The range of a fleet of aircraft

The problem discussed in this paper is to determine the range of a fleet of n aircraft with fuel capacities g gallons and fuel efficiencies ri gallons per mile (i= 1,..., n). It is assumed that the aircraft may share fuel in flight and that any of the aircraft may be abandoned at any stage. The range is defined to be the greatest distance which can be attained in this way. Initially the fleet is supposed to have g gallons of fuel. A theoretical solution is obtained by the method which Richard Bellman [1] calls dynamic programming. Explicit solutions are obtained in the case of two aircraft with different fuel capacities and fuel efficiencies and in the case of any number of aircraft with identical fuel capacities and identical fuel efficiencies. The problem is similar to the so-called jeep problem. The jeep problem was solved rigorously by N. J. Fine [2]. A solution was also obtained by O. Helmer [3, 4]. Fine cited an unpublished solution by L. Alaoglu. The problem was generalized by C. G. Phipps [5]. Phipps informally developed the special result which is deduced in [section] 4 of this paper

Segmented back-up bar Patent

Segmented back-up bar for butt welding large tubular structures such as rocket booster bodies or tank

Shortcuts to Spherically Symmetric Solutions: A Cautionary Note

Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function ansatz invalidates it, as illustrated by the incorrect solutions of [1].Comment: 2 pages. Amplified derivation, accepted for publication in Class Quant Gra

Plasmas generated by ultra-violet light rather than electron impact

We analyze, in both plane and cylindrical geometries, a collisionless plasma consisting of an inner region where generation occurs by UV illumination, and an un-illuminated outer region with no generation. Ions generated in the inner region flow outwards through the outer region and into a wall. We solve for this system's steady state, first in the quasi-neutral regime (where the Debye length ${\lambda}_D$ vanishes and analytic solutions exist) and then in the general case, which we solve numerically. In the general case a double layer forms where the illuminated and un-illuminated regions meet, and an approximately quasi-neutral plasma connects the double layer to the wall sheath; in plane geometry the ions coast through the quasi-neutral section at slightly more than the Bohm speed $c_s$. The system, although simple, therefore has two novel features: a double layer that does not require counter-streaming ions and electrons, and a quasi-neutral plasma where ions travel in straight lines with at least the Bohm speed. We close with a pr\'{e}cis of our asymptotic solutions of this system, and suggest how our theoretical conclusions might be extended and tested in the laboratory.Comment: 10 pages, 3 figures, accepted by Physics of Plasma

Subtleties on energy calculations in the image method

In this pedagogical work we point out a subtle mistake that can be done by undergraduate or graduate students in the computation of the electrostatic energy of a system containing charges and perfect conductors if they naively use the image method. Specifically, we show that the naive expressions for the electrostatic energy for these systems obtained directly from the image method are wrong by a factor 1/2. We start our discussion with well known examples, namely, point charge-perfectly conducting wall and point charge-perfectly conducting sphere and then proceed to the demonstration of general results, valid for conductors of arbitrary shapes.Comment: 9 pages, 2 figures; Major change in this version: subsection added to Sect.4 (theorem generalization). Minor changes: title replaced; corrections to the English; some explanatory comments adde

Novel clamps align large rocket cases, eliminate back-up bars

Welding clamps, placed inside and outside a rocket case, hold it in proper alignment during tungsten inert gas welding. These metal blocks, connected by a stainless steel band, eliminate the need for backup bars

Meson-like Baryons and the Spin-Orbit Puzzle

I describe a special class of meson-like \Lambda_Q excited states and present evidence supporting the similarity of their spin-independent spectra to those of mesons. I then examine spin-dependent forces in these baryons, showing that predicted effects of spin-orbit forces are small for them for the same reason they are small for the analogous mesons: a fortuitous cancellation between large spin-orbit forces due to one-gluon-exchange and equally large inverted spin-orbit forces due to Thomas precession in the confining potential. In addition to eliminating the baryon spin-orbit puzzle in these states, this solution provides a new perspective on spin-orbit forces in all baryons.Comment: 24 pages, 4 figure

Radio-frequency discharges in Oxygen. Part 1: Modeling

In this series of three papers we present results from a combined experimental and theoretical effort to quantitatively describe capacitively coupled radio-frequency discharges in oxygen. The particle-in-cell Monte-Carlo model on which the theoretical description is based will be described in the present paper. It treats space charge fields and transport processes on an equal footing with the most important plasma-chemical reactions. For given external voltage and pressure, the model determines the electric potential within the discharge and the distribution functions for electrons, negatively charged atomic oxygen, and positively charged molecular oxygen. Previously used scattering and reaction cross section data are critically assessed and in some cases modified. To validate our model, we compare the densities in the bulk of the discharge with experimental data and find good agreement, indicating that essential aspects of an oxygen discharge are captured.Comment: 11 pages, 10 figure