Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Probing the Nature of Black Holes with Gravitational Waves

In this thesis, I present a number of studies intended to improve our understanding of black holes using gravitational waves. Although black holes are relatively well understood from a theory perspective, many questions remain about the nature of the black holes in our Universe. According to general relativity, astrophysical black holes are fully described by just their mass and spin. Yet, relying on electromagnetic-based observatories alone, we still know very little about the distribution of black hole masses or spins. Moreover, as merging black holes are invisible to these electromagnetic observatories, we cannot rely on them to provide us with information about the binary black hole merger rate or binary black hole formation channels. However, by observing gravitational wave signals from these inherently dark binaries, we will soon have some answers to these questions. Indeed, the Laser Interferometer Gravitational-Wave Observatory (LIGO) has already revealed a great deal of new information about binary black holes; giving us an early glimpse into their mass and spin distributions and placing the first constraints on the binary black hole merger rate. This thesis contributes to the goal of probing the nature of black holes with gravitational waves. Binary black holes can form as an isolated binary in the galactic field or through dynamical encounters in high-density environments. Dynamical formation can significantly alter the binary parameters, which then become imprinted on the gravitational waveform. By simulating varying black hole populations in high-density globular clusters, we identify a population of highly eccentric binary black hole mergers that are characteristic of dynamical formation. Although these systems would circularize by the time they are visible in LIGO's frequency band, the future Laser Interferometer Space Antenna (LISA) is capable of distinguishing this population of eccentric mergers from the circular mergers expected of isolated field-formed binaries. As these dynamically formed binaries depend on the size of the underlying black hole population in globular clusters, we can utilize the dynamically formed merger rate to infer globular cluster black hole populations -- allowing us to reveal information about binary black hole birth environments. In order to properly estimate the parameters of binary black holes from detected gravitational wave signals, such as their masses and spins, high-accuracy waveforms are a needed. The highest accuracy waveforms are those produced by numerical relativity simulations, which solve the full Einstein equations. Using the Spectral Einstein Code (SpEC), we expand the reach of numerical relativity to simulate binary black holes with nearly extremal spins, i.e., black holes with spins near the maximal value χ = 1. These waveforms are used to calibrate existing waveform approximants used in LIGO data analyses. This ensures that the systematic errors in these approximants are small enough that if highly-spinning systems are observed, the spins are recovered without bias. Although rapidly spinning binaries have remained elusive thus far, these waveforms ensure that the highest-spin systems can be detected in the quest to uncover the spin distribution of black holes. The end state of a binary black hole merger is a newly born, single black hole that rings down like a struck bell, sending its last few ripples of gravitational waves out into the spacetime. Embedded in this 'ringdown' signal are a multitude of specific frequencies. Einstein's theory of general relativity precisely predicts the ringdown frequencies of a black hole with a given mass and spin. The statement that a black hole is entirely described by just these two parameters is known as the no-hair theorem. For black holes that obey the laws of general relativity (and consequently, the no-hair theorem), these frequencies serve as a fingerprint for the black hole. However, if the objects we observe are not Einstein's black holes, but instead something more exotic, the frequencies will not have this property and this would be a spectacular surprise. A minimum of two tones are required for this test, each with an associated frequency and damping time that depend only on the mass and spin. The conventional no-hair test relies on the so-called 'fundamental' tones of a black hole. A test relying on the fundamental modes is not expected to be feasible for another ~10-15 years, after detector sensitivity has improved significantly. However, by analyzing the ringdown of high-accuracy numerical relativity waveforms, we show that modes beyond the fundamental, known as 'overtones', are detectable in current detectors. The overtones are short-lived, but this is countered by the fact that they can initially be much stronger than the fundamental mode. By measuring two tones in the ringdown of GW150914 we perform a first test of the no-hair theorem. While the current constraints are rather loose, this first test serves as a proof of principle. This is just one example of the powerful tests that can be employed with overtones using present day detectors and the even more precise tests that can be accomplished with LISA in the future.</p

Proceedings of the Fifth NASA/NSF/DOD Workshop on Aerospace Computational Control

The Fifth Annual Workshop on Aerospace Computational Control was one in a series of workshops sponsored by NASA, NSF, and the DOD. The purpose of these workshops is to address computational issues in the analysis, design, and testing of flexible multibody control systems for aerospace applications. The intention in holding these workshops is to bring together users, researchers, and developers of computational tools in aerospace systems (spacecraft, space robotics, aerospace transportation vehicles, etc.) for the purpose of exchanging ideas on the state of the art in computational tools and techniques

