An investigation of cotton for parachute cloth

This is a resume of the work of the Bureau of Standards on a cotton parachute cloth for use as a substitute for silk in the event of an emergency curtailing the supply. Cotton yarn of high strength in proportion to its weight and otherwise specially suitable for parachute cloth was developed. Cloth woven from this yarn in the bureau mill was equal or superior to parachute silk in strength and tear resistance, met the requirements with respect to air permeability, and weighed only a few tenths of an ounce per square yard more than the silk cloth. Practical trials of cotton parachutes carried out by the Navy Department clearly indicate that the cotton parachute closely approaches the silk parachute in performance as to rate of descent, opening time, strength and ability to function when stored in the pack for sixty days. The increase in weight of the equipment resulting from the use of cotton cloth instead of silk is considered to be well within practicable limits. A specification for cotton parachute cloth and the way in which the requirements of the specification have been met are given. Cotton yarns suitable for parachute cloth are now being woven commercially in the United States

Development of a scanning acousto-optic based differential intensity and phase system for optical metrology

An optical technique is described which simultaneously and independently measures the difference in intensity and phase of light reflected from two close areas on a sample surface. Line scans or images of the object are then formed by scanning the light across the surface. The key element is a Bragg cell which is used to divide a well collimated beam of light into two probing beams amplitude modulated in phase quadrature, with a relative frequency shift. A comprehensive review is given of current profilometry techniques, and in particular optical methods. Emphasis is given in developing a thorough description of the system. Analysis of the acousto-optic interaction is combined within a mathematical framework which gives a general description of how the differential phase and intensity responses depend on the form of the modulated electrical Bragg cell drive. The analysis is applied to determine the tolerances necessary in the construction of this type of system. The use of a scanning mirror in a differential phase system is discussed and analysis is presented to model the effects of lens aberrations. Three implementations of the technique have been built and experimental results are shown from prepared specimens which have, i) predominantly phase contrast - a silicon wafer which has had a series of parallel tracks etched, ranging in depth from 180 to 700Å; ii) predominantly intensity contrast - a silicon wafer half implanted with As+ ions; iii) a mixture of phase and intensity information - a deposited aluminium step on a silicon substrate. Unlike any previous method, this system can measure true differential phase and intensity simultaneously. The real advantage of this is clearly demonstrated in the case of the third specimen where there is a change in surface conductivity across the sample. The two measurements may then help resolve uncertainties present in interpreting topography from phase data

Are all things created equal? The incidental in archaeology

Archaeologists evince a strong tendency to impute significance to the material traces they study, a propensity that has been especially marked since the post-processual emphasis on meaning and that has taken on renewed vigour with the turn to materiality. But are there not situations in which things are rather incidental or insignificant? This set of essays emerged from a workshop held in Berlin in April 2018, in which a group of scholars was invited to discuss the place of the incidental in social life in general and in archaeology in particular. Rather than lengthy formal papers, we offer an introduction that presents a general set of reflections on the issue of the incidentalness of things, followed by essays that pursue particular directions raised by that introduction as well as our discussions in Berlin. It is our hope that these brief forays into a complex topic will stimulate further work on this subject

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Since the proof of the four color theorem in 1976, computer-generated proofs have become a reality in mathematics and computer science. During the last decade, we have seen formal proofs using verified proof assistants being used to verify the validity of such proofs. In this paper, we describe a formalized theory of size-optimal sorting networks. From this formalization we extract a certified checker that successfully verifies computer-generated proofs of optimality on up to 8 inputs. The checker relies on an untrusted oracle to shortcut the search for witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c

Photons as quasi-charged particles

The Schrodinger motion of a charged quantum particle in an electromagnetic potential can be simulated by the paraxial dynamics of photons propagating through a spatially inhomogeneous medium. The inhomogeneity induces geometric effects that generate an artificial vector potential to which signal photons are coupled. This phenomenon can be implemented with slow light propagating through an a gas of double-Lambda atoms in an electromagnetically-induced transparency setting with spatially varied control fields. It can lead to a reduced dispersion of signal photons and a topological phase shift of Aharonov-Bohm type

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR

Volume estimates for equiangular hyperbolic Coxeter polyhedra

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to \pi/n for some fixed integer n at least 2. It is a consequence of Andreev's theorem that either n=3 and the polyhedron has all ideal vertices or that n=2. Volume estimates are given for all equiangular hyperbolic Coxeter polyhedra.Comment: 27 pages, 11 figures; corrected typo in Theorem 2.

A new proof that alternating links are non-trivial

We use a simple geometric argument and small cancellation properties of link groups to prove that alternating links are non-trivial. This proof uses only classic results in topology and combinatorial group theory.Comment: Minor changes. To appear in Fundamenta Mathematica

Excitations in time-dependent density-functional theory

An approximate solution to the time-dependent density functional theory (TDDFT) response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for G\"orling-Levy perturbation theory results, and a method for estimating expectation values of the unknown exchange-correlation kernel.Comment: 4 pages, 1 tabl

Fullerene graphs have exponentially many perfect matchings

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.Comment: 7 pages, 3 figure