Point interactions in acoustics: one dimensional models

A one dimensional system made up of a compressible fluid and several mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed for different settings of the oscillators array. The dynamical models are formulated in terms of singular perturbations of the decoupled dynamics of the acoustic field and the mechanical oscillators. Detailed spectral properties of the generators of the dynamics are given for each model we consider. In the case of a periodic array of mechanical oscillators it is shown that the energy spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure

Polymer/riblet combination for hydrodynamic skin friction reduction

A process is disclosed for reducing skin friction and inhibiting the effects of liquid turbulence in a system involving the flow of a liquid along the surface of a body, e.g., a marine vehicle. This process includes injecting a drag reducing polymer into the valleys of adjacent, evenly spaced, longitudinal grooves extending along the length of the surface of the body, so that the rate of diffusion of the polymer from individual grooves into the liquid flow is predictably controlled by the groove dimensions. When the polymer has diffused over the tips of the grooves into the near wall region of the boundary layer, the polymer effectively reduces the turbulent skin friction. A substantial drag reducing effect is achieved with less polymer than must be used to lower skin friction when the surface of the body is smooth

Distribution of the very first PopIII stars and their relation to bright z~6 quasars

We discuss the link between dark matter halos hosting the first PopIII stars and the rare, massive, halos that are generally considered to host bright quasars at high redshift z~6. The main question that we intend to answer is whether the super-massive black holes powering these QSOs grew out from the seeds planted by the first intermediate massive black holes created in the universe. This question involves a dynamical range of 10^13 in mass and we address it by combining N-body simulations of structure formation to identify the most massive halos at z~6 with a Monte Carlo method based on linear theory to obtain the location and formation times of the first light halos within the whole simulation box. We show that the descendants of the first ~10^6 Msun virialized halos do not, on average, end up in the most massive halos at z~6, but rather live in a large variety of environments. The oldest PopIII progenitors of the most massive halos at z~6, form instead from density peaks that are on average one and a half standard deviations more common than the first PopIII star formed in the volume occupied by one bright high-z QSO. The intermediate mass black hole seeds planted by the very first PopIII stars at z>40 can easily grow to masses m_BH>10^9.5 Msun by z=6 assuming Eddington accretion with radiative efficiency \epsilon~0.1. Quenching of the black hole accretion is therefore crucial to avoid an overabundance of supermassive black holes at lower redshift. This can be obtained if the mass accretion is limited to a fraction \eta~6*10^{-3} of the total baryon mass of the halo hosting the black hole. The resulting high end slope of the black hole mass function at z=6 is \alpha ~ -3.7, a value within the 1\sigma error bar for the bright end slope of the observed quasar luminosity function at z=6.Comment: 30 pages, 9 figures, ApJ accepte

Hydrodynamic skin-friction reduction

A process for reducing skin friction, inhibiting the effects of liquid turbulence, and decreasing heat transfer in a system involving flow of a liquid along a surface of a body includes applying a substantially integral sheet of a gas, e.g., air, immediately adjacent to the surface of the body; a marine vehicle, which has a longitudinally grooved surface in proximity with the liquid and with a surface material having high contact angle between the liquid and said wall to reduce interaction of the liquid; water, with the surface of the body; and the hull of the marine vehicle

Controllability of spin-boson systems

In this paper we study the so-called spin-boson system, namely {a two-level system} in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes--Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost every value of the interaction parameter

Calibration of transonic and supersonic wind tunnels

State-of-the art instrumentation and procedures for calibrating transonic (0.6 less than M less than 1.4) and supersonic (M less than or equal to 3.5) wind tunnels were reviewed and evaluated. Major emphasis was given to transonic tunnels. Continuous, blowdown and intermittent tunnels were considered. The required measurements of pressure, temperature, flow angularity, noise and humidity were discussed, and the effects of measurement uncertainties were summarized. A comprehensive review of instrumentation currently used to calibrate empty tunnel flow conditions was included. The recent results of relevant research are noted and recommendations for achieving improved data accuracy are made where appropriate. It is concluded, for general testing purposes, that satisfactory calibration measurements can be achieved in both transonic and supersonic tunnels. The goal of calibrating transonic tunnels to within 0.001 in centerline Mach number appears to be feasible with existing instrumentation, provided correct calibration procedures are carefully followed. A comparable accuracy can be achieved off-centerline with carefully designed, conventional probes, except near Mach 1. In the range 0.95 less than M less than 1.05, the laser Doppler velocimeter appears to offer the most promise for improved calibration accuracy off-centerline

On the Ehrenfest theorem of quantum mechanics

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.Comment: To appear in J. Math. Phy

The effects of space radiation on a chemically modified graphite-epoxy composite material

The effects of the space environment on the engineering properties and chemistry of a chemically modified T300/934 graphite-epoxy composite system are characterized. The material was subjected to 1.0 x 10 to the 10th power rads of 1.0 MeV electron irradiation under vacuum to simulate 30 years in geosynchronous earth orbit. Monotonic tension tests were performed at room temperature (75 F/24 C) and elevated temperature (250 F/121 C) on 4-ply unidirectional laminates. From these tests, inplane engineering and strength properties (E sub 1, E sub 2, Nu sub 12, G sub 12, X sub T, Y sub T) were determined. Cyclic tests were also performed to characterize energy dissipation changes due to irradiation and elevated temperature. Large diameter graphite fibers were tested to determine the effects of radiation on their stiffness and strength. No significant changes were observed. Dynamic-mechanical analysis demonstrated that the glass transition temperature was reduced by 50 F(28 C) after irradiation. Thermomechanical analysis showed the occurrence of volatile products generated upon heating of the irradiated material. The chemical modification of the epoxy did not aid in producing a material which was more radiation resistant than the standard T300/934 graphite-epoxy system. Irradiation was found to cause crosslinking and chain scission in the polymer. The latter produced low molecular weight products which plasticize the material at elevated temperatures and cause apparent material stiffening at low stresses at room temperature

Quantum cosmology of scalar-tensor theories and self-adjointness

In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable.Comment: Latex file, 12 pages. Small changes made in the paper, and a a new appendix adde