Renormalization of the relativistic delta potential in one dimension

Several authors have noted an ambiguity with the Dirac equation in one dimension. In the case of a delta-function potential, the coupling constant is subject to an apparently arbitrary renormalization when the delta function is approximated in different ways. We explain these differences in terms of strong resolvent limits of self-adjoint operators onL ²(R), and obtain a precise formula for the renormalized coupling constant in the case of separable potentials. The examples in the literature follow as special cases.Research supported in part by a grant from the National Science Foundation.     

Transient gas flow around boreholes

We present numerical solutions and analytical approximate solutions to problems of gas flow in porous media arising in the modelling of outbursts in coal mines and the efficient recovery of methane from coal seams.     

A FULLY AUTOMATED DUAL-WAVELENGTH PHOTOMETER FOR PHYTOCHROME MEASUREMENTS AND ITS APPLICATION TO PHYTOCHROME FROM CHLOROPHYLLCONTAINING EXTRACE

Abstract The photometer described here measures phytochrome photoreversibility of as many as 20 samples fully automatically. Monochromatic light of two laser diodes (670 and 780 nm) is used as a source for the measuring light beam. The whole measuring procedure is controlled by a computer linked to a lock-in amplifier. This arrangement permits a rather simple construction and allows automatic zeroing and sample change.
In addition the application of a Triton phase partitioning method to allow phytochrome photoreversibility mea surements of extracts of green tissue is described. A single phase partitioning with a chlorophylYphytochrome mixture reduced chlorophyll concentration to less than 10%. Repeated phase partitioning of crude extracts from green moss protonemata reduced chlorophyll content to less than 2% while leaving the phytochrome concentration almost unchanged. In some instances this method has advantages over polyethyleneimine precipitation, which is commonly used to obtain chlorophyll-free extracts.     

Light on dark laser addressed smectic liquid crystal projection displays

Two techniques for producing dense uniform bulk scattering in cells containing smectic A liquid crystals have been examined for use in a large area liquid crystal projection display. Textures obtained using both thermal pulses and by dynamic scattering in the smectic A phase were evaluated for their uniformity and scattering density. The conditions required for optimum scattering are described in terms of the electrical characteristics of the scattering pulses used, the effects of different surface alignment treatments and of the nematic bandwidth of the materials employed. The two techniques are compared with respect to their suitability for large area, high information content, white on black, laser addressed liquid crystal light valves.     

Supermembranes

An example is given of the spontaneous breaking of D = 4, N = 2 global supersymmetry down to N = 1. The example is a four-dimensional membrane in a six-dimensional supersymmetric gauge theory. The effective low-energy action for the membrane is a generalization of the Green—Schwarz covariant action.     

Convergence of an element-partitioned subcycling algorithm for the semi-discrete heat equation

A convergence analysis is performed for an element-partitioned subcycling algorithm for the semi-discrete heat equation. It is shown that the algorithm generally attains first-order rate-of-convergence.     

Effect of molecular structure on mesomorphism XXI. Monodisperse tetrameric model compounds for liquid crystalline polymers

Twinned dimeric mesogens having a rigid-flexible-rigid molecular structure have been shown to be appropriate models for some properties of regularly alternating (rigid-flexible)_n main chain liquid crystalline polymers (lcps). A family of tetrameric monodisperse liquid crystalline model compounds chemically related to known main chain liquid crystalline polymers of the 4-alkoxyphenyl 4'-alkoxy-benzoate type has been synthesized. The tetramers are nematogenic. Alternations in thermodynamic parameters (ΔH, ΔS) for the N-I transition as a function of spacer chain length indicate conformational behaviour of the internal spacers dominates mesophase properties.