An integrated design approach to power systems : from power flows to electricity markets

Power system is at the brink of change. Engineering needs, economic forces and environmental factors are the main drivers of this change. The vision is to build a smart electrical grid and a smarter market mechanism around it to fulfill mandates on clean energy. Looking at engineering and economic issues in isolation is no longer an option today; it needs an integrated design approach. In this thesis, I shall revisit some of the classical questions on the engineering operation of power systems that deals with the nonconvexity of power flow equations. Then I shall explore some issues of the interaction of these power flow equations on the electricity markets to address the fundamental issue of market power in a deregulated market environment. Finally, motivated by the emergence of new storage technologies, I present an interesting result on the investment decision problem of placing storage over a power network. The goal of this study is to demonstrate that modern optimization and game theory can provide unique insights into this complex system. Some of the ideas carry over to applications beyond power systems.

Kinetic theory of normal quantum fluids

Close to equilibrium, a normal Bose or Fermi fluid can be described by an exact kinetic equation whose kernel is nonlocal in space and time. The general expression derived for the kernel is evaluated to second order in the interparticle potential. The result is a wavevector- and frequency-dependent generalization of the linear Uehling-Uhlenbeck kernel with the Born approximation cross section.

The theory is formulated in terms of second-quantized phase space operators whose equilibrium averages are the n-particle Wigner distribution functions. Convenient expressions for the commutators and anticommutators of the phase space operators are obtained. The two-particle equilibrium distribution function is analyzed in terms of momentum-dependent quantum generalizations of the classical pair distribution function h(k) and direct correlation function c(k). The kinetic equation is presented as the equation of motion of a two -particle correlation function, the phase space density-density anticommutator, and is derived by a formal closure of the quantum BBGKY hierarchy. An alternative derivation using a projection operator is also given. It is shown that the method used for approximating the kernel by a second order expansion preserves all the sum rules to the same order, and that the second-order kernel satisfies the appropriate positivity and symmetry conditions.

Study of dynamical behaviour and fermionization of a bosonic gas in funnel potential

This paper presents a funnel external potential model to investigate dynamic properties of ultracold Bose gas. By using variational method, we obtain the ground-state energy and density properties of ultracold Bose atoms. The results show that the ultracold Bose gas confined in a funnel potential experiences the transition from three-dimensional regime to quasi-one-dimensional regime in a small aspect ratio, and undergoes fermionization process as the aspect ratio increases.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

Lock Acquisition and Sensitivity Analysis of Advanced LIGO Interferometers

Laser interferometer gravitational wave observatory (LIGO) consists of two complex large-scale laser interferometers designed for direct detection of gravitational waves from distant astrophysical sources in the frequency range 10Hz - 5kHz. Direct detection of space-time ripples will support Einstein's general theory of relativity and provide invaluable information and new insight into physics of the Universe.

Initial phase of LIGO started in 2002, and since then data was collected during six science runs. Instrument sensitivity was improving from run to run due to the effort of commissioning team. Initial LIGO has reached designed sensitivity during the last science run, which ended in October 2010.

In parallel with commissioning and data analysis with the initial detector, LIGO group worked on research and development of the next generation detectors. Major instrument upgrade from initial to advanced LIGO started in 2010 and lasted till 2014.

This thesis describes results of commissioning work done at LIGO Livingston site from 2013 until 2015 in parallel with and after the installation of the instrument. This thesis also discusses new techniques and tools developed at the 40m prototype including adaptive filtering, estimation of quantization noise in digital filters and design of isolation kits for ground seismometers.

The first part of this thesis is devoted to the description of methods for bringing interferometer to the linear regime when collection of data becomes possible. States of longitudinal and angular controls of interferometer degrees of freedom during lock acquisition process and in low noise configuration are discussed in details.

Once interferometer is locked and transitioned to low noise regime, instrument produces astrophysics data that should be calibrated to units of meters or strain. The second part of this thesis describes online calibration technique set up in both observatories to monitor the quality of the collected data in real time. Sensitivity analysis was done to understand and eliminate noise sources of the instrument.

