Heat kernels on the AdS(2) cone and logarithmic corrections to extremal black hole entropy

We develop new techniques to efficiently evaluate heat kernel coefficients for the Laplacian in the short-time expansion on spheres and hyperboloids with conical singularities. We then apply these techniques to explicitly compute the logarithmic contribution to black hole entropy from an N = 4 vector multiplet about a Z(N) orbifold of the near-horizon geometry of quarter-BPS black holes in N = 4 supergravity. We find that this vanishes, matching perfectly with the prediction from the microstate counting. We also discuss possible generalisations of our heat kernel results to higher-spin fields over ZN orbifolds of higher-dimensional spheres and hyperboloids.

Faster computation of the Karhunen-Loeve expansion using its domain independence property

The goal of this work is to reduce the cost of computing the coefficients in the Karhunen-Loeve (KL) expansion. The KL expansion serves as a useful and efficient tool for discretizing second-order stochastic processes with known covariance function. Its applications in engineering mechanics include discretizing random field models for elastic moduli, fluid properties, and structural response. The main computational cost of finding the coefficients of this expansion arises from numerically solving an integral eigenvalue problem with the covariance function as the integration kernel. Mathematically this is a homogeneous Fredholm equation of second type. One widely used method for solving this integral eigenvalue problem is to use finite element (FE) bases for discretizing the eigenfunctions, followed by a Galerkin projection. This method is computationally expensive. In the current work it is first shown that the shape of the physical domain in a random field does not affect the realizations of the field estimated using KL expansion, although the individual KL terms are affected. Based on this domain independence property, a numerical integration based scheme accompanied by a modification of the domain, is proposed. In addition to presenting mathematical arguments to establish the domain independence, numerical studies are also conducted to demonstrate and test the proposed method. Numerically it is demonstrated that compared to the Galerkin method the computational speed gain in the proposed method is of three to four orders of magnitude for a two dimensional example, and of one to two orders of magnitude for a three dimensional example, while retaining the same level of accuracy. It is also shown that for separable covariance kernels a further cost reduction of three to four orders of magnitude can be achieved. Both normal and lognormal fields are considered in the numerical studies. (c) 2014 Elsevier B.V. All rights reserved.

DESIGN OF AN EXPERIMENTAL TEST FACILITY FOR SUPERCRITICAL CO2 BRAYTON CYCLE

A supercritical CO2 test facility is currently being developed at Indian Institute of Science, Bangalore, India to analyze the performance of a closed loop Brayton cycle for concentrated solar power (CSP) generation. The loop has been designed for an external heat input of 20 kW a pressure range of 75-135 bar, flow rate of 11 kg/min, and a maximum cycle temperature of 525 degrees C. The operation of the loop and the various parametric tests planned to be performed are discussed in this paper The paper addresses various aspects of the loop design with emphasis on design of various components such as regenerator and expansion device. The regenerator design is critical due to sharp property variations in CO2 occurring during the heat exchange process between the hot and cold streams. Two types of heat exchanger configurations 1) tube-in-tube (TITHE) and 2) printed circuit heat exchanger (PCHE) are analyzed and compared. A PCHE is found to be similar to 5 times compact compared to a TITHE for identical heat transfer and pressure drops. The expansion device is being custom designed to achieve the desired pressure drop for a range of operating temperatures. It is found that capillary of 5.5 mm inner diameter and similar to 2 meter length is sufficient to achieve a pressure drop from 130 to 75 bar at a maximum cycle temperature of 525 degrees C.

Anisotropic thermopiezoelectric solids with an elliptic inclusion or a hole under uniform heat flow

The two-dimensional problem of a thermopiezoelectric material containing an elliptic inclusion or a hole subjected to a remote uniform heat flow is studied. Based on the extended Lekhnitskii formulation for thermopiezoelectricity, conformal mapping and Laurent series expansion, the explicit and closed-form solutions are obtained both inside and outside the inclusion (or hole). For a hole problem, the exact electric boundary conditions on the hole surface are used. The results show that the electroelastic fields inside the inclusion or the electric field inside the hole are linear functions of the coordinates. When the elliptic hole degenerates into a slit crack, the electroelastic fields and the intensity factors are obtained. The effect of the heat how direction and the dielectric constant of air inside the crack on the thermal electroelastic fields are discussed. Comparison is made with two special cases of which the closed solutions exist and it is shown that our results are valid.

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.

