body increases very rapidly with temperature. The instrument was calibrated and shown to exceed its design goal of temperature measurements between 300 and 2000 C, and its accuracy in the face of imprecise knowledge of the hot object's emissivity was demonstrated

Planetary systems around close binary stars: the case of the very dusty, Sun-like, spectroscopic binary BD+20 307

Field star BD+20 307 is the dustiest known main sequence star, based on the fraction of its bolometric luminosity, 4%, that is emitted at infrared wavelengths. The particles that carry this large IR luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short period, double-line, spectroscopic binary whose components have very different lithium abundances, vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).Comment: accepted for ApJ, December 10, 200

The Dwarf Irregular Galaxy UGC 7636 Exposed: Stripping At Work In The Virgo Cluster

We present the results of optical spectroscopy of a newly discovered H II region residing in the H I gas cloud located between the dwarf irregular galaxy UGC 7636 and the giant elliptical galaxy NGC 4472 in the Virgo Cluster. By comparing UGC 7636 with dwarf irregular galaxies in the field, we show that the H I cloud must have originated from UGC 7636 because (1) the oxygen abundance of the cloud agrees with that expected for a galaxy with the blue luminosity of UGC 7636, and (2) M_{H I}/L_B for UGC 7636 becomes consistent with the measured oxygen abundance of the cloud if the H I mass of the cloud is added back into UGC 7636. It is likely that tides from NGC 4472 first loosened the H I gas, after which ram-pressure stripping removed the gas from UGC 7636.Comment: 12 pages, 2 eps figures (AASTeX 5.0); accepted for publication in ApJ Letter

High-Q-factor Al [subscript 2]O[subscript 3] micro-trench cavities integrated with silicon nitride waveguides on silicon

We report on the design and performance of high-Q integrated optical micro-trench cavities on silicon. The microcavities are co-integrated with silicon nitride bus waveguides and fabricated using wafer-scale silicon-photonics-compatible processing steps. The amorphous aluminum oxide resonator material is deposited via sputtering in a single straightforward post-processing step. We examine the theoretical and experimental optical properties of the aluminum oxide micro-trench cavities for different bend radii, film thicknesses and near-infrared wavelengths and demonstrate experimental Q factors of > 10[superscript 6]. We propose that this high-Q micro-trench cavity design can be applied to incorporate a wide variety of novel microcavity materials, including rare-earth-doped films for microlasers, into wafer-scale silicon photonics platforms