Coupling of noise sources to gravitational wave channel can be reduced if robust feedforward and optimal feedback control loops are implemented. The last part of this thesis describes static and adaptive feedforward noise cancellation techniques applied to Advanced LIGO interferometers and tested at the 40m prototype. Applications of optimal time domain feedback control techniques and estimators to aLIGO control loops are also discussed.

Commissioning work is still ongoing at the sites. First science run of advanced LIGO is planned for September 2015 and will last for 3-4 months. This run will be followed by a set of small instrument upgrades that will be installed on a time scale of few months. Second science run will start in spring 2016 and last for about 6 months. Since current sensitivity of advanced LIGO is already more than factor of 3 higher compared to initial detectors and keeps improving on a monthly basis, upcoming science runs have a good chance for the first direct detection of gravitational waves.

Continuous stochastic processes

A general review of stochastic processes is given in the introduction; definitions, properties and a rough classification are presented together with the position and scope of the author's work as it fits into the general scheme.

The first section presents a brief summary of the pertinent analytical properties of continuous stochastic processes and their probability-theoretic foundations which are used in the sequel.

The remaining two sections (II and III), comprising the body of the work, are the author's contribution to the theory. It turns out that a very inclusive class of continuous stochastic processes are characterized by a fundamental partial differential equation and its adjoint (the Fokker-Planck equations). The coefficients appearing in those equations assimilate, in a most concise way, all the salient properties of the process, freed from boundary value considerations. The writer’s work consists in characterizing the processes through these coefficients without recourse to solving the partial differential equations.

First, a class of coefficients leading to a unique, continuous process is presented, and several facts are proven to show why this class is restricted. Then, in terms of the coefficients, the unconditional statistics are deduced, these being the mean, variance and covariance. The most general class of coefficients leading to the Gaussian distribution is deduced, and a complete characterization of these processes is presented. By specializing the coefficients, all the known stochastic processes may be readily studied, and some examples of these are presented; viz. the Einstein process, Bachelier process, Ornstein-Uhlenbeck process, etc. The calculations are effectively reduced down to ordinary first order differential equations, and in addition to giving a comprehensive characterization, the derivations are materially simplified over the solution to the original partial differential equations.

In the last section the properties of the integral process are presented. After an expository section on the definition, meaning, and importance of the integral process, a particular example is carried through starting from basic definition. This illustrates the fundamental properties, and an inherent paradox. Next the basic coefficients of the integral process are studied in terms of the original coefficients, and the integral process is uniquely characterized. It is shown that the integral process, with a slight modification, is a continuous Markoff process.

The elementary statistics of the integral process are deduced: means, variances, and covariances, in terms of the original coefficients. It is shown that an integral process is never temporally homogeneous in a non-degenerate process.

Finally, in terms of the original class of admissible coefficients, the statistics of the integral process are explicitly presented, and the integral process of all known continuous processes are specified.

Relativistic velocity - potential hydrodynamics and stellar stability

The equations of relativistic, perfect-fluid hydrodynamics are cast in Eulerian form using six scalar "velocity-potential" fields, each of which has an equation of evolution. These equations determine the motion of the fluid through the equation

U_ʋ=µ^-1 (ø,_ʋ + αβ,_ʋ + ƟS,_ʋ).

Einstein's equations and the velocity-potential hydrodynamical equations follow from a variational principle whose action is

I = (R + 16π p) (-g)^1/2 d⁴x,

where R is the scalar curvature of spacetime and p is the pressure of the fluid. These equations are also cast into Hamiltonian form, with Hamiltonian density –T₀⁰ (-g^oo)^-1/2.

The second variation of the action is used as the Lagrangian governing the evolution of small perturbations of differentially rotating stellar models. In Newtonian gravity this leads to linear dynamical stability criteria already known. In general relativity it leads to a new sufficient condition for the stability of such models against arbitrary perturbations.

