58,923 research outputs found
Relativistic N-Boson Systems Bound by Oscillator Pair Potentials
We study the lowest energy E of a relativistic system of N identical bosons
bound by harmonic-oscillator pair potentials in three spatial dimensions. In
natural units the system has the semirelativistic ``spinless-Salpeter''
Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N gamma |r_i -
r_j|^2, gamma > 0. We derive the following energy bounds: E(N) = min_{r>0} [N
(m^2 + 2 (N-1) P^2 / (N r^2))^1/2 + N (N-1) gamma r^2 / 2], N \ge 2, where
P=1.376 yields a lower bound and P=3/2 yields an upper bound for all N \ge 2. A
sharper lower bound is given by the function P = P(mu), where mu =
m(N/(gamma(N-1)^2))^(1/3), which makes the formula for E(2) exact: with this
choice of P, the bounds coincide for all N \ge 2 in the Schroedinger limit m
--> infinity.Comment: v2: A scale analysis of P is now included; this leads to revised
energy bounds, which coalesce in the large-m limi
Discrete spectra of semirelativistic Hamiltonians from envelope theory
We analyze the (discrete) spectrum of the semirelativistic
``spinless-Salpeter'' Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), beta > 0,
where V(r) represents an attractive, spherically symmetric potential in three
dimensions. In order to locate the eigenvalues of H, we extend the ``envelope
theory,'' originally formulated only for nonrelativistic Schroedinger
operators, to the case of Hamiltonians H involving the relativistic
kinetic-energy operator. If V(r) is a convex transformation of the Coulomb
potential -1/r and a concave transformation of the harmonic-oscillator
potential r^2, both upper and lower bounds on the discrete eigenvalues of H can
be constructed, which may all be expressed in the form E = min_{r>0} [ \beta
\sqrt{m^2 + P^2/r^2} + V(r) ] for suitable values of the numbers P here
provided. At the critical point, the relative growth to the Coulomb potential
h(r) = -1/r must be bounded by dV/dh < 2 \beta/\pi.Comment: 20 pages, 2 tables, 4 figure
An investigation into the information habits of scientists and engineers in industry
Information center for research and development in industrie
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
Quality-weld parameters for microwelding techniques and equipment
Limited-amplitude, controlled-decay process improves the reliability of microwelding. The system consists in building a capacitor-discharge welder for control of the shape of the weld pulse. Standard welders may be modified
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
Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions
The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case
Standard interest profiles - Development of technical subjects Final report
NASA university program for technology transfer, and development of Standard Interest Profiles /SIP
Materials testing of the IUS techroll seal material
As a part of the investigation of the control system failure Inertial Upper Stage on IUS-1 flight to position a Tracking and Data Relay Satellite (TDRS) in geosynchronous orbit, the materials utilized in the techroll seal are evaluated for possible failure models. Studies undertaken included effect of temperature on the strength of the system, effect of fatigue on the strength of the system, thermogravimetric analysis, thermomechanical analysis, differential scanning calorimeter analysis, dynamic mechanical analysis, and peel test. The most likely failure mode is excessive temperature in the seal. In addition, the seal material is susceptible to fatigue damage which could be a contributing factor
JointZone: users' view of an adaptive online learning resource for rheumatology
This paper describes an online learning resource for rheumatology that was designed for a wide constituency of users including primarily undergraduate medical students and health professionals. Although the online resources afford an informal learning environment, the site was pedagogically designed to comply with the general recommendations of the Standing Committee on Training and Education of EULAR (European League Against Rheumatism) for a rheumatology core curriculum. Any Internet user may freely browse the site content with optional registration providing access to adaptive features that personalize the user’s view, for example, providing a reading history and targeted support based on scores from completed case studies. The site has now been available since early 2003, and an online survey of site registrants indicates that well structured pedagogical materials that reflect a learners’ dominant ‘community of practice’ appear to be a successful aid to informal learning
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