A simple theoretical description of the behaviour of intumescent paints

A simple theoretical description is given of the behaviour of a layer of intumescent paint under the action of a constant heat input at one surface. The physical model of Buckmaster, Anderson and Nachman is used and several new results are derived. In particular a relationship is derived between the tune it takes for the temperature at the inner surface of the layer to rise to a given value and the parameters characterising the layer of paint. Other results depend upon the assumption that the front at which intumenscence takes place moves through the layer slowly compared with decay tunes of thermal transients within the layer

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

Redundant data management system

Redundant data management system solves problem of operating redundant equipment in real time environment where failures are detected, isolated, and switched in simple manner. System consists of quadruply-redundant computer, input/output control units, and data buses. System inherently contains failure detection, isolation, and switching function

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

Convexity and potential sums for Salpeter-like Hamiltonians

The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r) is a central potential in R^3, is concave in p^2 and convex in p. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By extending the notion of 'kinetic potential' we are able to find general energy bounds on the ground-state energy E corresponding to potentials with the form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 + 1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower' P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some specific examples are discussed, to show the quality of the bounds.Comment: 21 pages, 4 figure

A. Paul Sigurd\u27s Decision

In lieu of an abstract, below is the essay\u27s first paragraph. Well, son, I don\u27t think anyone really knew how he got it. Some said it was always his and that he was always there. Yet others said that he inherited it from his father. And many be1ieved that it was given to him by an impulsive woman - the Hester Prynne type - who, being in dire straits, had to get rid of it. A few even said that he built it himself when lie was a young man. Me? I never cared how he got it; the fact was that he had it and he was there. But I must confess I always wondered why, I mean with no boats coming into the harbor anymore. And did you know that he used to paint it white every spring? And that he used to put the light on every night? Every night it could be seen from the mainland. Going around and around and around. But why? No boats had come into the harbor for nearly twenty years

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

Guidance for an aeroassisted orbital transfer vehicle

The use of atmospheric drag for slowing satellite in high energy, high apogee orbits to a lower energy, lower apogee orbit about the Earth is investigated. The high energy orbit is assumed to intercept the Earth's atmosphere. Guidance for the atmospheric phase of the trajectory may be done using the aerodynamic forces generated by the passage through the atmosphere. This research was concerned with the investigation of several methods of guidance during the atmospheric phase to cause a significant reduction in the final velocity as the vehicle leaves the atmosphere. In addition, the velocity direction was controlled to exit to a desired target orbit. Lastly excess aerodynamic lift was used to effect a plane change between the entry orbit plane and the exit orbit plane to achieve a desired orbit plane. The guidance methods were applied to a 3 degree-of-freedom simulation which included an oblate Earth gravity model and a rotating atmosphere. Simulation results were compared on the basis of speed of computation of the guidance parameters and amount of added velocity necessary to achieve the desired orbit

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

Hydrogen-fueled postal vehicle performance evaluation

Fuel consumption, range, and emissions data were obtained while operating a hydrogen-fueled postal delivery vehicle over a defined Postal Service Driving Cycle and the 1975 Urban Driving Cycle. The vehicle's fuel consumption was 0.366 pounds of hydrogen per mile over the postal driving cycle and 0.22 pounds of hydrogen per mile over the urban driving cycle. These data correspond to 6.2 and 10.6 mpg equivalent gasoline mileage for the two driving cycles, respectively. The vehicle's range was 24.2 miles while being operated on the postal driving cycle. Vehicle emissions were measured over the urban driving cycle. HC and CO emissions were quite low, as would be expected. The oxides of nitrogen were found to be 4.86 gm/mi, a value which is well above the current Federal and California standards. Vehicle limitations discussed include excessive engine flashbacks, inadequate acceleration capability the engine air/fuel ratio, the water injection systems, and the cab temperature. Other concerns are safety considerations, iron-titanium hydride observed in the fuel system, evidence of water in the engine rocker cover, and the vehicle maintenance required during the evaluation