Thin metastructures with engineered thermal expansion

The geometry and constituent materials of metastructures can be used to engineer the thermal expansion coefficient. In this thesis, we design, fabricate, and test thin thermally stable metastructures consisting of bi-metallic unit cells and show how the coefficient of thermal expansion (CTE) of these metastructures can be finely and coarsely tuned by varying the CTE of the constituent materials and the unit cell geometry. Planar and three-dimensional finite element method modeling is used to drive the design and inform experiments, and predict the response of these metastructures. We demonstrate computationally the significance of out-of-plane effects in the metastructure response. We develop an experimental setup using digital image correlation and an infrared camera to experimentally measure full displacement and temperature fields during testing and accurately measure the metastructures’ CTE. We experimentally demonstrate high aspect ratio metastructures of Ti/Al and Kovar/Al which exhibit near-zero and negative CTE, respectively. We demonstrate robust fabrication procedures for thermally stable samples with high aspect ratios in thin foil and thin film scales. We investigate the lattice structure and mechanical properties of thin films comprising a near-zero CTE metastructure. The mechanics developed in this work can be used to engineer metastructures of arbitrary CTE and can be extended to three dimensions.

Test particle motion in a Lorentz gas

This is a two-part thesis concerning the motion of a test particle in a bath. In part one we use an expansion of the operator PLe^it(1-P)LLP to shape the Zwanzig equation into a generalized Fokker-Planck equation which involves a diffusion tensor depending on the test particle's momentum and the time.

In part two the resultant equation is studied in some detail for the case of test particle motion in a weakly coupled Lorentz Gas. The diffusion tensor for this system is considered. Some of its properties are calculated; it is computed explicitly for the case of a Gaussian potential of interaction.

The equation for the test particle distribution function can be put into the form of an inhomogeneous Schroedinger equation. The term corresponding to the potential energy in the Schroedinger equation is considered. Its structure is studied, and some of its simplest features are used to find the Green's function in the limiting situations of low density and long time.

Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

Anisotropic expansion and SNIa: An open issue

We review the appropriateness of using SNIa observations to detect potential signatures of anisotropic expansion in the Universe. We focus on Union2 and SNLS3 SNIa datasets and use the hemispherical comparison method to detect possible anisotropic features. Unlike some previous works where nondiagonal elements of the covariance matrix were neglected, we use the full covariance matrix of the SNIa data, thus obtaining more realistic and not underestimated errors. As a matter of fact, the significance of previously claimed detections of a preferred direction in the Union2 dataset completely disappears once we include the effects of using the full covariance matrix. Moreover, we also find that such apreferred direction is aligned with the orthogonal direction of the SDSS observational plane and this suggests a clear indication that the SDSS subsample of the Union2 dataset introduces a significant bias, making the detected preferred direction unphysical. We thus find that current SNIa surveys are inappropriate to test anisotropic features due to their highly non-homogeneous angular distribution in the sky. In addition, after removal of the highest in homogeneous sub-samples, the number of SNIa is too low. Finally, we take advantage of the particular distribution of SNLS SNIa sub- sample in the SNLS3 data set, in which the observations were taken along four different directions. We fit each direction independently and find consistent results at the 1 sigma level. Although the likelihoods peak at relatively different values of Omega(m), the low number of data along each direction gives rise to large errors so that the likelihoods are sufficiently broad as to overlap within 1 sigma. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http:// creativecommons. org/licenses/by/4.0/).

Mode shape expansion using perturbed force vector approach

A new technique for mode shape expansion in structural dynamic applications is presented based on the perturbed force vector approach. The proposed technique can directly adopt the measured incomplete modal data and include the effect of the perturbation between the analytical and test models. The results show that the proposed technique can provide very accurate expanded mode shapes, especially in cases when significant modelling error exists in the analytical model and limited measurements are available.

Testing the role of expansion in the prospective control of locomotion

The constant bearing angle (CBA) strategy is a prospective strategy that permits the interception of moving objects. The purpose of the present study is to test this strategy. Participants were asked to walk through a virtual environment and to change, if necessary, their walking speed so as to intercept approaching targets. The targets followed either a rectilinear or a curvilinear trajectory and target size was manipulated both within trials (target size was gradually changed during the trial in order to bias expansion) and between trials (targets of different sizes were used). The curvature manipulation had a large effect on the kinematics of walking, which is in agreement with the CBA strategy. The target size manipulations also affected the kinematics of walking. Although these effects of target size are not predicted by the CBA strategy, quantitative comparisons of observed kinematics and the kinematics predicted by the CBA strategy showed good fits. Furthermore, predictions based on the CBA strategy were deemed superior to predictions based on a required velocity (V-REQ) model. The role of target size and expansion in the prospective control of walking is discussed.

Late industrialization and the increased merit selection hypothesis - Ireland as a test case

The Irish case provides a particularly appropriate test of the increasing merit selection hypothesis deriving from the liberal theory of industrialization. This is so not only because the lateness and speed of economic change allows us to capture such change through a set of national surveys conducted in the past three decades, but also because such change was based on a sustained policy of increased openness to international competitive forces. The functional requirements of the economy and a rapid increase in the supply of those with higher educational qualifications provided an ideal context in which to observe the movement from ascription to achievement predicted by the liberal theory. However, while changes in the class structure and a rapid expansion of educational opportunity had significant consequences in terms of absolute mobility, there was no evidence of a significant shift towards meritocratic principles. At the same time as the service class increased their advantage over other classes in the pursuit of educational qualifications, the impact of educational qualifications on class destination diminished. Controlling for education, we find that the impact of class origin effects is substantial and shows little sign of diminishing over time. In our conclusion we discuss the implications of our findings in the context of the recent debate on meritocracy.

