65,458 research outputs found
Limits of space-times in five dimensions and their relation to the Segre Types
A limiting diagram for the Segre classification in 5-dimensional space-times
is obtained, extending a recent work on limits of the energy-momentum tensor in
general relativity. Some of Geroch's results on limits of space-times in
general relativity are also extended to the context of five-dimensional
Kaluza-Klein space-times.Comment: Late
Apparatus for measuring electric field strength on the surface of a model vehicle Patent
Space environment simulation system for measuring spacecraft electric field strength in plasma sheat
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
Limits of the energy-momentum tensor in general relativity
A limiting diagram for the Segre classification of the energy-momentum tensor
is obtained and discussed in connection with a Penrose specialization diagram
for the Segre types. A generalization of the coordinate-free approach to limits
of Paiva et al. to include non-vacuum space-times is made. Geroch's work on
limits of space-times is also extended. The same argument also justifies part
of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page
Evaluation of the micro-carburetor
A prototype sonic, variable-venturi automotive carburetor was evaluated for its effects on vehicle performance, fuel economy, and exhaust emissions. A 350 CID Chevrolet Impala vehicle was tested on a chassis dynamometer over the 1975 Federal Test Procedure, urban driving cycle. The Micro-carburetor was tested and compared with stock and modified-stock engine configurations. Subsequently, the test vehicle's performance characteristics were examined with the stock carburetor and again with the Micro-carburetor in a series of on-road driveability tests. The test engine was then removed from the vehicle and installed on an engine dynamometer. Engine tests were conducted to compare the fuel economy, thermal efficiency, and cylinder-to-cylinder mixture distribution of the Micro-carburetor to that of the stock configuration. Test results show increases in thermal efficiency and improvements in fuel economy at all test conditions. Improve fuel/air mixture preparation is implied from the information presented. Further improvements in fuel economy and exhaust emissions are possible through a detailed recalibration of the Micro-carburetor
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
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
Investigation of plane-strain flaw growth in thick-walled tanks Final report, 26 Jun. 1964 - 26 Oct. 1965
Flaw growth rates and fracture toughness data for materials used in thick walled cylindrical tank
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