Cryogenic wind tunnels: Unique capabilities for the aerodynamicist

The cryogenic wind-tunnel concept as a practical means for improving ground simulation of transonic flight conditions. The Langley 1/3-meter transonic cryogenic tunnel is operational, and the design of a cryogenic National Transonic Facility is undertaken. A review of some of the unique capabilities of cryogenic wind tunnels is presented. In particular, the advantages of having independent control of tunnel Mach number, total pressure, and total temperature are highlighted. This separate control over the three tunnel parameters will open new frontiers in Mach number, Reynolds number, aeroelastic, and model-tunnel interaction studies

Onset of condensation effects as detected by total pressure probes in the Langley 0.3-meter transonic cryogenic tunnel

Total pressure probes mounted in the test section of a 0.3 meter transonic cryogenic tunnel were used to detect the onset of condensation effects for free stream Mach numbers of 0.50, 0.75, 0.85, and 0.95 and for total pressure between one and five atmospheres. The amount of supercooling was found to be about 3 K and suggests that condensation was occurring on pre-existing liquid nitrogen droplets resulting from incomplete evaporation of the liquid nitrogen injected to cool the tunnel. The liquid nitrogen injection process presently being used for the 0.3 m tunnel was found to result in a wide spectrum of droplet sizes being injected into the flow. Since the relatively larger droplets took much more time to evaporate than the more numerous smaller droplets, the larger ones reached the test section first as the tunnel operating temperature was reduced. However, condensation effects in the test section were not immediately measurable because there was not a sufficient number of the larger droplets to have an influence on the thermodynamics of the flow

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Energy bounds for the spinless Salpeter equation: harmonic oscillator

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + \beta\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.Comment: 8 pages, 1 figur

A Physical Axiomatic Approach to Schrodinger's Equation

The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular its linearity, in intuitive terms. Furthermore it allows for a physically motivated and systematic investigation of potential generalisations which are briefly discussed.Comment: Extended version. 14 page

Floating substrate process: Large-area silicon sheet task low-cost solar array project

Supercooling of silicon-tin alloy melts was studied. Values as high as 78 C at 1100 C and 39 C at 1200 C were observed, corresponding to supersaturation parameter values 0.025 and 0.053 at 1050 C and 1150 C, respectively. The interaction of tin with silane gas streams was investigated over the temperature range 1000 to 1200 C. Single-pass conversion efficiencies exceeding 30% were obtained. The growth habit of spontaneously-nucleated surface growth was determined to be consistent with dendritic and web growth from singly-twinned triangular nucleii. Surface growth of interlocking silicon crystals, thin enough to follow the surface of the liquid and with growth velocity as high as 5 mm/min, was obtained. Large area single-crystal growth along the melt surface was not achieved. Small single-crystal surface growth was obtained which did not propagate beyond a few millimeters

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

A Bohmian approach to quantum fractals

A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and other trajectory--based approaches) in providing a complete interpretation of quantum mechanics. Here, this assertion is overcome by means of a formal extension of Bohmian mechanics based on a limiting approach. Within this novel formulation, the particle dynamics is always satisfactorily described by a well defined equation of motion. In particular, in the case of guidance under quantum fractals, the corresponding trajectories will also be fractal.Comment: 19 pages, 3 figures (revised version