Simulation of large turbulent structures with the parabolic Navier-Stokes equations

The theoretical basis for well posed marching of a Parabolic Navier-Stokes (PNS) computational technique for supersonic flow is discussed and examples given to verify the analysis. It is demonstrated that stable computations can be made even with very small steps in the marching direction. The method is applied to cones at large angle of attack in high Reynolds number, supersonic flow. Streamline trajectories generated from the numerical solutions demonstrate the development of vortex structures on the lee side of the cone

Superfluid Phase Stability of 3^3He in Axially Anisotropic Aerogel

Measurements of superfluid $^3$He in 98% aerogel demonstrate the existence of a metastable \emph{A}-like phase and a stable \emph{B}-like phase. It has been suggested that the relative stability of these two phases is controlled by anisotropic quasiparticle scattering in the aerogel. Anisotropic scattering produced by axial compression of the aerogel has been predicted to stabilize the axial state of superfluid $^3$He. To explore this possiblity, we used transverse acoustic impedance to map out the phase diagram of superfluid $^3$He in a $\sim 98$% porous silica aerogel subjected to 17% axial compression. We have previously shown that axial anisotropy in aerogel leads to optical birefringence and that optical cross-polarization studies can be used to characterize such anisotropy. Consequently, we have performed optical cross-polarization experiments to verify the presence and uniformity of the axial anisotropy in our aerogel sample. We find that uniform axial anisotropy introduced by 17% compression does not stabilize the \emph{A}-like phase. We also find an increase in the supercooling of the \emph{A}-like phase at lower pressure, indicating a modification to \emph{B}-like phase nucleation in \emph{globally} anisotropic aerogels.Comment: 4 pages, 4 figures, submitted to LT25 (25th International Conference on Low Temperature Physics

Pressures measured in flight on the aft fuselage and external nozzle of a twin-jet fighter

Fuselage, boundary layer, and nozzle pressures were measured in flight for a twin jet fighter over a Mach number range from 0.60 to 2.00 at test altitudes of 6100, 10,700, and 13,700 meters for angles of attack ranging from 0 deg to 7 deg. Test data were analyzed to find the effects of the propulsion system geometry. The flight variables, and flow interference. The aft fuselage flow field was complex and showed the influence of the vertical tail, nacelle contour, and the wing. Changes in the boattail angle of either engine affected upper fuselage and lower fuselage pressure coefficients upstream of the nozzle. Boundary layer profiles at the forward and aft locations on the upper nacelles were relatively insensitive to Mach number and altitude. Boundary layer thickness decreased at both stations as angle of attack increased above 4 deg. Nozzle pressure coefficient was influenced by the vertical tail, horizontal tail boom, and nozzle interfairing; the last two tended to separate flow over the top of the nozzle from flow over the bottom of the nozzle. The left nozzle axial force coefficient was most affected by Mach number and left nozzle boattail angle. At Mach 0.90, the nozzle axial force coefficient was 0.0013

The use of Levy-Lees variables in three-dimensional boundary-layer flows

A method for solving a general class of three-dimensional boundary layer flows is developed. In the development, Levy-Lees variables are extended to three dimensions and equations are placed in these similarity variables. An implicit finite difference scheme which is stable for negative transverse velocities is used to solve these equations. The method developed is applied to obtain solutions for sharp and spherically blunted circular cones at angle of attack. Longitudinal and transverse distributions are presented for these cases. Good agreement is found with the results obtained by other numerical schemes and the experimental data of Tracy, for sharp circular cones at angle of attack. For spherically blunted cones at angle of attack, the results are in good agreement with axisymmetric sphere results up to the region where spherical symmetry holds

Exact Results on the Space of Vacua of Four Dimensional SUSY Gauge Theories

We consider four dimensional quantum field theories which have a continuous manifold of inequivalent exact ground states -- a moduli space of vacua. Classically, the singular points on the moduli space are associated with extra massless particles. Quantum mechanically these singularities can be smoothed out. Alternatively, new massless states appear there. These may be the elementary massless particles or new massless bound states.Comment: 19 pages, RU-94-1

Advanced modulation technology development for earth station demodulator applications

The purpose of this contract was to develop a high rate (200 Mbps), bandwidth efficient, modulation format using low cost hardware, in 1990's technology. The modulation format chosen is 16-ary continuous phase frequency shift keying (CPFSK). The implementation of the modulation format uses a unique combination of a limiter/discriminator followed by an accumulator to determine transmitted phase. An important feature of the modulation scheme is the way coding is applied to efficiently gain back the performance lost by the close spacing of the phase points

Precision measurements of the zero temperature dielectric constant and density of liquid 4^4He

The resonant frequencies of three-dimensional microwave cavities are explicitly dependent on the dielectric constant of the material filling the cavity, making them an ideal system for probing material properties. In particular, dielectric constant measurements allow one to extract the helium density through the Clausius-Mossotti relation. By filling a cylindrical aluminum cavity with superfluid helium, we make precision measurements of the dielectric constant of liquid $^4$He at saturated vapor pressure for range of temperatures 30 -- 300 mK and at pressures of 0-25.0 bar at 30 mK, essentially the zero temperature limit for the properties of $^4$He. After reviewing previous measurements, we find systematic discrepancy between low and high frequency determination of the dielectric constant in the zero-temperature limit and moderate discrepancy with previously reported values of pressure-dependent density. Our precision measurements suggest 3D microwave cavities are a promising choice for refining previously measured values in helium, with potential applications in metrology.Comment: 10 pages, 9 figure

Darboux Transformations, Infinitesimal Symmetries and Conservation Laws for Nonlocal Two-Dimensional Toda Lattice

The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The connections between the solutions of overdetermined linear systems and their expansions in series at singular points neighborhood are presented. The solutions of the nonlocal Toda lattice and infinite hierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde

Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

The new physics of non-equilibrium condensates: insights from classical dynamics

We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an undamped model which show spontaneous coherent states with persistent oscillations in the magnitude of the order parameter. These states are generalisations of superradiant ringing to the case of inhomogeneous broadening. They correspond to the persistent gap oscillations proposed in fermionic atomic condensates, and arise from a variety of initial conditions. We show that introducing randomness into the couplings can suppress the oscillations, leading to a limiting dynamics with a time-independent order parameter. This demonstrates that non-equilibrium generalisations of polariton condensates can be created even without dissipation. We explain the dynamical origins of the coherence in terms of instabilities of the normal state, and consider how it can additionally develop through scattering and dissipation.Comment: 10 pages, 4 figures, submitted for a special issue of J. Phys.: Condensed Matter on "Optical coherence and collective phenomena in nanostructures". v2: added discussion of links to exact solution