Divergence preservation in the ADI algorithms for electromagnetics

The recent advances in alternating direct implicit (ADI) methods promise important new capability for time domain plasma simulations, namely the elimination of numerical stability limits on the time step. But the utility of these methods in simulations with charge and current sources, such as in electromagnetic particle-in-cell (EMPIC) computations, has been uncertain, as the methods introduced so far do not have the property of divergence preservation. This property is related to charge conservation and self-consistency, and is critical for accurate and robust EMPIC simulation. This paper contains a complete study of these ADI methods in the presence of charge and current sources. It is shown that there are four significantly distinct cases, with four more related by duality. Of those, only one preserves divergence and, thus, is guaranteed to be stable in the presence of moving charged particles. Computational verification of this property is accomplished by implementation in existing 3D-EMPIC simulation software. Of the other three cases, two are verified unstable, as expected, and one remains stable, despite the lack of divergence preservation. This other stable algorithm is shown to be related to the divergence preserving case by a similarity transformation, effectively providing the complement of the divergence preserving field in the finite-difference energy quantity.     

Bicontinuous cubic phase of monoolein and water as medium for electrophoresis of both membrane-bound probes and DNA

Porous hydrogels such as agarose are commonly used to analyze DNA and water-soluble proteins by electrophoresis. However, the hydrophilic environment of these gels is not suitable for separation of important amphiphilic molecules such as native membrane proteins. We show that an amphiphilic liquid crystal of the lipid monoolein and water can be used as a medium for electrophoresis of amphiphilic molecules. In fact, both membrane-bound fluorescent probes and water-soluble oligonucleotides can migrate through the same bicontinuous cubic crystal because both the lipid membrane and the aqueous phase are continuous. Both types of analytes exhibit a field-independent electrophoretic mobility, which suggests that the lipid crystal structure is not perturbed by their migration. Diffusion studies with four membrane probes indicate that membrane-bound analytes experience a friction in the cubic phase that increases with increasing size of the hydrophilic headgroup, while the size of the membrane-anchoring part has comparatively small effect on the retardation.     

A Shear-Corrected Formulation for the Sandwich Twist Specimen

The sandwich plate twist test method involves torsion loading of a panel by application of concentrated loads at two diagonally opposite corners and supporting the panel at the other two corners. Compliance measured in this test can be used to extract the shear moduli of monolithic, composite and sandwich plates, and it may also be employed for determination of the twist stiffness, D ₆₆ . Previous studies of the plate twist specimen have shown that classical laminated plate theory does not adequately predict the compliance of sandwich panels with a low density/modulus core, as a result of transverse shear deformation. This work proposes a “shear-corrected” model for accurate prediction of the plate twist compliance by incorporation of the transverse shear stiffnesses of the core. This model was used to extract the transverse shear modulus of a range of low density PVC foam cores from the measured panel twist compliance. Good agreement with published PVC foam core shear modulus values was obtained.     

Epitaxial NiO (1 0 0) and NiO (1 1 1) films grown by atomic layer deposition

Epitaxial NiO (1 1 1) and NiO (1 0 0) films have been grown by atomic layer deposition on both MgO (1 0 0) and α-Al₂O₃ (0 0 l) substrates at temperatures as low as 200 °C by using bis(2,2,6,6-tetramethyl-3,5-heptanedionato)Ni(II) and water as precursors. The films grown on the MgO (1 0 0) substrate show the expected cube on cube growth while the NiO (1 1 1) films grow with a twin rotated 180° on the α-Al₂O₃ (0 0 l) substrate surface. The films had columnar microstructures on both substrate types. The single grains were running throughout the whole film thickness and were significantly smaller in the direction parallel to the surface. Thin NiO (1 1 1) films can be grown with high crystal quality with a FWHM of 0.02–0.05° in the rocking curve measurements.     

Molecular adsorption and growth of n-butane adlayers on Pt(1 1 1)

The molecular adsorption of n-butane and the growth of n-butane adlayers on Pt(1 1 1) was investigated using molecular beam techniques, temperature-programmed desorption (TPD) and low-energy electron diffraction (LEED). It is found that as the surface coverage of n-butane increases, structural changes occur in the adlayer at surface temperatures near 98 K that are accompanied by changes in the binding energy and mobility of the adsorbed species. The film growth process can be divided into four distinct coverage regimes. At low coverages (θ<0.14 ML, where 1 ML is defined as one butane molecule per Pt atom) a disordered monolayer forms in which the butane molecules prefer to lie parallel to the surface in order to minimize their binding energy. At coverages from 0.14 to 0.20 ML, ordered regions develop within the monolayer in which the butane molecules also lie parallel to the surface. The binding energy in the ordered phase is lower than that in the disordered phase due to repulsive intermolecular interactions. A more densely-packed ordered phase begins to form at 98 K after the low-coverage ordered phase saturates at 0.20 ML. The experimental results suggest that the n-butane molecules tilt away from the surface in the high-coverage ordered phase. Finally, a disordered second layer phase forms after the high coverage ordered phase saturates at 0.35 ML. The molecules in the second layer are very mobile at 98 K and rapidly diffuse to the edges of the beam spot. Interchange of molecules between the second layer and ordered monolayer is found to govern the net rate of second layer diffusion at surface temperatures less than 133 K. The adsorption probability of n-butane on Pt(1 1 1) continuously increases with increasing coverage, with no significant dependencies on the structure of the n-butane adlayer. This finding indicates that the long-range arrangements and molecular orientations of a mobile alkane adlayer have a negligible influence on the intrinsic adsorption dynamics, suggesting that the energy transfer processes that facilitate adsorption are highly localized.     

Optimization and characterization of the chiral separation of citalopram and its demethylated metabolites by response-surface methodology

Summary Response-surface modelling and sequential optimization have been used for optimization and characterization of the separation of the enantiomers of citalopram, desmethylcitalopram, and didesmethylcitalopram on an acetylated β-cyclodextrin column. In the model chosen the separation conditions mobile phase methanol content, buffer concentration, column temperature, and pH were varied to investigate their influence on the chromatography. It was found that what is good for selectivity within an enantiomer pair is bad for selectivity between enantiomer pairs. Because within-pair and between-pair selectivity does not reach its optimum at the same conditions, a middle course approach has to be followed. Use of an experimental design for this investigation enabled understanding of the mechanisms of within- and between-pair separation for citalopram, desmethylcitalopram, and didesmethylcitalopram. Sequential optimization can be a quicker means of optimizing a chromatographic separation; response-surface modelling, in addition to enabling optimization of the chromatographic process, also serves as a tool for leaming more about the separation mechanism.     

The compton spectrometer

This is the story about how knowledge of the Compton profile led to the technical development of a useful apparatus. It is also the story of interdisciplinary collaboration between condensed matter theorists and medical physicists.     

On the homotopy fixed point problem for free loop spaces and other function complexes

Let G be a finite group, let X and Y be finite G-complexes, and suppose that for each K G, Y ^K is dim(X ^K)-connected and simple. G acts on the function complex F(X, Y) by conjugation of maps. We give a complete analysis of the homotopy fixed point set of the space F(X, Y). As a corollary, we are able to analyze at a prime p, the homotopy fixed point set of the circle action on X, where X denotes the free loop space of X, and X is a simply connected finite complex.Supported in part by NSF DMS 86-02430.To A. Grothendieck on the occasion of his sixtieth birthday