Laser-plasma interactions as tools for studying processes in quantum electrodynamics

Conventional particle accelerators and astronomical observations have long been some of the only tools for studying processes in high energy physics. The development of laser-plasma sources and high gradient accelerators will therefore be a key asset to these studies. In particular, laser-plasma accelerators have favourable spatial and temporal properties for studies into intense processes, and can be readily coupled to a wide array of other laser-plasma sources creating unique environments. Here, coupling to an X-ray source and intense laser focus were used to study processes in quantum electrodynamics. To study the linear Breit-Wheeler process, a 40 ps laser was used to drive a volumetric X-ray emitter. Line emission from a thin-foil Ge target, produced a highly efficient (3.4%), dense source of 1.3 − 1.9 keV X-rays, with 3 ± 1 (stat.) ±0.4 (sys.) ×10^{12} photons/eV/sphere. These X-rays were collided with bremsstrahlung gamma rays (with energies up to 800 MeV) to investigate electron-positron pair production. The X-ray source was well-optimised for studying this interaction, and would allow the detection of Breit-Wheeler pairs if used with a moderately improved electron beam for generating bremsstrahlung (3× the highest electron energy and 5× the total charge, as achieved previously). This would constitute the first laser-plasma photon- photon collider with low virtuality (energy off mass-shell ≈ 10^{−20} MeV^2). In order to differentiate between competing models of electron radiation reaction in strong field quantum electrodynamics, a narrow energy-spread electron beam was studied. By utilising shock injection into a laser wakefield accelerator, a high energy (1260±40 MeV), narrow energy- spread (4.1±0.9 %) beam was generated. This is one of only a few studies that have successfully achieved these electron beam properties. While the shot-to-shot reproducibility of the electron beam was limited to 60%, the relative energy-spread was sufficiently small that differentiation of radiation reaction models could be readily achieved in future experiments. With the upcoming commissioning of many multi-PW laser facilities, these studies demonstrate how active research into quantum electrodynamics can be achieved on the smaller, more accessible, laser-laboratory scale.Open Acces

Publications of Goddard Space Flight Center, 1964. Volume I - Space sciences

This publication is a collection of articles, papers, talks, and reports generated by the scientific and engineering staff of Goddard Space Flight Center in the year 1964. Many of these articles were originally published in scientific or engineering Journals or as official NASA technical publications, while other are documents of a more informal nature. All are reprinted here as nearly verbatim as typography and format will permit. These articles are grouped into broad subject categories, but no detailed subdivision has been made. Within each category, the articles are arranged alphabetically by author. An overall author index is given in the back of the volume. The years 1963, 1964, and 1965 are being published as whole-year issues, and the resulting size dictates the use of two volumes; the first volume is titled Space Sciences, and the second Space Technology. It is anticipated, however, that future issues will be quarterly single volumes

The Long-Wave Debate; Selected Papers from an IIASA International Meeting, Weimar, GDR, June 10-14, 1985

For over a century, some economists have pointed out that upswings and down turns in economic activity (along with some key economic variables) seem to follow a surprisingly regular pattern -- a pattern sometimes labeled simply "Kondratieff long waves" in honor of the Russian economist who first rigorously described some of the phenomena leading to these changes. What might to be causes and consequences of these long-term fluctuations? What is the relationship between these so-called long waves and other structural changes, technical revolutions, financial and monetary variables? Finally, if the mechanisms of long waves can be understood, will it be possible to avoid the recurrent recessions in economic development that are as painful for the less developed countries as for the developed ones -- be they socialist or capitalist in orientation? By invitation, an international panel of distinguished scholars met in Weimar, GDR, to discuss these fascinating questions about the existence and nature of long waves. This conference was organized and sponsored jointly by the International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria and the Institute of Theory, History and Organization of Science of the GDR Academy of Sciences, Berlin. A select group of 30 contributions comprise THE LONG-WAVE DEBATE, which thus represents the state of the art in the theory and empirical observation of long-term economic cycles

Kristallstrukturbestimmung organischer Pigmente aus Röntgen-Pulverdaten und Kristallstrukturmodellierung niedrig-dimensionaler Festkörper mit Kraftfeld-Methoden

