Phase transitions of nematic rubbers

Single crystal nematic elastomers undergo a transition from a strongly ordered phase N to an "isotropic" phase I. We show that: (a) samples produced under tension by the Finkelmann procedure are intrinsically anisotropic and should show a small (temperature dependent) birefringence in the high temperature I phase. (b) for the I->Ntransition via cooling there is a spinodal limit but for the N->I transition via heating there is no soft mode at the standard spinodal temperature. (c) the N->I transition is reminiscent of a martensitic transformation: nucleation of the I phase should occur in the form of platelets, making a well defined angle with the director.Comment: 7 pages, 3 figures (To appear in Europhys. Lett.

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

Smectic-C tilt under shear in Smectic-A elastomers

Stenull and Lubensky [Phys. Rev. E {\bf 76}, 011706 (2007)] have argued that shear strain and tilt of the director relative to the layer normal are coupled in smectic elastomers and that the imposition of one necessarily leads to the development of the other. This means, in particular, that a Smectic-A elastomer subjected to a simple shear will develop Smectic-C-like tilt of the director. Recently, Kramer and Finkelmann [arXiv:0708.2024, Phys. Rev. E {\bf 78}, 021704 (2008)] performed shear experiments on Smectic-A elastomers using two different shear geometries. One of the experiments, which implements simple shear, produces clear evidence for the development of Smectic-C-like tilt. Here, we generalize a model for smectic elastomers introduced by Adams and Warner [Phys. Rev. E {\bf 71}, 021708 (2005)] and use it to study the magnitude of Smectic-C-like tilt under shear for the two geometries investigated by Kramer and Finkelmann. Using reasonable estimates of model parameters, we estimate the tilt angle for both geometries, and we compare our estimates to the experimental results. The other shear geometry is problematic since it introduces additional in-plane compressions in a sheet-like sample, thus inducing instabilities that we discuss.Comment: 8 pages, 5 figure

Imprinted Networks as Chiral Pumps

We investigate the interaction between a chirally imprinted network and a solvent of chiral molecules. We find, a liquid crystalline polymer network is preferentially swollen by one component of a racemic solvent. This ability to separate is linked to the chiral order parameter of the network, and can be reversibly controlled via temperature or a mechanical deformation. It is maximal near the point at which the network loses its imprinted structure. One possible practical application of this effect would be a mechanical device for sorting mixed chiral molecules.Comment: 4 pages, 5 figure

Flight-test of the glide-slope track and flare-control laws for an automatic landing system for a powered-lift STOL airplane

An automatic landing system was developed for the Augmentor Wing Jet STOL Research Airplane to establish the feasibility and examine the operating characteristics of a powered-lift STOL transport flying a steep, microwave landing system (MLS) glide slope to automatically land on a STOL port. The flight test results address the longitudinal aspects of automatic powered lift STOL airplane operation including glide slope tracking on the backside of the power curve, flare, and touchdown. Three different autoland control laws were evaluated to demonstrate the tradeoff between control complexity and the resulting performance. The flight test and simulation methodology used in developing conventional jet transport systems was applied to the powered-lift STOL airplane. The results obtained suggest that an automatic landing system for a powered-lift STOL airplane operating into an MLS-equipped STOL port is feasible. However, the airplane must be provided with a means of rapidly regulation lift to satisfactorily provide the glide slope tracking and control of touchdown sink rate needed for automatic landings

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There is an analogy with the classical problem of an electric field applied to a cholesteric liquid crystal, but with important differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between director anchoring to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.Comment: 4 pages, RevTeX 3 style, 3 EPS figure

High Speed Photometry of SDSS J013701.06-091234.9

We present high speed photometry of the Sloan Digital Sky Survey cataclysmic variable SDSS J013701.06-091234.9 in quiescence and during its 2003 December superoutburst. The orbital modulation at 79.71\pm0.01 min is double humped; the superhump period is 81.702\pm0.007 min. Towards the end of the outburst late superhumps with a period of 81.29\pm0.01 min were observed. We argue that this is a system of very low mass transfer rate, and that it probably has a long outburst interval.Comment: 5 pages, 8 figures. Accepted for publication in MNRA

Photonic gaps in cholesteric elastomers under deformation

Cholesteric liquid crystal elastomers have interesting and potentially very useful photonic properties. In an ideal monodomain configuration of these materials, one finds a Bragg-reflection of light in a narrow wavelength range and a particular circular polarization. This is due to the periodic structure of the material along one dimension. In many practical cases, the cholesteric rubber possesses a sufficient degree of quenched disorder, which makes the selective reflection broadband. We investigate experimentally the problem of how the transmittance of light is affected by mechanical deformation of the elastomer, and the relation to changes in liquid crystalline structure. We explore a series of samples which have been synthesized with photonic stop-gaps across the visible range. This allows us to compare results with detailed theoretical predictions regarding the evolution of stop-gaps in cholesteric elastomers

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

The Interpretations For the Low and High Frequency QPO Correlations of X-ray Sources Among White Dwarfs, Neutron Stars and Black Holes

It is found that there exists an empirical linear relation between the high frequency \nhigh and low frequency \nlow of quasi-periodic oscillations (QPOs) for black hole candidate (BHC), neutron star (NS) and white dwarf (WD) in the binary systems, which spans five orders of magnitude in frequency. For the NS Z (Atoll) sources, $\nu_{high}$ and $\nu_{low}$ are identified as the lower kHz QPO frequency and horizontal branch oscillations (HBOs) \nh (broad noise components); for the black hole candidates and low-luminosity neutron stars, they are the QPOs and broad noise components at frequencies between 1 and 10 Hz; for WDs, they are the ``dwarf nova oscillations'' (DNOs) and QPOs of cataclysmic variables (CVs). To interpret this relation, our model ascribes $\nu_{high}$ to the Alfv\'en wave oscillation frequency at a preferred radius and $\nu_{low}$ to the same mechanism at another radius. Then, we can obtain \nlow = 0.08 \nhigh and the relation between the upper kHz QPO frequency \nt and HBO to be \nh \simeq 56 ({\rm Hz}) (\nt/{\rm kHz})^{2}, which are in accordance with the observed empirical relations. Furthermore, some implications of model are discussed, including why QPO frequencies of white dwarfs and neutron stars span five orders of magnitude in frequency. \\Comment: 11 pages, 1 figure, accepted by PAS