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

Investigating the hard X-ray emission from the hottest Abell cluster A2163 with Suzaku

We present the results from Suzaku observations of the hottest Abell galaxy cluster A2163 at $z=0.2$. To study the physics of gas heating in cluster mergers, we investigated hard X-ray emission from the merging cluster A2163, which hosts the brightest synchrotron radio halo. We analyzed hard X-ray spectra accumulated from two-pointed Suzaku observations. Non-thermal hard X-ray emission should result from the inverse Compton (IC) scattering of relativistic electrons by the CMB photons. To measure this emission, the dominant thermal emission in the hard X-ray band must be modeled in detail. To this end, we analyzed the combined broad-band X-ray data of A2163 collected by Suzaku and XMM-Newton, assuming single- and multi-temperature models for thermal emission and the power-law model for non-thermal emission. From the Suzaku data, we detected significant hard X-ray emission from A2163 in the 12-60 keV band at the $28\sigma$ level (or at the $5.5\sigma$ level if a systematic error is considered). The Suzaku HXD spectrum alone is consistent with the single-T thermal model of gas temperature $kT=14$ keV. From the XMM data, we constructed a multi-T model including a very hot ($kT=18$ keV) component in the NE region. Incorporating the multi-T and the power-law models into a two-component model with a radio-band photon index, the 12-60 keV energy flux of non-thermal emission is constrained within $5.3 \pm 0.9 (\pm 3.8)\times 10^{-12}~{\rm erg\, s^{-1} cm^{-2}}$. The 90% upper limit of detected IC emission is marginal ($< 1.2\times 10^{-11}~{\rm erg\, s^{-1} cm^{-2}}$ in the 12-60 keV). The estimated magnetic field in A2163 is $B > 0.098~{\rm \mu G}$. While the present results represent a three-fold increase in the accuracy of the broad band spectral model of A2163, more sensitive hard X-ray observations are needed to decisively test for the presence of hard X-ray emission due to IC emission.Comment: 7 pages, 7 figures, A&A accepted. Minor correctio

A coalescence/dispersion model for turbulent flame stability

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77010/1/AIAA-1982-1158-855.pd

The Quark-Gluon Plasma in a Finite Volume

The statistical mechanics of quarks and gluons are investigated within the context of the canonical ensemble. Recursive techniques are developed which enforce the exact conservation of baryon number, total isospin, electric charge, strangeness, and color. Bose and Fermi-Dirac statistics are also accounted for to all orders. The energy, entropy and particle number densities are shown to be significantly reduced for volumes less than 5 cubic fm.Comment: 8 pages, 3 figure

An XMM-Newton observation of the nova-like variable UX UMa: spatially and spectrally resolved two-component X-ray emission

In the optical and ultraviolet regions of the electromagnetic spectrum, UX Ursae Majoris is a deeply eclipsing cataclysmic variable. However, no soft X-ray eclipse was detected in ROSAT observations. We have obtained a 38 ksec XMM-Newton observation to further constrain the origin of the X-rays. The combination of spectral and timing information allows us to identify two components in the X-ray emission of the system. The soft component, dominant below photon energies of 2 keV, can be fitted with a multi-temperature plasma model and is uneclipsed. The hard component, dominant above 3 keV, can be fitted with a kT ~ 5 keV plasma model and appears to be deeply eclipsed. We suggest that the most likely source of the hard X-ray emission in UX UMa, and other systems in high mass transfer states, is the boundary layer.Comment: To appear in MNRAS Letter

Canonical and Microcanonical Distributions for Fermi Systems

Recursion relations are presented that allow exact calculation of canonical and microcanonical partition functions of degenerate Fermi systems, assuming no explicit two-body interactions. Calculations of the level density, sorted by angular momentum, are presented for Ni-56 are presented. The issue of treating unbound states is also addressed.Comment: 5 pages, 5 figure

Isospin Fluctuations from a Thermally Equilibrated Hadron Gas

Partition functions, multiplicity distributions, and isospin fluctuations are calculated for canonical ensembles in which additive quantum numbers as well as total isospin are strictly conserved. When properly accounting for Bose-Einstein symmetrization, the multiplicity distributions of neutral pions in a pion gas are significantly broader as compared to the non-degenerate case. Inclusion of resonances compensates for this broadening effect. Recursion relations are derived which allow calculation of exact results with modest computer time.Comment: 10 pages, 5 figure

Structural tailoring of engine blades (STAEBL)

A mathematical optimization procedure was developed for the structural tailoring of engine blades and was used to structurally tailor two engine fan blades constructed of composite materials without midspan shrouds. The first was a solid blade made from superhybrid composites, and the second was a hollow blade with metal matrix composite inlays. Three major computerized functions were needed to complete the procedure: approximate analysis with the established input variables, optimization of an objective function, and refined analysis for design verification