Full wave electromagnetics for simulating high speed quantum well laser diode modulation

A unique discretization scheme that couples Maxwell’s full wave vector field equations self-consistently with nonlinear charge and energy transport is presented. The scheme is used to simulate laser modulation achieved in a simple electrically pumped quantum well laser diode by dynamically heating the degenerate quantum charge gases with high frequency radiation.     

Measurement of total Zn and Zn isotope ratios by quadrupole ICP-MS for evaluation of Zn uptake in gills of brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss)

This study evaluates the potential use of stable zinc isotopes in toxicity studies measuring zinc uptake by the gills of brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss). The use of stable isotopes in such studies has several advantages over the use of radioisotopes, including cost, ease of handling, elimination of permit requirements, and waste disposal. A pilot study using brown trout was performed to evaluate sample preparation methods and the ability of a quadrupole inductively coupled plasma mass spectrometer (ICP-MS) system to successfully measure changes in the ⁶⁷Zn/⁶⁶Zn ratios for planned exposure levels and duration. After completion of the pilot study, a full-scale zinc exposure study using rainbow trout was performed. The results of these studies indicate that there are several factors that affect the precision of the measured ⁶⁷Zn/⁶⁶Zn ratios in the sample digests, including variations in sample size, endogenous zinc levels, and zinc uptake rates by individual fish. However, since these factors were incorporated in the calculation of the total zinc accumulated by the gills during the exposures, the data obtained were adequate for their intended use in calculating zinc binding and evaluating the influences of differences in water quality parameters.     

Tracking the free surface of time-dependent flows: image processing for the dam-break problem

The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the past few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge’s free-surface variations with time, we have developed a new imaging system, consisting of a digital camera coupled with a synchronized micro-mirror projector. The object’s surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 1 mm over a surface of 1.8 × 1.1 m². Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to-date in practical applications.     

Preparation of polybenzoxazole fibers via electrospinning and postspun thermal cyclization of polyhydroxyamide

Polybenzoxazole (PBO) fibers with a submicron diameter were successfully prepared by electrospinning its precursor, polyhydroxyamide (PHA), solutions to obtain the PHA fibers first, followed by appropriate thermal treatments for cyclization reaction. BisAPAF‐IC PHA with two different molecular weights (MWs) were synthesized from a low temperature polymerization of 2,2′‐bis(3‐amino‐4‐hydroxyphenyl) hexafluoropropane (BisAPAF) and isophthaloyl chloride (IC). Using dimethylacetamide (DMAc) and tetrahydrofuran (THF), solvent effects on the electrospinnability of PHA solutions were investigated. For balancing the solution properties, it was found that DMAc/THF mixture with a weight ratio of 1/9 was the best cosolvent to prepare smooth PHA fibers; uniform PHA fibers with a diameter of 325–720 nm were obtained by using 20 wt % PHA/(DMAc/THF) solutions. For a fixed PHA concentration, solutions with a lower MW of PHA yielded thinner electrospun fibers under the same electrospinning condition. After obtaining the electrospun BisAPAF‐IC PHA fibers, subsequent thermal cyclization up to 350 °C produced the corresponding thermally stable BisAPAF‐IC PBO fibers with a diameter of 305–645 nm. The structure of the precursor fibers and the fully cyclized fibers were characterized by FTIR. For the cyclized BisAPAF‐IC PBO fibers, thermogravimetric analysis showed a 5% weight loss temperature at 523 °C in nitrogen atmosphere. The interconnected fiber structure in the BisAPAF‐IC PBO fiber mats was irrelevant to the curing process, but resulted from the jet merging during the whipping process as revealed by the high speed camera images. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 8159–8169, 2008     

Shannon sampling II: Connections to learning theory

We continue our study [S. Smale, D.X. Zhou, Shannon sampling and function reconstruction from point values, Bull. Amer. Math. Soc. 41 (2004) 279–305] of Shannon sampling and function reconstruction. In this paper, the error analysis is improved. Then we show how our approach can be applied to learning theory: a functional analysis framework is presented; dimension independent probability estimates are given not only for the error in the L² spaces, but also for the error in the reproducing kernel Hilbert space where the learning algorithm is performed. Covering number arguments are replaced by estimates of integral operators.