The folded, tetrameric phosph(III)azane macrocycle [(P(mu-NtBu))2(1,4-(NH)2C6H4)]4

The tetrameric macrocycle [(P(mu-NtBu))2(1,4-(NH)2C6H4)]4, obtained from the reaction of the phosphazane dimer [ClP(mu-NtBu)]2 with p-phenylenediamine, has an unusual folded conformation in the solid state and contains a roughly tetrahedral arrangement of endo N-H groups for the potential coordination of anions.     

Phonon mediated interaction for triplet pairing in Pd

The pairing interaction due to phonon exchange is calculated for the triplet p-state of Pd, using the atomic-site representation for the heavy d electrons. It is found that this interaction is repulsive, λ^Ph₁ < 0, and that its magnitude is small compared with the singlet s-state interaction of BCS, λ^Ph₀. The net interaction due to both phonons and spin-fluctuations is attractive but it is so small that the observation of a triplet p-state in Pd appears unlikely at the lowest accessible temperatures.     

Electron beam duplication of integrated optical circuits and masks

An electron beam duplication technique has been developed that permits the rapid (2–15 min) fabrication of masks suitable for integrated optical elements (2000 A precision over a 5 × 5 cm area). The technique is based on the use of a master mask, which, when exposed to UV light emits electrons in the desired pattern. The electrons are then accelarated and focused onto the substrate. We have used this technique to duplicate complex optical waveguide structures in electron resist (polyphenylsiloxane) and to prepare masks for the fabrication of waveguides in inorganic materials (SiO₂).     

Antenna length and polarization response of antenna-coupled MOM diode infrared detectors

This work focuses on the fabrication and response of dipole antenna-coupled metal–oxide–metal diode detectors to long-wave infrared radiation. The detectors are fabricated using a single electron beam lithography step and a shadow evaporation technique. The detector’s characteristics are presented, which include response as a function of incident infrared power and polarization angle. In addition, the effect of dipole antenna length on detection characteristics for 10.6 μm radiation has been measured to determine resonant lengths. The response of the detector shows a first resonance at a dipole length of 3.1 μm, a second resonance at 9.3 μm, and third at 15.5 μm. The zeros intermediate to the resonances are also evident.     

Targeting large phosp(III)azane macrocyles [{P(mu-NR)}(2)(LL)](n) (n> or = 2)

The condensation reactions of the dimer [ClP(micro-NR)](2) with organic diacids [LL(H)(2)], possessing linear orientations of their organic groups, result in the formation of phospha(III)zane macrocyles of the type [{P(mu-NR)}(2)(LL)](n) of various sizes. The series of macrocycles [{P(mu-N(t)Bu)}(2){1,5-(NH)(2)C(10)H(6)}](3), [{P(mu-NCy)}(2)(1,5-O(2)C(10)H(6))](n) [n = 3; n = 4], [{P(mu-N(t)Bu)}(2){1,4-(NH)(2)C(6)H(4)}](4), [{P(mu-N(t)Bu)}(2)(1,4-O(2)C(6)H(4))], [{P(mu-NCy)}(2)(1,4-O(2)C(6)H(4))](3) and [{P(mu-N(t)Bu)}(2){(NH)C(6)H(4)OC(6)H(4)(NH)}](2) can be related to classical organic frameworks, like calixarenes.     

Determination of cholesterol absorption in humans: from radiolabel to stable isotope studies

Hypercholesterolemia is a major health risk. Dietary cholesterol absorption is one important factor affecting levels of plasma and tissue cholesterol. Considerable effort has thus been devoted to develop reliable in vivo clinical methodologies to determine dietary cholesterol absorption in humans. The present paper summarises radiolabelled experiments and major advances in stable isotope technologies to determine cholesterol absorption. Initially, direct methods employing gastro-intestinal intubation were developed. Later, indirect methods using oral–faecal cholesterol balance permitted calculation of cholesterol mass absorption. Once the use of radiolabelled [³H, ¹⁴C]cholesterol balance was developed in healthy humans, it was finally possible to distinguish exogenous and endogenous cholesterol. Non-invasive and safer stable isotope (²H, ¹³C, ¹⁸O) labelled cholesterol tracers then replaced radioisotopes for use in infants and adults. Stable isotopes and radioisotopes showed identical cholesterol kinetics. The most promising contemporary stable isotope assessment of cholesterol absorption is a dual stable isotope dual tracer approach based on simultaneous administration of oral and intravenous differentially labelled cholesterol tracers, followed by plasma sampling for 3–4?d. Online GC/Combustion/IRMS and GC/Pyrolysis/IRMS allow minimal amounts of dual stable isotope cholesterol tracers to be detected. Using the dual stable isotope dual tracer approach, the percent cholesterol absorption in adult volunteers has been determined to be 50–70%.     

Coupled spring equations

Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project.     

Duffing's equation and nonlinear resonance

The phenomenon of nonlinear resonance (sometimes called the ‘jump phenomenon’) is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto an unbounded one. This is a common occurrence when numerically solving differential equations with initial values very close to a separatrix that distinguishes between stable (bounded) solutions and unstable (unbounded) solutions. This numerical phenomenon is not discussed in most texts and it is the purpose of this article to describe the effect is such a way as to make it suitable for beginning students to understand why things happen the way they do. Given the modern trend for computer laboratory projects in beginning differential equations courses, it is important for students to be aware of one of the common failings of numerical solutions.