Numerical Simulation of Waveguides of Arbitrary Cross-Section

Finite difference equations are derived for the simulation of dielectric waveguides using an H_z-E_z formulation defined on a nonuniform triangular grid. The resulting equations may be solved as a banded eigenproblem for waveguide structures of arbitrary shape composed of regions of piecewise constant isotropic dielectric, and all transverse fields then computed from the solutions. Benchmark comparisons are presented for problems with analytic solutions, as well as a sample calculation of the propagation loss of a hollow Bragg fiber.     

Low-truncation-error finite difference equations for photonicssimulation. II. Vertical-cavity surface-emitting lasers

For part I see, ibid., p. 134, 1998. The basic approach outlined in the previous article is applied to the difficult problem of computing the optical modes of a vertical-cavity surface-emitting laser. The formulation utilizes a finite difference equation based upon the lowest order term of an infinite series solution of the scalar Helmholtz equation in a local region. This difference equation becomes exact in the one-dimensional (1-D) limit, and is thus ideally suited for nearly 1-D devices such as vertical-cavity lasers. The performance of the resulting code is tested on both a simple cylindrical cavity with known solutions and an oxide-confined vertical-cavity laser structure, and the results compared against second-order-accurate code based upon Crank-Nicolson differencing     

SPECT, CT, and MRI in head injury: acute abnormalities followed up at six months

We report a case of cervicofacial necrotizing fasciitis that developed after blepharoplasty, an occurrence that, to our knowledge, has not previously been reported in the medical literature. A patient who presented to our institution 3 days after undergoing blepharoplasty of the upper eyelid was diagnosed as having fulminant fasciitis involving extensive areas of the face, scalp, and neck. We review the case in detail and discuss clinical and radiological clues to diagnosis, surgical and medical management, wound care, and subsequent scar contracture. This case emphasizes the need for individualized, appropriate postoperative care and for an awareness of this rare, potentially fatal complication. Early recognition and aggressive treatment of cervicofacial fasciitis can arrest its rapid progression and prevent devastating sequelae.     

Overview of otolaryngic allergy management. An eclectic and cost-effective approach

In this paper, we studied three species of prosimian primate (Propithecus diadema edwardsi, Eulemur fulvus rufus, and Eulemur rubriventer) from June-July 1995 at the Ranomafana National Park to answer three questions: 1) how they handle and process seeds, 2) how the physical properties of seeds influence seed handling and seed fate, and 3) whether handling and processing patterns influence seed dispersal. Seeds from five plant species were collected from feces and examined for external damage (punctures and scrapes), weighed, measured, and checked daily for germination. P. d. edwardsi masticated seeds into two or more pieces while feeding. Seed fragments were either dropped under the parent tree or chewed and swallowed; seeds never emerged as recognizable units in feces. In contrast, both Eulemur species either dropped or swallowed seeds whole while feeding. E. rubriventer passed seeds that were longer, wider, and heavier than seeds passed by E.f. rufus. Although seeds emerged as separate units when passed by both Eulemur species, 65 Protorhus sp. seeds were scraped and/or punctured prior to being swallowed. Based on physical property tests, Protorhus seeds were more susceptible to mastication than undamaged seeds from Eugenia sp., Cissus sp., and Chrysophyllum madagascariensis. H. madagascariensis seeds also were undamaged but had physical properties comparable to Protorhus and may avoid being masticated due to their small size (2-3 mm). All damaged seeds were moldy or rotten within 6 days, and only 15% of the undamaged seeds passed by E. rubriventer germinated. None of the seeds passed by E.f. rufus germinated. Eulemur species also rested in the same tree after feeding and defecated prior to a new feeding bout or before moving, so seeds were most likely to be dispersed under the parent tree. Consequently, we concluded that these primate species do not appear to serve as effective seed dispersers for these plant species at this time of year.     

Opportunities in the electrowinning of molten titanium from titanium dioxide

The value chain of titanium products shows that the difference between the cost of titanium ingot and titanium dioxide is about $9/kg titanium. In contrast, the price of aluminum, which is produced in a similar way, is only about $1.7/kg. Electrowinning of molten titanium from titanium dioxide is therefore believed to have significant potential to reduce the cost of titanium products. The process is hampered by the high operating temperatures and sophisticated materials of construction required; the high affinity of titanium for carbon, oxygen, and nitrogen; and physical and chemical properties of the different titanium oxide species when reducing titanium from Ti₄₊ to metallic titanium. For more information, contact D.S. van Vuuren, CSIR, Materials and Manufacturing Technology Department, Meiring Naude Road, Pretoria, Gauteng 0181, South Africa; +27 12-841 2375; fax +27 841 2135; e-mail dvvuuren@csir.co.za.     

Consistency,Turing Computability and Gödel’s First Incompleteness Theorem

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with Gödel’s results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines.     

Product plots

We propose a new framework for visualising tables of counts, proportions and probabilities. We call our framework product plots, alluding to the computation of area as a product of height and width, and the statistical concept of generating a joint distribution from the product of conditional and marginal distributions. The framework, with extensions, is sufficient to encompass over 20 visualisations previously described in fields of statistical graphics and infovis, including bar charts, mosaic plots, treemaps, equal area plots and fluctuation diagrams.     

Carbon Diffusion in Lanthanum Erbium Carbide Stabilized in the Cubic Fluorite Structure

Lanthanum erbium carbide, La_0.5Er_0.5C₂, a salt-like carbide with a cubic fluorite phase structure, has been produced from ¹³C, allowing carbon diffusion rate to be determined using ¹²C. Carbon in salt-like carbides exhibits significant ionicity, and a high carbon diffusion rate would enable a new class of high temperature fuel cells based on carbon-ion transport. The complete lack of carbon diffusion data for salt-like carbides is the motivation for this work. The carbon diffusion rate in La_0.5Er_0.5C₂ has now been determined to be 2.0 ± 0.8 × 10⁻¹³ cm²/s at 850 °C, increasing to 1.8 ± 0.8 × 10⁻¹¹ cm²/s at 1150 °C, with an activation energy of about 95 kJ/mole. These diffusion rates are too low for a carbon-ion fuel cell, but a number of other salt-like carbides exist. Be₂C, in particular, is a salt-like carbide with an antifluorite structure, and should have higher carbon-ion diffusion than cubic La_0.5Er_0.5C₂ due to the unoccupied octahedral sites in the antifluorite structure, but Be₂C presents special difficulties due to the toxic nature of its hydrolysis products.     

Evidence for selective use of bone scans in early stage breast cancer

To determine the usefulness of bone scans in detecting metastatic disease in women with early stage breast cancer, records of 193 patients who had bone scans preformed and underwent breast conservation therapy at a single institution were reviewed. Patients with invasive T1 or T2 breast carcinomas were eligible for this study; patients with a true positive bone scan were excluded from conservation therapy and, thus, were excluded from this study. The incidence of false positive bone scans in this study population was 32.6% (63/193 patients). Patients over 50 years of age had a significantly greater incidence of false positive bone scans (p<0. 05). In the 63 patients with false positive bone scans, 101 radiographs were performed to exclude metastatic disease in areas of increased uptake identified on bone scan. No significant difference in the rate of false positive bone scans was seen in relation to tumor size, pathologic or clinical nodal status or hormone receptor activity of the primary tumor. Thus, selective use of bone scans is advocated in patients with early stage (T1 or T2) breast cancer.