Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested.Comment: 12 page

A method for determining landing runway length for a STOL aircraft

Based on data obtained from flight tests of the augmentor wing jet STOL research aircraft, a method is proposed for determining the length of the landing runway for powered-lift STOL aircraft. The suggested method determines runway landing length by summing three segments: the touchdown-dispersion distance, the transition distance from touchdown to application of brakes, and the stopping distance after brakes are applied. It is shown how the landing field length can be reduced either through improved autoland system design or by providing the pilot with appropriate information to allow him to identify a "low probability" long or short landing and to execute a go-around. The proposed method appears to determine a safe runway landing length for the STOL application and offers the potential for reducing runway length if great emphasis is placed on a short-runway capability. FAR Parts 25 and 121 appear conservative and suitable for the situation where no great emphasis is placed on reducing the runway length requirement

Iron-Line Emission as a Probe of Bardeen-Petterson Accretion Disks

In this work we show that Bardeen-Petterson accretion disks can exhibit unique, detectable features in relativistically broadened emission line profiles. Some of the unique characteristics include inverted line profiles with sharper red horns and softer blue horns and even profiles with more than 2 horns from a single rest-frame line. We demonstrate these points by constructing a series of synthetic line profiles using simple two-component disk models. We find that the resultant profiles are very sensitive to the two key parameters one would like to constrain, namely the Bardeen-Petterson transition radius r_{BP} and the relative tilt \beta between the two disk components over a range of likely values [10 < r_{BP}/(GM/c^2) < 40 ; 15deg < \beta < 45deg]. We use our findings to show that some of the ``extra'' line features observed in the spectrum of the Seyfert-I galaxy MCG--6-30-15 may be attributable to a Bardeen-Petterson disk structure. Similarly, we apply our findings to two likely Bardeen-Petterson candidate Galactic black holes - GRO J1655-40 and XTE J1550-564. We provide synthetic line profiles of these systems using observationally constrained sets of parameters. Although we do not formally fit the data for any of these systems, we confirm that our synthetic spectra are consistent with current observations.Comment: 13 pages, 11 figures, submitted to Ap

Program on stimulating operational private sector use of Earth observation satellite data

There are no author-identified significant results in this report

Millimeter wave transmission studies of YBa2Cu3O7-delta thin films in the 26.5 to 40.0 GHz frequency range

Millimeter wave transmission measurements through YBa2Cu3O(7-delta) thin films on MgO, ZrO2 and LaAlO3 substrates, are reported. The films (approx. 1 micron) were deposited by sequential evaporation and laser ablation techniques. Transition temperatures T sub c, ranging from 89.7 K for the Laser Ablated film on LaAlO3 to approximately 72 K for the sequentially evaporated film on MgO, were obtained. The values of the real and imaginary parts of the complex conductivity, sigma 1 and sigma 2, are obtained from the transmission data, assuming a two fluid model. The BCS approach is used to calculate values for an effective energy gap from the obtained values of sigma sub 1. A range of gap values from 2 DELTA o/K sub B T sub c = 4.19 to 4.35 was obtained. The magnetic penetration depth is evaluated from the deduced values of sigma 2. These results are discussed together with the frequency dependence of the normalized transmission amplitude, P/P sub c, below and above T sub c