Gravitation as a Super SL(2,C) Gauge Theory

We present a gauge theory of the super SL(2,C) group. The gauge potential is a connection of the Super SL(2,C) group. A MacDowell-Mansouri type of action is proposed where the action is quadratic in the Super SL(2,C) curvature and depends purely on gauge connection. By breaking the symmetry of the Super SL(2,C) topological gauge theory to SL(2,C), a metric is naturally defined.Comment: 4 pages, Proceedings of the 9th Marcel Grossmann Meeting, Rome, 2-8 July, 200

Quasi-Local "Conserved Quantities"

Using the Noether Charge formulation, we study a perturbation of the conserved gravitating system. By requiring the boundary term in the variation of the Hamiltonian to depend only on the symplectic structure, we propose a general prescription for defining quasi-local ``conserved quantities'' (i.e. in the situation when the gravitating system has a non-vanishing energy flux). Applications include energy-momentum and angular momentum at spatial and null infinity, asymptotically anti-deSitter spacetimes, and thermodynamics of the isolated horizons.Comment: 4 pages, contribution to the proceedings of the 9th Marcel Grossmann Meeting; typos correcte

Numerical analysis of transient combustion response to acoustic oscillations in axisymmetric rocket motors

A numerical analysis of unsteady motions in solid rocket motors with a nozzle has been conducted. The formulation treats the complete conservation equations for the gas phase and the one-dimensional equations in the radial direction for the condensed phase. A fully coupled implicit scheme based on a dual time-stepping integration algorithm has been adopted to solve the governing equations and associated boundary conditions. After obtaining a steady state solution, periodic pressure oscillations are imposed at the head end to simulate acoustic oscillations of a traveling-wave motion in the combustion chamber. The amplitude of the pressure oscillation is 1.0 % of the mean pressure and the frequency is 1790 Hz, corresponding to the twice of the fundamental frequency of the chamber. Magnitude and phase of pressure and axial velocity fluctuations are influenced by the upstream reflecting wave from the nozzle wall. Axial velocity near surface region oscillates in phase advance manner with reference to the acoustic pressure. Large vorticity fluctuations are observed in near surface region. The mass-flow-rate at the nozzle exit periodically oscillates with a time delay compared to the imposed pressure oscillations at the head end

Applications of Various Methods of Analysis to Combustion Instabilities in Solid Propellant Rockets

Instabilities of motions in a combustion chamber are consequences of the coupled dynamics of combustion processes and of the flow in the chamber. The extreme complexities of the problem always require approximations of various sorts to make progress in understanding the mechanisms and behavior of combustion instabilities. This paper covers recent progress in the subject, mainly summarizing efforts in two areas: approximate analysis based on a form of Galerkin's method, particularly useful for understanding the global linear and nonlinear dynamics of combustion instabilities and numerical simulations intended to accommodate as fully as possible fundamental chemical processes in both the condensed and gaseous phases. One purpose of current work is to bring closer together these approaches to produce more comprehensive and detailed realistic results applicable to the interpretation of observations and for design of new rockets for both space and military applications. Particularly important are the goals of determining the connections between chemical composition and instabilities; and the influences of geometry on nonlinear behavior