Piezoelectricity of Cholesteric Elastomers

We consider theoretically the properties of piezoelectricity in cholesteric elastomers. We deduce using symmetry considerations the piezoelectric contributions to the free energy in the context of a coarse-grained description of the material. In contrast to previous work we find that compressions or elongations of the material along the pitch axis do not produce a piezoelectric response, in agreement with fundamental symmetry considerations. Rather only suitable shear strains or local rotations produce a polarization. We propose some molecular mechanisms to explain these effects.Comment: 11 pages, 1 Postscript figure; Late

Kolmogorov-Smirnov Tests For Distribution Function Similarity With Applications To Portfolios of Common Stock

If the elements of the choice set in a decision model involving randomness are not arbitrary, but restricted appropriately, an expected utility ordering of them can be represented by a mean standard deviation ranking function. These restrictions can apply to the form of, or can specify relationships among, the distribution functions. A particularly useful restriction is one which requires that elements in the choice set, when normalized to have a zero mean and unit variance, be identically distributed. No restriction is placed on the form of any individual distribution function. This research empirically tests for this and other useful restrictions on the relationships among the elements of a set of random variables. Observations from the random variables are used to test whether or not they have distribution functions which are appropriately related to one another. The tests are applied to rate of return data for portfolios of common stock. The tests indicate that one cannot reject the hypothesis that the distribution functions of these portfolios are sufficiently similar to imply that the efficient set of portfolios for any risk averse expected utility maximizer is contained in the mean-standard deviation efficient set.

Role of electrostatics in the texture of islands in free standing ferroelectric liquid crystal films

Curved textures of ferroelectric smectic C* liquid crystals produce space charge when they involve divergence of the spontaneous polarization field. Impurity ions can partially screen this space charge, reducing long range interactions to local ones. Through studies of the textures of islands on very thin free-standing smectic films, we see evidence of this effect, in which materials with a large spontaneous polarization have static structures described by a large effective bend elastic constant. To address this issue, we calculated the electrostatic free energy of a free standing film of ferroelectric liquid crystal, showing how the screened coulomb interaction contributes a term to the effective bend elastic constant, in the static long wavelength limit. We report experiments which support the main features of this model

Trends in Self-Employment Among White and Black Men: 1910-1990

We examine trends in self-employment among white and black men from 1910 to 1990 using Census and CPS microdata. Self-employment rates fell over most of the century and then started to rise after 1970. For white men, we find that the decline was due to declining rates within industries, but was counterbalanced somewhat by a shift in employment towards high self-employment industries. Recently, the increase in self-employment was caused by an end to the within industry decline and the continuing shift in employment towards high self-employment industries. We find that the trends in self-employment average returns do not easily explain the decline in self-employment from 1950 to 1970, nor the increase from 1970 to 1990. We also find that changes in tax rates, social security benefits, and immigration patterns do not explain the recent upturn in self-employment. For black men, we find that the self-employment rate remained at a level of roughly one-third the white rate from 1910 to 1990. The large and constant gap between the black and the white rates is not due to blacks being concentrated in low self-employment rate industries, but is consistent with job opportunities outside of self-employment increasing relative to those in self-employment. However, more recently the relative earnings of blacks in self-employment rose more than relative earnings for whites the near constancy of the relative self-employment rates more surprising. We also find that absent continuing forces holding down black self-employment, a simple inter-generational model of self-employment suggests that black and white rates would converge quickly.