Supersymmetric Polytropic Gas Dynamics

We construct the N=1 supersymmetric extension of the polytropic gas dynamics. We give both the Lagrangian as well as the Hamiltonian description of this system. We construct the infinite set of "Eulerian'' conserved charges associated with this system and show that they are in involution, thereby proving complete integrability of this system. We construct the SUSY -B extension of this system as well and comment on the similarities and differences between this system and an earlier construction of the supersymmetric Chaplygin gas. We also derive the N=1 supersymmetric extension of the elastic medium equations, which, however, do not appear to be integrable.Comment: 15 page

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density $\to\infty$). Our estimates allow us to interchange the thermodynamic with the mean-field limit.Comment: 27 pages, typos corrected, a few more explanations adde

Fluid and gas dynamics

A clearer understanding of the interactions of the hot gas flow with the structure in the duct system, the flow passages of the rotating machinery, and the thrust chamber nozzle is sought for the purpose of finding ways and means to increase the life and performance of the systems. The objective of the transient nozzle test is to understand the shock-boundary layer interactions during transient flow and the resulting large side forces acting on the nozzle skirt. The Fluctuating Pressures in Ducts study deals mainly with the fluid-structural interactions of the lox post tube banks in the injector. The Ablative Nozzle Insert Study (H4) has as its goal the performance improvement of the space shuttle main engine