Determination of the second order susceptibility tensor in banana-shaped liquid crystals

Optical second harmonic generation (SHG) measurements have been carried out on the B2 phases of three liquid crystal materials composed of conventional banana-shaped molecules (P-10-O-PIMB, P-8-O-PIMB and P-8-PIMB). Quantitative values of the second order susceptibilities d_ij have been deduced from SHG measurements at oblique incidences on polydomain racemic samples under an electric field. The d_ij coefficients are in the range 1-10 pm V^-1.     

An inter-comparison of far-infrared line-by-line radiative transfer models

A considerable fraction (>40%) of the outgoing longwave radiation escapes from the Earth's atmosphere-surface system within a region of the spectrum known as the far-infrared (wave-numbers less than 650 cm⁻¹). Dominated by the line and continuum spectral features of the pure rotation band of water vapor, the far-infrared has a strong influence upon the radiative balance of the troposphere, and hence upon the climate of the Earth. Despite the importance of the far-infrared contribution, however, very few spectrally resolved observations have been made of the atmosphere for wave-numbers less than 650 cm⁻¹. The National Aeronautics and Space Administration (NASA), under its Instrument Incubator Program (IIP), is currently developing technology that will enable routine, space-based spectral measurements of the far-infrared. As part of NASA's IIP, the Far-Infrared Spectroscopy of the Troposphere (FIRST) project is developing an instrument that will have the capability of measuring the spectrum over the range from 100 to 1000 cm⁻¹ at a resolution of 0.6 cm⁻¹. To properly analyze the data from the FIRST instrument, accurate radiative transfer models will be required. Unlike the mid-infrared, however, no inter-comparison of codes has been performed for the far-infrared. Thus, in parallel with the development of the FIRST instrument, an investigation has been undertaken to inter-compare radiative transfer models for potential use in the analysis of far-infrared measurements. The initial phase of this investigation has focused upon the inter-comparison of six distinct line-by-line models. The results from this study have demonstrated remarkably good agreement among the models, with differences being of order 0.5%, thereby providing a high measure of confidence in our ability to accurately compute spectral radiances in the far-infrared.     

On the zeros of the Scorer functions

Asymptotic approximations are developed for zeros of the solutions Gi(z) and Hi(z) of the inhomogeneous Airy differential equation . The solutions are also called Scorer functions. Tables are given with numerical values of the zeros.     

Network reinforcement

We give an algorithm for the following problem: given a graph G=(V,E) with edge-weights and a nonnegative integer k, find a minimum cost set of edges that contains k disjoint spanning trees. This also solves the following reinforcement problem: given a network, a number k and a set of candidate edges, each of them with an associated cost, find a minimum cost set of candidate edges to be added to the network so it contains k disjoint spanning trees. The number k is seen as a measure of the invulnerability of a network. Our algorithm has the same asymptotic complexity as |V| applications of the minimum cut algorithm of Goldberg & Tarjan. Received: April, 2004     

Transverse Dimension of R~n Actions on Compact Foliated Manifolds

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