Phylogeny and ancient DNA of Sus provides insights into neolithic expansion in Island Southeast Asia and Oceania

Human settlement of Oceania marked the culmination of a global colonization process that began when humans first left Africa at least 90,000 years ago. The precise origins and dispersal routes of the Austronesian peoples and the associated Lapita culture remain contentious, and numerous disparate models of dispersal (based primarily on linguistic, genetic, and archeological data) have been proposed. Here, through the use of mtDNA from 781 modern and ancient Sus specimens, we provide evidence for an early human-mediated translocation of the Sulawesi warty pig (Sus celebensis) to Flores and Timor and two later separate human-mediated dispersals of domestic pig (Sus scrofa) through Island Southeast Asia into Oceania. Of the later dispersal routes, one is unequivocally associated with the Neolithic (Lapita) and later Polynesian migrations and links modern and archeological Javan, Sumatran, Wallacean, and Oceanic pigs with mainland Southeast Asian S. scrofa. Archeological and genetic evidence shows these pigs were certainly introduced to islands east of the Wallace Line, including New Guinea, and that so-called "wild" pigs within this region are most likely feral descendants of domestic pigs introduced by early agriculturalists. The other later pig dispersal links mainland East Asian pigs to western Micronesia, Taiwan, and the Philippines. These results provide important data with which to test current models for human dispersal in the region. © 2007 by The National Academy of Sciences of the USA.

A data-mining-based methodology for transmission expansion planning

In recent decades, all over the world, competition in the electric power sector has deeply changed the way this sector’s agents play their roles. In most countries, electric process deregulation was conducted in stages, beginning with the clients of higher voltage levels and with larger electricity consumption, and later extended to all electrical consumers. The sector liberalization and the operation of competitive electricity markets were expected to lower prices and improve quality of service, leading to greater consumer satisfaction. Transmission and distribution remain noncompetitive business areas, due to the large infrastructure investments required. However, the industry has yet to clearly establish the best business model for transmission in a competitive environment. After generation, the electricity needs to be delivered to the electrical system nodes where demand requires it, taking into consideration transmission constraints and electrical losses. If the amount of power flowing through a certain line is close to or surpasses the safety limits, then cheap but distant generation might have to be replaced by more expensive closer generation to reduce the exceeded power flows. In a congested area, the optimal price of electricity rises to the marginal cost of the local generation or to the level needed to ration demand to the amount of available electricity. Even without congestion, some power will be lost in the transmission system through heat dissipation, so prices reflect that it is more expensive to supply electricity at the far end of a heavily loaded line than close to an electric power generation. Locational marginal pricing (LMP), resulting from bidding competition, represents electrical and economical values at nodes or in areas that may provide economical indicator signals to the market agents. This article proposes a data-mining-based methodology that helps characterize zonal prices in real power transmission networks. To test our methodology, we used an LMP database from the California Independent System Operator for 2009 to identify economical zones. (CAISO is a nonprofit public benefit corporation charged with operating the majority of California’s high-voltage wholesale power grid.) To group the buses into typical classes that represent a set of buses with the approximate LMP value, we used two-step and k-means clustering algorithms. By analyzing the various LMP components, our goal was to extract knowledge to support the ISO in investment and network-expansion planning.

Systematic construction of models for the exchange hole of density functional theory.

Dans ce travail, nous étendons le nombre de conditions physiques actuellement con- nues du trou d’échange exact avec la dérivation de l’expansion de quatrième ordre du trou d’échange sphérique moyenne exacte. Nous comparons les expansions de deux- ième et de quatrième ordre avec le trou d’échange exact pour des systèmes atomiques et moléculaires. Nous avons constaté que, en général, l’expansion du quatrième ordre reproduit plus fidèlement le trou d’échange exact pour les petites valeurs de la distance interélectronique. Nous démontrons que les ensembles de base de type gaussiennes ont une influence significative sur les termes de cette nouvelle condition, en étudiant com- ment les oscillations causées par ces ensembles de bases affectent son premier terme. Aussi, nous proposons quatre modèles de trous d’échange analytiques auxquels nous imposons toutes les conditions actuellement connues du trou d’échange exact et la nou- velle présentée dans ce travail. Nous évaluons la performance des modèles en calculant des énergies d’échange et ses contributions à des énergies d’atomisation. On constate que les oscillations causeés par les bases de type gaussiennes peuvent compromettre la précision et la solution des modèles.