Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

NASA Hybrid Wing Aircraft Aeroacoustic Test Documentation Report

This report summarizes results of the Hybrid Wing Body (HWB) N2A-EXTE model aeroacoustic test. The N2A-EXTE model was tested in the NASA Langley 14- by 22-Foot Subsonic Tunnel (14x22 Tunnel) from September 12, 2012 until January 28, 2013 and was designated as test T598. This document contains the following main sections: Section 1 - Introduction, Section 2 - Main Personnel, Section 3 - Test Equipment, Section 4 - Data Acquisition Systems, Section 5 - Instrumentation and Calibration, Section 6 - Test Matrix, Section 7 - Data Processing, and Section 8 - Summary. Due to the amount of material to be documented, this HWB test documentation report does not cover analysis of acquired data, which is to be presented separately by the principal investigators. Also, no attempt was made to include preliminary risk reduction tests (such as Broadband Engine Noise Simulator and Compact Jet Engine Simulator characterization tests, shielding measurement technique studies, and speaker calibration method studies), which were performed in support of this HWB test. Separate reports containing these preliminary tests are referenced where applicable

Hybrid Wing Body Aircraft Acoustic Test Preparations and Facility Upgrades

NASA is investigating the potential of acoustic shielding as a means to reduce the noise footprint at airport communities. A subsonic transport aircraft and Langley's 14- by 22-foot Subsonic Wind Tunnel were chosen to test the proposed "low noise" technology. The present experiment studies the basic components of propulsion-airframe shielding in a representative flow regime. To this end, a 5.8-percent scale hybrid wing body model was built with dual state-of-the-art engine noise simulators. The results will provide benchmark shielding data and key hybrid wing body aircraft noise data. The test matrix for the experiment contains both aerodynamic and acoustic test configurations, broadband turbomachinery and hot jet engine noise simulators, and various airframe configurations which include landing gear, cruise and drooped wing leading edges, trailing edge elevons and vertical tail options. To aid in this study, two major facility upgrades have occurred. First, a propane delivery system has been installed to provide the acoustic characteristics with realistic temperature conditions for a hot gas engine; and second, a traversing microphone array and side towers have been added to gain full spectral and directivity noise characteristics

STUDY OF DISLOCATION LOOPS IN ALKALI HALIDE CRYSTALS BY DIFFUSE X-RAY SCATTERING

C'est un fait connu depuis quelque temps que des oscillations d'intensité caractéristique se produisent dans les figures de diffraction diffuse du fait du champ de déplacement de gros défauts tels que les amas et les boucles de dislocations. A côté de la diffraction due au champ de déplacement, la structure centrale des défauts étendus peut engendrer une ligne supplémentaire près des pics de Bragg. Ce n'est que récemment qu'il a été prouvé théoriquement qu'il y a pour les boucles de dislocation une corrélation entre les oscillations et cette ligne supplémentaire. La position de la ligne supplémentaire par rapport à un point voisin du réseau réciproque dépend de l'orientation du vecteur de Burgers et du vecteur du réseau réciproque. Des résultats de diffraction diffuse des rayons X sur des cristaux d'halogénures alcalins irradiés contenant de grands amas de défauts sont présentés. Les résultats sont discutés en termes de boucles dont les rayons dépendent des doses.It has been known for some time that characteristic intensity oscillations occur in diffuse scattering patterns due to the displacement field of strong defects like clusters and dislocation loops. Besides the scattering of the displacement field the core structure of extended defects may cause an extra line close to the Bragg-peak. Only recently it has been found theoretically that for dislocation loops there is a correlation between oscillations and the extra line. The position of the extra line relative to a nearby reciprocal lattice point depends on the orientation of the Burgers vector and the reciprocal lattice vector as well. X-ray diffuse scattering results on irradiated alkali halide crystals containing large defect clusters are presented. Results are discussed in terms of loops with dose — dependend size

Coherent X-ray scattering by phonons

Interference effects arising from coherently coupled X-ray beams inelastically scattered from phonons have been used to determine phonon eigenvectors in Si and GaAs crystals. An outline of the method, experimental requirements, and theoretical background is presented. The experimental results are analyzed with the help of different lattice dynamical model calculations. Best overall agreement is found with phonon eigendata based on the bond charge model