By introducing three scalar fields defined by

ρ ᵴ = ∇λ + ∇x(xi + ∇xɣi)

(where ᵴ is the vector displacement of the perturbed fluid element, ρ is the mass-density, and i, is an arbitrary vector), the Newtonian stability criteria are greatly simplified for the purpose of practical applications. The relativistic stability criterion is not yet in a form that permits practical calculations, but ways to place it in such a form are discussed.

Kiribilen kosmologia kuantikorako sarrera

Gradu amaierako lan hau kiribilen kosmologia kuantikorako sarrera bat da. Lan honek 4 kapi- tulu ditu. Lehenengoan, sarrera bezala grabitazio kuantikoak izan duen bilakaera historikoa jaso da, halako teoria bat garatzeko motibazioak eta zailtasunak, eta honen garapenean kosmologia kuantikoak duen papera azalduz. Lanean, oro har, grabitazio kuantikoaren teoria bat eraikitzeko formalismo “kanonikoa” jarraitu da, alegia, erlatibitate orokorraren formulazio hamiltondarra era- biliz teoria kuantikoa garatzea. Bigarren kapituluan grabitazioaren teoria klasikoaren formulazio hamiltondarra garatu da, lehenik Arnowitt-Deser-Misner formalismoaren (Einstein-en geometro- dinamika bezala ere ezaguna denaren) bidez eta ondoren Ashtekar-en aldagaiak erabiliz. Bietan hamiltondar guztiz lotua lortzen da, hots, loturen konbinazio lineala den hamiltondarra. Lotu- ren bidezko formulazio hauen kuantizazioaren eta kribilen adierazpenaren oinarrizko aspektuak jaso dira bigarren kapituluan. Hirugarren kapituluan kosmologiaren teoria klasikoa Friedmann- Lemaˆ ıtre-Robertson-Walker metrika laua erabiliz azaltzen da era laburrean lehenik, eta ondoren Wheeler-DeWitt teoria kuantikoa eta kiribilen kosmologia kuantikoa eta hauek erabiliz lorturiko zenbait emaitza aipatzen dira. Azkenik, ondorioen atalarekin amaitzen da lana. Lana euskaraz idatzita dago.

Spin squeezing, macrorealism and the heisenberg uncertainty principle

169 p.

Closed G2 forms and special metrics

170 p.

Propagação de ondas em teorias alternativas da gravitação

Uma forma de generalizar a teoria de Einstein da gravitação é incorporar na lagrangiana termos que dependem de escalares formados com os tensores de Ricci e Riemann, tais como (Ricci)2, ou (Riemann)2. Estas teorias tem sido estudadas intensamente nos últimos anos, já que elas podem ser usadas para descrever a expansão acelerada do universo no modelo cosmológico standard. Entre os desfios de modificar a teoria de Einstein, se encontra o de limitar a ambiguidade na escolha da dependência da lagrangiana com os escalares antes mencionados. A proposta desta dissertação é a de colocar limites sobre as possíveis lagrangianas impondo que as ondas (isto é, perturbações lineares) se propaguem no vácuo sem que apareça, shocks.

Quantum Emulation of Gravitational Waves

Gravitational waves, as predicted by Einstein's general relativity theory, appear as ripples in the fabric of spacetime traveling at the speed of light. We prove that the propagation of small amplitude gravitational waves in a curved spacetime is equivalent to the propagation of a subspace of electromagnetic states. We use this result to propose the use of entangled photons to emulate the evolution of gravitational waves in curved spacetimes by means of experimental electromagnetic setups featuring metamaterials.

