Application of the ray tracing method in studying tracks in SSNTDs

The ray tracing method was applied to study etched tracks from α-particles in CR-39 solid-state nuclear track detectors. The transmission mode of a microscope operation was simulated. A track was considered as a set of small triangular elements, and the brightness of all elements was calculated systematically through the entire track to create the final image. Preliminary results are given for α-particle tracks in the CR-39 detector for initial energies of 4 and 4.5 MeV, and incident angles of 40 and 90°, respectively. Total reflection, as well as the slope of a surface element in the track wall, were identified as the main factors that affect the brightness of that element. At this stage, comparisons with experimental results can be made in terms of the average grey levels for the entire tracks.     

A combined OH/acetone planar laser-induced fluorescence imaging technique for visualizing combusting flows

A combined OH/acetone planar laser-induced fluorescence (PLIF) imaging technique that provides simultaneous visualizations of regions of unburned fuel and of combustion in a reacting flow is described. OH marks the location of chemical reaction and of combustion products, and acetone vapor, which is seeded into the fuel stream, marks unburned fuel. A single pulse from an ultraviolet laser is used to simultaneously excite both the OH and acetone, and the fluorescence from each is detected on separate cameras. Acetone spectroscopy and chemistry are reviewed to provide a basis for interpreting acetone fluorescence signals in high-temperature combusting environments. The imaging technique is applied to two nonpremixed turbulent reacting flows to assess the utility of the technique for visualizing the instantaneous flow structure and to illustrate the dependence of the interpretation of the acetone PLIF images on the flow conditions.Support was provided for this work by the Air Force Office of Scientific Research, Aerospace Sciences Directorate, with Julian Tishkoff as Technical Monitor, and is gratefully acknowledged. The contributions of Mr. T. C. Island in operating the supersonic flow facility are also greatly appreciated.     

Computer-aided heuristic analysis of fluid models

A new kind of symbolic program to aid the heuristic simplification of fluid models is presented. The program, AOM, employs order of magnitude analysis and method of dominant balance to generate simplified models. It has two novel features: (1) it uses heuristic techniques to decide what equations to solve and what algebra to do, and (2) it explains its deduction steps. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i.e., terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels to simplify complicated fluid models such as the triple-deck equations. Three annotated examples are presented to explain the operations of AOM. The implications for the development of computer-aided analysis programs for fluid dynamics and education are discussed.This research was funded in part by NSF NYI Award ECS-9357773 and CCR-9109567.     

An improved optical TE-TM mode splitter and modulator using a Ti-LiNbO3 Y-junction waveguide

An optical TE-TM mode splitter and modulator with an improved design using a Y-junction waveguide by Ti-diffusion in a Y-cut LiNbO₃ substrate has been fabricated and characterized. Improvements in fabrication and measurement techniques are discussed. Experimental results on the device characteristics are presented.     

Congruence and Conjunctivity of Matrices

Congruence of arbitrary square matrices over an arbitrary field is treated here by elementary classical methods, and likewise for conjunctivity of arbitrary square matrices over an arbitrary field with involution. Uniqueness results are emphasized, since they are largely neglected in the literature. In particular, it is shown that a matrix S is congruent [conjunctive] to S₀⊕S₁ with S₁ nonsingular, and that if S₁ here is of maximal size among all nonsingular matrices R₁ for which R₀⊕R₁ is congruent [conjunctive] to S, then the congruence [conjunctivity] class of S determines that of S₁. Partially canonical forms (most of them already known) are derived, to the extent that they do not depend on the field. Nearly canonical forms are derived for “neutral” matrices (those congruent or conjunctive with block matrices $\text{O}\text{N}\text{M}\text{O}$ with the two zero blocks being square). For a neutral matrix S over a field F,the F-congruence [F-conjunctivity] class of S is determined by the F-equivalence class of the pencil S+tS' [S+tS¹] and, if the pencil is nonsingular, by the F[t]-equivalence class of S+tS' [S+tS¹].