In dieser Arbeit geht es um Kristallstrukturbestimmung und -modellierung ausgewählter organischer Pigmente sowie metallorganischer Polymere. Der feste – und insbesondere kristalline – Zustand der Materie ist von (im wahrsten Sinne des Wortes) tragender und weitreichender Bedeutung für die moderne Wissenschaft, Technologie, den Alltag überhaupt. Die Kenntnis über den inneren (mikroskopischen)Aufbau des Festkörpers ermöglicht es zunächst, seine (makroskopischen) Eigenschaften zu verstehen. Genannt seien z. B. nicht-lineare optische Eigenschaften, die in der typischen anisotropen Struktur des kristallinen Festkörpers begründet liegen, mechanische Stabilität von Werkstoffen wie Metallen oder Legierungen, aber auch die Eigenschaften von Pigmenten: Was macht eine Substanz zu einem Pigment? Wann ist ein Pigment ein gutes, wann ein weniger gutes Pigment? Die Antworten auf diese Fragen finden sich u. a. in der Kristallstruktur: Packungsdichte, (Schwer-)löslichkeit, etc. Die Eigenschaften von Substanzen mit sichtbaren Low-Spin–High-Spin-Übergängen lassen sich auch nur verstehen, wenn der innere Aufbau, die Kristallstruktur, bekannt ist. Was geht im Inneren vor, wenn solche Substanzen einem äußeren Einfluss wie beispielsweise Temperaturänderung ausgesetzt werden? Ist es nicht so, dass z. B. ein High-Spin-Fe2+-Ion einen größeren effektiven Radius als ein Low-Spin-Fe2+-Ion hat? Dehnt sich die Kristallstruktur aus, „atmet“ sie? Die Kenntnis der Kristallstruktur ermöglicht es nicht nur, die Eigenschaften zu verstehen. Umgekehrt ist es auch möglich, diese Eigenschaften gezielt zu manipulieren: Verbesserung der Pigmenteigenschaften durch Herabsetzen der Löslichkeit, Veränderung der elektronischen und magnetischen Kopplungen in niedrig-dimensionalen Polymerketten, um nur zwei zu nennen. Zum Leidwesen des Chemikers, des Physikers und des Kristallographen besteht in den Eigenschaften, die z. B. Pigmente als „gut“ auszeichnen, das größte Problem: die mangelnde Löslichkeit der Verbindung. Es ist genau diese Eigenschaft, die dafür sorgt, meist keine Einkristalle züchten zu können, massive Schwierigkeiten beim Umkristallisieren zu haben und letztendlich – wenn keine Einkristalle vorliegen – bei der Strukturbestimmung aus Pulverdaten breite, überlappende Reflexe separieren zu müssen. Dennoch gibt es nützliche und bewährte Methoden, auch aus (sogar nur mäßigen) Pulverdaten eine Kristallstruktur zu lösen. Genannt seien hier quantenchemische Rechnungen, die unter Umständen sehr rechen- und zeitintensiv sein können, oder Kraftfeld-Methoden, die zwar nicht sehr exakte, aber immerhin doch brauchbare Ergebnisse mit vertretbarem Zeit- und Rechenaufwand liefern. Diese Methoden sind insbesondere dann zur Vorhersage von Kristallstrukturen geeignet, wenn das Pulverdiagramm nicht indizierbar ist. Wenn die Struktur erst gelöst ist, ist die bewährte Methode der Strukturverfeinerung die Rietveld-Methode. Obwohl oder gerade weil die Methode mittlerweile zu einer „Black- Box“-Methode geworden ist, ist die genaue Analyse und Interpretation der Ergebnisse unabdingbar. Es gibt genügend Beispiele, in denen vermeintlich gute Ergebnisse (struktur-)chemisch sinnlos sind. Themenstellung Pigmente spielen in der Industrie eine wesentliche Rolle. Im Gegensatz zu Farbstoffen sind Pigmente im Anwendungsmedium unlöslich, sie werden feinkristallin dispergiert, um z. B. in Autolacken oder Kunststoffen eingesetzt zu werden. Im Rahmen dieser Arbeit wurden die Kristallstrukturen von 13 Pigmenten bestimmt. Zu den genannten Kristallstrukturbestimmungen kommt ein Kapitel mit einer grundsätzlichen Fragestellung: Wo sind die Grenzen der Strukturbestimmung aus Pulverdaten? Wann ist eine Kristallstruktur „richtig“ oder „falsch“? Ein letztes Pigment verknüpft die beiden vorangehenden Punkte. Das letzte Kapitel behandelt die Erstellung von 5 Modellstrukturen aus zwei Substanzklassen für niedrig-dimensionale metall-organische Festkörper. Beide Substanzklassen wurden im Rahmen der Forschergruppe 412 („Spin- und Ladungsträgerkorrelationen in niedrigdimensionalenmetallorganischen Festkörpern“)der DFG hinsichtlich elektronischer und magnetischer Eigenschaften untersucht