Ciclo de vida e posição socioeconômica: contribuições sociológicas para o entendimento da relação entre desigualdade social e saúde no Brasil

Nesta tese, pretendemos investigar a relação entre ciclo de vida, posição socioeconômica e disparidades sociais no Brasil. Inicialmente, apresentamos trabalhos brasileiros e estrangeiros que descrevem associações entre a posição socioeconômica dos indivíduos e o estado de saúde. A abrangência dessa ligação levou sociólogos a sistematizarem uma elegante teoria que trata os recursos socioeconômicos como causas fundamentais do adoecimento e da mortalidade. Fazemos uma exposição relativamente detalhada dessa perspectiva. A apresentação dos dois debates estabelece a justificativa do trabalho e mapeia os espaços na literatura para os quais pretendemos contribuir. No segundo capítulo iniciamos nossa investigação, com o aprofundamento de uma dimensão tida como central no entendimento sociológico da desigualdade: classe social. Esse conceito é tido por pesquisadores, tanto vinculados à sociologia como em outras disciplinas, como uma via explicativa interessante na abordagem das disparidades sociais em saúde. No entanto, essa opinião não é consensual, e vários sociólogos contemporâneos fazem severas críticas à essa dimensão e às teorias que a balizam. Fazemos um aprofundamento nesses debates e uma reflexão sobre sua pertinência para o contexto brasileiro. Balizamos nossas conclusões através de uma investigação que mobiliza métodos e dados inéditos sobre a estrutura ocupacional brasileira. Através da investigação da validade empírica e conceitual de uma das operacionalizações de classe mais comuns na literatura internacional, a tipologia EGP, testamos como características do mercado de trabalho brasileiro se relacionam a essa dimensão. Nossos resultados, atingidos a partir de modelos log-lineares de classes latentes (latent class analysis) mostram que as particularidades do mercado de trabalho brasileiro são importantes na consideração sobre essa variável, mas não inviabilizam sua utilização. Munidos desse resultado, partimos para o último capítulo do trabalho. Nele, aprofundamos a discussão sobre desigualdade e saúde através da apresentação de teorias sobre o ciclo de vida, que informam dois debates específicos que investigamos empiricamente. O primeiro deles diz respeito à acumulação de vantagens e desvantagens ao longo do ciclo de vida e a estruturação das disparidades sociais em saúde. O segundo diz respeito à transmissão intergeracional da desigualdade e a desigualdade em saúde. Apresentamos essas correntes teóricas, que inspiram a elaboração de nossas hipóteses. Junto a elas, adicionamos uma outra hipótese inspirada nas discussões apresentadas nos capítulos anteriores. Nossos resultados demonstram a relevância de abordagens sociológicas para o estudo da desigualdade em saúde. Mostramos como nível educacional e idade interagem na estruturação das disparidades sociais em saúde, evidências indiretas de como as trajetórias sociais proporcionadas pela educação expõe indivíduos a condições que os expõe sua saúde a diferentes tipos de desgaste. Igualmente, mostramos evidências que apontam para como etapas relacionadas à infância e adolescência dos indivíduos têm efeitos sobre seu estado de saúde contemporâneo. Por fim, refletimos sobre os limites da variável de classe para o entendimento da estruturação das disparidades sociais em saúde no Brasil.

"Heroes" and "Villains" of World History across Cultures

Emergent properties of global political culture were examined using data from the World History Survey (WHS) involving 6,902 university students in 37 countries evaluating 40 figures from world history. Multidimensional scaling and factor analysis techniques found only limited forms of universality in evaluations across Western, Catholic/Orthodox, Muslim, and Asian country clusters. The highest consensus across cultures involved scientific innovators, with Einstein having the most positive evaluation overall. Peaceful humanitarians like Mother Theresa and Gandhi followed. There was much less cross-cultural consistency in the evaluation of negative figures, led by Hitler, Osama bin Laden, and Saddam Hussein. After more traditional empirical methods (e.g., factor analysis) failed to identify meaningful cross-cultural patterns, Latent Profile Analysis (LPA) was used to identify four global representational profiles: Secular and Religious Idealists were overwhelmingly prevalent in Christian countries, and Political Realists were common in Muslim and Asian countries. We discuss possible consequences and interpretations of these different representational profiles.