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

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

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

Electro-Mechanical Fredericks Effects in Nematic Gels

The solid nematic equivalent of the Fredericks transition is found to depend on a critical field rather than a critical voltage as in the classical case. This arises because director anchoring is principally to the solid rubbery matrix of the nematic gel rather than to the sample surfaces. Moreover, above the threshold field, we find a competition between quartic (soft) and conventional harmonic elasticity which dictates the director response. By including a small degree of initial director misorientation, the calculated field variation of optical anisotropy agrees well with the conoscopy measurements of Chang et al (Phys.Rev.E56, 595, 1997) of the electro-optical response of nematic gels.Comment: Latex (revtex style), 5 EPS figures, submitted to PRE, corrections to discussion of fig.3, cosmetic change

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

The HELP System for Medical Decision Making

Conference PaperBiomedical Informatic

Analysis of wing truss stresses including the effect of redundancies

Airplane wing trusses are generally designed to contain redundant members (stagger wires and external drag wires) which, according to common practice, are not taken into account in calculations, so as to simplify the stress analysis by rendering the structure statically determinate. A more accurate method, in which the redundancies are included, involves a solution by means of Castigliano's method of least work. For the purpose of demonstrating the practical application of the method of least work this report presents examples for stresses of several cases of loading worked out for a structure similar to that of the Curtiss JN-4h. Case 1 was taken as the condition of velocity of 100 miles per hour combined with the angle of attack of maximum lift. Case 1a assumed the same loading but neglected the distortion of wooden members in the least-work analysis. So little error was involved in case 1a that this simplified method was employed for each succeeding case. Case 2 assumed a diving speed of 120 miles per hour and an angle of attack of no lift. Case 3 was worked out for the conditions imposed by the sand load recommended in NACA technical note no. 6