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.

Comparing the performance of geometrically similar airplanes

This note has been prepared for the National Advisory Committee for Aeronautics. It deals with the model rules relating to aeronautical problems, and shows how the characteristics of one airplane can be determined from those of another airplane of different weight or size, and of similar type. If certain rules for the ratios of the dimensions, the weights and the horsepower are followed, a small low-powered airplane can be used for obtaining information as to performance, stability, controllability and maneuverability of a larger prototype, and contrariwise

Extended N=2 Superconformal Structure of Gravity and W-Gravity Coupled to Matter

We show that almost all string theories, including the bosonic string, the superstring and $W$-string theories, possess a twisted N=2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the \brs operators of the $W_n$-string can be obtained by hamiltonian reduction of $SL(n|n-1)$. The tachyonic and ground ring states of $W$-strings are described in the light of the N=2 superconformal structure, and the ground ring generators for the non-critical $W_3$-string are explicitly constructed. The relationship to $G/G$ models and quantum integrable systems is also briefly described.Comment: 48 page

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

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

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

Iteration Method to Derive Exact Rotation Curves from Position-Velocity Diagrams of Spiral Galaxies

We present an iteration method to derive exact rotation curves (RC) of spiral galaxies from observed position-velocity diagrams (PVD), which comprises the following procedure. An initial rotation curve, RC0, is adopted from an observed PV diagram (PV0), obtained by any simple method such as the peak-intensity method. Using this rotation curve and an observed radial distribution of intensity (emissivity), we construct a simulated PV diagram (PV1). The difference between a rotation curve obtained from this PV1 and the original RC (e.g., difference between peak-intensity velocities) is used to correct the initial RC to obtain a corrected rotation curve, RC1. This RC1 is used to calculated another PVD (PV2) using the observed intensity distribution, and to obtain the second iterated RC (RC2). This iteration is repeated until PV$i$ converges to PV0, so that the differences between PV$i$ and PV0 becomes minimum. Finally RC$i$ is adopted as the most reliable rotation curve. We apply this method to some observed PVDs of nearby galaxies, and show that the iteration successfully converges to give reliable rotation curves. We show that the method is powerful to detect central massive objects.Comment: To appear in ApJ.Letters, 5 pages Latex with 4 figure

Radio and near-infrared observations of the steep spectrum Galactic plane radio source WKB 0314+57.8

Radio and near-infared observations towards the steep spectrum Galactic plane radio source WKB 0314+57.8 are presented, in order to clarify the nature of this source. The radio observations include archival and survey data, together with new Giant Metrewave Radio Telescope observations at 617 MHz. The near-infrared observations are in the J and K bands, from the Gemini instrument on the Shane 3-m telescope. The radio observations show that WKB 0314+57.8 is extended, with an very steep spectrum (with flux density proportional to frequency to -2.5 power between 40 MHz and 1.5 GHz). The colour--magnitude diagram constructed from near-infrared observations of the field suggests the presence of a z approx 0.08 galaxy cluster behind the Galactic plane, reddened by about 6 magnitudes of visual extinction. Although the steep spectrum source has no obvious identification, two other radio sources in the field covered by the near-infrared observations have tentative identifications with galaxies. These observations indicate that WKB 0314+57.8 is a relic source in a cluster of galaxies, not a pulsar.Comment: 6 pages, to appear in MNRAS, typos correcte

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

Dwarf Nova Oscillations and Quasi-Periodic Oscillations in Cataclysmic Variables - VIII. VW Hyi in outburst observed with the Southern African Large Telescope

We analyse four light curves obtained at high time resolution (~ 0.1 s) with the 11-m Southern African Large Telescope, at the ends of two normal outbursts and one superoutburst of the dwarf nova VW Hyi. All of these contain at least some Dwarf Nova Oscillations (DNOs), which, when at their highest amplitudes, are seen in unprecedented detail. In addition to the expected DNOs with periods > 20 s we find a previously unknown modulation at 13.39 s, but none at shorter periods. The various DNOs and their interaction with the longer period Quasi-periodic Oscillations are interpreted in terms of the model of magnetically controlled flow from an accretion disc proposed earlier in this series of papers. Our observations include rare DNOs very late in outburst; we find that the fundamental period does not increase beyond ~ 90 s, which is the same value that the independent ``longer period DNOs'' converge on.Comment: Accepted for publication in MNRAS. 7 pages, 10 figures, 2 table