Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

NASA Tech Briefs, January 1989

Topics include: Electronic Components & and Circuits. Electronic Systems, A Physical Sciences, Materials, Computer Programs, Mechanics, Machinery, Fabrication Technology, Mathematics and Information Sciences, and Life Sciences

Searching for Gravitational Waves Using Pulsar Timing Arrays

Gravitational Waves (GWs) are tiny ripples in the fabric of spacetime predicted by Einstein\u27s theory of General Relativity. Pulsar timing arrays (PTAs) offer a unique opportunity to detect low frequency GWs in the near future. Such a detection would be complementary to both LISA and LIGO GW efforts. In this frequency band, the expected source of GWs are Supermassive Black Hole Binaries (SMBHBs) that will most likely form an ensemble creating a stochastic GW background with possibly a few nearby/massive sources that will be individually resolvable. A direct detection of GWs will open a new window into the fields of astronomy and astrophysics by allowing us to constrain the coalescence rate of SMBHBs, providing us with further tests on the theory of General Relativity, and giving us access to properties of black holes not accessible by current astronomical techniques. This dissertation work focuses primarily on the development of several robust data analysis pipelines for the detection and characterization of continuous GWs and a stochastic GW background. The data analysis problem for PTAs is quite difficult as one must fully take into account the timing model that must be fit in order to obtain the residuals, uneven sampling (including large gaps), and potential red noise processes. The data analysis techniques presented here handle all of these effects completely while allowing additional freedom in parameterizing the noise present in the data. The accumulation of work from this dissertation has resulted in a fully functional, robust, and efficient data analysis pipeline that has been successfully applied to the 5- and 9-year NANOGrav data releases

Quantum sensing

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits. The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science. In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist.Comment: 45 pages, 13 figures. Submitted to Rev. Mod. Phy

Mechanical design of structures -Optimization of structures under fatigue life criterion

MasterThese lectures are devoted to the presentation of a new computational procedure for fatigue analysis of structures. This method, which is based on the theory of hys-teresis operators, consists to reduce computation of the damage D caused by a time varying stress t ∈ [0, T ] → Σ e (t) to the energy dissipated in the hysteresis loops of the image H µ (Σ e) of Σ e by an appropriately calibrated Preisach operator H µ. We then see that this formalism allows to reduce the structure optimization problem, which consists to seek design parameters u minimizing the damage in some given parts of a structure, to the minimization of the mapping u → D(u) = T 0 H µ (Σ e , t) d t where Σ e (x u) is a numerical mapping governed by a system of second order differential equations M uẍ + W uẋ + K u x = F (t) describing the dynamical behavior of the considered structure. Furthermore, we provide and validate a series of algorithms allowing to solve the optimization problem by a steepest descent method tailored to manage large dynamical problems derived from finite element models. At last, the theoretical results obtained in this course are illustrated with the help of numerous examples, intended for supporting the relevancy of the approach and providing implementation templates in design engineering software