Higher Order Graviton Scattering in M(atrix) Theory

In matrix theory the effective action for graviton-graviton scattering is a double expansion in the relative velocity and inverse separation. We discuss the systematics of this expansion and subject matrix theory to a new test. Low energy supergravity predicts the coefficient of the $v^6/r^{14}$ term, a two-loop effect, in agreement with explicit matrix model calculation.Comment: 15 pages, 1 epsf figure, LaTeX. Minor change

Exact solution for the Green's function describing time-dependent thermal Comptonization

We obtain an exact, closed-form expression for the time-dependent Green's function solution to the Kompaneets equation. The result, which is expressed as the integral of a product of two Whittaker functions, describes the evolution in energy space of a photon distribution that is initially monoenergetic. Effects of spatial transport within a homogeneous scattering cloud are also included within the formalism. The Kompaneets equation that we solve includes both the recoil and energy diffusion terms, and therefore our solution for the Green's function approaches the Wien spectrum at large times. We show that the Green's function can be used to generate all of the previously known steady-state and time-dependent solutions to the Kompaneets equation. The new solution allows the direct determination of the spectrum, without the need to numerically solve the partial differential equation. Based upon the Green's function, we obtain a new time-dependent solution for the photon distribution resulting from the reprocessing of an optically thin bremsstrahlung initial spectrum with a low-energy cutoff. The new bremsstrahlung solution possesses a finite photon number density, and therefore it displays proper equilibration to a Wien spectrum at large times. The relevance of our results for the interpretation of emission from variable X-ray sources is discussed, with particular attention to the production of hard X-ray time lags, and the Compton broadening of narrow features such as iron lines.Comment: text plus 9 figures, MNRAS 2003, in pres

Photoelectric energy spectrometer Patent

Spectrometer using photoelectric effect to obtain spectral dat

Analysis of solar panel effect on louver performance

Mathematical analysis of solar panel effect on temperature control of spacecraft in solar heat environmen

On the integration of products of Whittaker functions with respect to the second index

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is permitted to have any complex value, within certain restrictions required for convergence. The method utilizes complex contour integration along with various symmetry relations satisfied by the Whittaker functions. The new results derived in this paper are complementary to the previously known integrals of products of Whittaker functions, which generally treat integration with respect to either the first index or the primary argument. A physical application involving radiative transport is discussed.Comment: Accepted for publication in the Journal of Mathematical Physic