High-temperature expansions to fifteenth order

High-temperature series expansions of the susceptibility and second moment to 15th order are calculated for zero external field on the linear chain (LC), plane square (PSQ), simple cubic (SC), and body-centered cubic (BCC) lattices. Checks for specific models against pertinent work in the literature are detailed.     

Physical properties of glycosaminoglycan hydrogels

The chemical composition of glycosaminoglycan (GAG) hydrogels was found to have a profound effect on the physical properties of gels. Hyaluronan (HA) and chondroitin sulfate (CS) were each modified with adipic dihydrazide (ADH) with carbodiimide chemistry. The resulting polymer was crosslinked with various concentrations of poly(ethylene glycol) dialdehyde (PEG‐diald) to produce a series of hydrogels. The physical properties of these GAG hydrogels varied in a concentration‐dependent fashion. Maximal crosslinking was observed at a theoretical crosslinking of 50% for the HA‐ADH‐PEG‐diald hydrogels and 75% for the CS‐ADH‐PEG‐diald hydrogels. Adding PEG‐diald beyond the optimum for crosslinking prolonged the in vitro enzymatic degradation time of the hydrogels. The swelling of the crosslinked GAG hydrogels was correlated with the amount of PEG‐diald used rather than with the crosslinking density. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4344–4356, 2004     

The Interaction of Shocks with Dispersive Waves II. Incompressible-Integrable Limit

This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations.     

Hyperfine magnetic fields at sp-sites in Co2YZ Heusler alloys

The systematics of hyperfine magnetic fields at sp impurities on the Z-sites in Co based Heusler alloys are investigated. New TDPAC measurements of Cd hyperfine fields are reported.     

Echo planar imaging of perfluorocarbons

Emulsions of perfluorotributylamine (FTBA) and perflubron were evaluated for their utility in ¹⁹F echo planar imaging. Fluorine images of the emulsions were obtained in a phantom and two mice that had been predosed. Both agents, but particularly perflubron, show potential for fluorine echo planar studies because of the long spin-spin relaxation times of the CF₃ resonances. High resolution thin slice images obtained in as little as 26.6 ms are presented.     

Book Reviews

Unsigned book reviews are by the Book Review Editor.     

Unified Interactive Multiple Objective Programming: An Open Architecture For Accommodating New Procedures

It has previously been shown that nine of the most prominent procedures of interactive multiple objective programming can be considered as special cases of a common procedure called the unified algorithm. In this paper, we show how four additional procedures can be similarly included in the unified approach. Also, the paper presents a procedure-switching matrix that depicts the possibilities for switching from one procedure to another, one iteration to the next, in the unified algorithm if so directed by a user.     

Synthesis and characterization of a semiflexible liquid crystalline polyester with a broad nematic region

In this paper, we report on the synthesis and detailed characterization of a new semiflexible nematic liquid crystalline polyester which could serve as a 'model' polyester for a variety of physical and physico-chemical investigations. The polymer is a nematic liquid over a wide temperature range-from the glass transition temperature at ∼95°C to the isotropic transition at ∼240°C. We expect this polyester to be particularly useful for studying the effect of flow on the orientation of liquid crystalline polymers, as well as the production and removal of disclinations.