Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Algorithmic challenges in green data centers

With data centers being the supporting infrastructure for a wide range of IT services, their efficiency has become a big concern to operators, as well as to society, for both economic and environmental reasons. The goal of this thesis is to design energy-efficient algorithms that reduce energy cost while minimizing compromise to service. We focus on the algorithmic challenges at different levels of energy optimization across the data center stack. The algorithmic challenge at the device level is to improve the energy efficiency of a single computational device via techniques such as job scheduling and speed scaling. We analyze the common speed scaling algorithms in both the worst-case model and stochastic model to answer some fundamental issues in the design of speed scaling algorithms. The algorithmic challenge at the local data center level is to dynamically allocate resources (e.g., servers) and to dispatch the workload in a data center. We develop an online algorithm to make a data center more power-proportional by dynamically adapting the number of active servers. The algorithmic challenge at the global data center level is to dispatch the workload across multiple data centers, considering the geographical diversity of electricity price, availability of renewable energy, and network propagation delay. We propose algorithms to jointly optimize routing and provisioning in an online manner. Motivated by the above online decision problems, we move on to study a general class of online problem named "smoothed online convex optimization", which seeks to minimize the sum of a sequence of convex functions when "smooth" solutions are preferred. This model allows us to bridge different research communities and help us get a more fundamental understanding of general online decision problems.

From Shadow to Green: Linking Environmental Fiscal Reforms and the Informal Economy

47 p.

The Green Paradox and Learning-by-doing in the Renewable Energy Sector

21 p.

A dynamic CGE modelling approach for analyzing trade-offs in climate change policy options: the case of Green Climate Fund

38 p.

Toxic blue-green algae: The "problem" in perspective

The incidence of blue-green algal blooms and surface scum-formation are certainly not new phenomena. Many British and European authors have been faithfully describing the unmistakable symptoms of blue-green algal scums for over 800 years. There is no disputing that blue-green algal toxins are extremely harmful. Three quite separate categories of compound have been separated: neurotoxins; hepatotoxins and lipopolysaccharides. There is a popular association between blue-green algae and eutrophication. Certainly the main nuisance species - of Microcystis, Anabaena and Aphanizomenon are rare in oligotrophic lakes and reservoirs. Several approaches have been proposed for the control of blue-green algae. Distinction is made between methods for discharging algae already present (eg algicides; straw bales; viruses; parasitic fungi and herbivorous ciliates), and methods for averting an anticipated abundance in the future (phosphorous control, artificial circulation etc).

The influence of blue-green algae on development of the zooplankton. [Translation of: Byull.mosk.Obshch.Ispyt.Prir.(Biol.) 67, 128-131, 1962]

Many have observed the reduction of the quantity of zooplankton in the presence of water blooms. It is known that in seas zooplankton as it were avoids places of accumulation of blue-green algae. By observations on one of the tributaries of the Rybinsk reservoir - the River Shumorovka - the authors tried by simultaneous collections to trace the changes in numbers, not only of zoo- and phytoplankton but also of bacteria. The plankton was collected by quantitative nets with suitable numbers of gauze and bacteria were taken account of by the method of direct calculation on membrane filters. It can be seen that the development of blue-green algae appears as an important factor, determining not only the intensity but also the direction of the process of production of zooplankton.

Discovery of viruses lysing blue-green algae in the Dneprovsk reservoirs. [Translation of: Water blooms (ed. A. V. Topachevskii) pp.171-174. Kiev, Naukova Dumka, 1968]

Viruses, which are characterised by a relative simplicity of chemical composition, are involved with all the groups of the animal and plant world. The discovery of viruses of lower organisms has special interest. Along with the already known viruses lysing bacteria and actinomycetes, viruses have been discovered in recent years which lyse algae. During investigations of water from water-bloom patches and of mud taken from zones of massive accumulation of blue-green algae in the Dneprovsk reservoirs, the authors obtained viruses lysing algae. The revealing of viruses producing lysis of blue-green algae, which one could use in the control of water-blooms, has the greatest interest. With this aim, samples of water were collected from various zones of water-bloom patches in the Kremenchug, Dneprovsk and Kukhov reservoirs. For viruses lysing algae we propose the name 'algophages'. Along with the existence of viruses of algae of the phage type, one cannot deny the possibility of the existence of viruses of another type, multiplying in the cells of algae and causing their virus illnesses.

The possibilities and dangers in using malachite green in pisciculture.[Translation from: Informatsionnyi Byulleten Biologiya Vnutrennikh Vod No.3 17-21, 1969.]

For many years a dye has been used in the practise of pisciculture and pond management, which is known by the name of malachite green, and is used to combat fungus on fish, fish eggs and external animal parasites on fish. The authors describe the problem of the application of malachite green in pisciculture and undertake special, complementary research.

Refractive-index change and sensitivity improvement in holographic recording in LiNbO3:Ce:Cu crystals with green light

Nonvolatile holographic recording is performed with green light in LiNbO3:Ce:Cu crystals. The refractive-index change and the recording sensitivity are times better than those obtained by recording with red light, and higher optical fixing efficiency is obtained. Correspondingly, theoretical investigations are given.

The impact of Cow Green Reservoir on invertebrate populations in the River Tees

Cow Green is a new reservoir situated in Pennine moorland. It has an area of 312 ha, a capacity of 40 . 9 x 10 SUP-6 m SUP-3 and a maximum depth of 22 . 8 m. The function of the reservoir is to regulate flow in the River Tees to provide industrial Teesside with sufficient water during the dry spells. Invertebrate studies were carried out in the Tees to monitor changes resulting from the construction of the reservoir both in the flooded basin and below the dam. The overall effect of the reservoir on the Tees has been to increase the numbers and biomass of certain taxa, but generally not at the expense of previous fauna. Some of the positive effects, ie. increase in number and biomass, and maintenance of faunal diversity, may in part be attributable to the presence of the rapids and waterfall. Turbulence resulting from this rapid flow over heterogeneous bottom is sufficient to prevent clogging of interstitial spaces by silt and to maintain the variety of ecological niches necessary for a diverse fauna.

Effects of Cow Green Reservoir upon downstream fish populations

Post impoundment observations on the fish populations of the River Tees, downstream from the Cow Green Reservoir were made between 1971 and 1980. Both bullhead (Cottus gobio L.) and brown trout (Salmo trutta L.) population densities increased in the river after impoundment but changes in growth rate were small. Investigations into the stomach contents of the two species reflects the results of other work on increases of benthos in the river. Following regulation there was an increase in the quantity of Ephemerella ignita found in trout stomachs while in the bullhead, regulation caused an increase in the importance of Mollusca and a decrease in importance of Ephemeroptera and Plecoptera.

On concentrated loads and Green's functions in elastostatics

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.