Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent

CREKID: A computer code for transient, gas-phase combustion of kinetics

A new algorithm was developed for fast, automatic integration of chemical kinetic rate equations describing homogeneous, gas-phase combustion at constant pressure. Particular attention is paid to the distinguishing physical and computational characteristics of the induction, heat-release and equilibration regimes. The two-part predictor-corrector algorithm, based on an exponentially-fitted trapezoidal rule, includes filtering of ill-posed initial conditions, automatic selection of Newton-Jacobi or Newton iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm was found to compare favorably with LSODE on two representative test problems drawn from combustion kinetics

Post-flight analyses of the crystals from the M0003-14 quartz crystal microbalance experiment

Quartz Crystal Microbalances constructed by QCM Research were flown on the leading and trailing edges of LDEF as one of the sub-experiments of M0003. Response of the crystals coated with 150 A of In2O3 was recorded during the first 424 days of the mission. A second QCM with crystals coated with 150 A of ZnS was also flown but not monitored. After the flight, the QCM's were disassembled and analyzed in The Aerospace Corporation laboratories. The samples included the crystals from the leading and trailing edge samples of both types of coatings along with the reference crystals, which were inside the QCM housing. Analyses were performed by scanning electron microscopy, energy dispersive x-ray analyses, x-ray photoelectron spectroscopy, ion microprobe mass analysis, and reflectance spectroscopy in the infrared and UV/visible regions. The crystals are contaminated predominantly with silicone compounds. The contamination is higher on the leading edge than on the trailing edge and higher on the exposed crystals than on the reference crystals

The ASCA Spectrum of the Vela Pulsar Jet

ROSAT observations of the Vela pulsar and its surroundings revealed a collimated X-ray feature almost 45' in length (Markwardt & Ogelman 1995), interpreted as the signature ``cocoon'' of a one-sided jet from the Vela pulsar. We report on a new ASCA observation of the Vela pulsar jet at its head, the point where the jet is believed to interact with the supernova remnant. The head is clearly detected, and its X-ray spectrum is remarkably similar to the surrounding supernova remnant spectrum, extending to X-ray energies of at least 7 keV. A ROSAT+ASCA spectrum can be fit by two-component emission models but not standard one-component models. The lower energy component is thermal and has a temperature of 0.29+/-0.03 keV (1 sigma); the higher energy component can be fit by either a thermal component of temperature ~4 keV or a power law with photon index ~2.0. Compared to the ROSAT-only results, the mechanical properties of the jet and its cocoon do not change much. If the observed spectrum is that of a hot jet cocoon, then the speed of the jet is at least 800 km s^-1, depending on the angle of inclination. The mechanical power driving the jet is >10^36 erg s^-1, and the mass flow rate at the head is > 10^-6 M_sun yr^-1. We conclude that the jet must be entraining material all along its length in order to generate such a large mass flow rate. We also explore the possibility that the cocoon emission is synchrotron radiation instead of thermal.Comment: 12 pages, LaTeX in AAS v4.0 preprint style, two PS figures, accepted for publication in the ApJ Letter

Pulsar Radio Emission Altitude from Curvature Radiation

We assume that the relativistic sources moving along the dipolar magnetic field lines emit curvature radiation. The beamed emission occurs in the direction of tangents to the field lines, and to receive it, the sight line must align with the tangent within the beaming angle 1/gamma, where gamma is the particle Lorentz factor. By solving the viewing geometry in an inclined and rotating dipole magnetic field, we show that, at any given pulse phase, observer tends to receive radiation only from the specific heights allowed by the geometry. We find outer conal components are emitted at higher altitudes compared to inner components including the core. At any pulse phase, low frequency emission comes from higher altitudes than high frequency emission. We have modeled the emission heights of pulse components of PSR B0329+54, and estimated field line curvature radii and particle Lorentz factors in the emission regions.Comment: 14 pages, 3 figures. Accepted for Astrophysical Journal, 200

The Sasa-Satsuma higher order nonlinear Schrodinger equation and its bilinearization and multi-soliton solutions

Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton solutions. Unfortunately the construction of multi-soliton solutions to this equation presents difficulties due to its complicated bilinearization. We discuss briefly some previous attempts and then give the correct bilinearization based on the interpretation of the Sasa-Satsuma equation as a reduction of the three-component Kadomtsev-Petvishvili hierarchy. In the process we also get bilinearizations and multi-soliton formulae for a two component generalization of the Sasa-Satsuma equation (the Yajima-Oikawa-Tasgal-Potasek model), and for a (2+1)-dimensional generalization.Comment: 13 pages in RevTex, added reference

On the Origin of the Wide HI Absorption Line Toward Sgr A*

We have imaged a region of about 5' extent surrounding Sgr A* in the HI 21 cm-line absorption using the Very Large Array. A Gaussian decomposition of the optical depth spectra at positions within about 2' (approx. 5 pc at 8.5 kpc) of Sgr A* detects a wide line underlying the many narrow absorption lines. The wide line has a mean peak optical depth of 0.32 +/- 0.12 centered at a mean velocity of V(lsr) = -4 +/- 15 km/s. The mean full width at half maximum is 119 +/- 42 km/s. Such a wide line is absent in the spectra at positions beyond about 2' from Sgr A*. The position-velocity diagrams in optical depth reveal that the wide line originates in various components of the circumnuclear disk (radius approx. 1.3') surrounding Sgr A*. These components contribute to the optical depth of the wide line in different velocity ranges. The position-velocity diagrams do not reveal any diffuse feature which could be attributed to a large number of HI clouds along the line of sight to Sgr A*. Consequently, the wide line has no implications either to a global population of shocked HI clouds in the Galaxy or to the energetics of the interstellar medium as was earlier thought.Comment: LaTeX, 12 pages and 9 figures, accepted for publication in J. Astrophys. Ast

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