The Formal Underpinnings of the Response Functions used in X-Ray Spectral Analysis

This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data where they may be identified with the quantities contained in the Ancillary Response File (ARF), the Redistribution Matrix File (RMF), and the Exposure Map. Starting from first-principles, explicit mathematical expressions for these functions, for both imaging and dispersive modes, are arrived at in terms of the underlying instrumental characteristics of the telescope including the effects of pointing motion. The response functions are presented in the context of integral equations relating the expected detector count rate to the source spectrum incident upon the telescope. Their application to the analysis of several source distributions is considered. These include multiple, possibly overlapping, and spectrally distinct point sources, as well as extended sources. Assumptions and limitations behind the usage of these functions, as well as their practical computation are addressed.Comment: 22 pages, 3 figures (LaTeX

The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity Theory

The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit $a(t)\to 0$. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the $a\to 0$ limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.Comment: Tex, 13 page

Effective Hamiltonian Approach to the Master Equation

A method of exactly solving the master equation is presented in this letter. The explicit form of the solution is determined by the time evolution of a composite system including an auxiliary system and the open system in question. The effective Hamiltonian governing the time evolution of the composed system are derived from the master equation. Two examples, the dissipative two-level system and the damped harmonic oscillator, are presented to illustrate the solving procedure. PACS number(s): 05.30.-d, 05.40.+j, 42.50.CtComment: 4 pages, no figure

The surgery obstruction groups of the infinite dihedral group

This paper computes the quadratic Witt groups (the Wall L-groups) of the polynomial ring Z[t] and the integral group ring of the infinite dihedral group, with various involutions. We show that some of these groups are infinite direct sums of cyclic groups of order 2 and 4. The techniques used are quadratic linking forms over Z[t] and Arf invariants.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper29.abs.htm

Energy-Conserving Lattice Boltzmann Thermal Model in Two Dimensions

A discrete velocity model is presented for lattice Boltzmann thermal fluid dynamics. This model is implemented and tested in two dimensions with a finite difference scheme. Comparison with analytical solutions shows an excellent agreement even for wide temperature differences. An alternative approximate approach is then presented for traditional lattice transport schemes

Geostatistical analysis of an experimental stratigraphy

[1] A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln( K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln( K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/ floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process - dependent and problem-scale-dependent