Studies on Quasinormal Modes and Late-time Tails in Black Hole Spacetimes

This thesis Entitled Studies on Quasinormal modes and Late-time tails black hole spacetimes. In this thesis, the signature of these new theories are probed on the evolution of field perturbations on the black hole spacetimes in the theory. Chapter 1 gives a general introduction to black holes and its perturbation formalism. Various concepts in the area covered by the thesis are also elucidated in this chapter. Chapter 2 describes the evolution of massive, charged scalar field perturbations around a Reissner-Nordstrom black hole surrounded by a static and spherically symmetric quintessence. Chapter 3 comprises the evolution of massless scalar, electromagnetic and gravitational fields around spherically symmetric black hole whose asymptotes are defined by the quintessence, with special interest on the late-time behavior. Chapter 4 examines the evolution of Dirac field around a Schwarzschild black hole surrounded by quintessence. Detailed numerical simulations are done to analyze the nature of field on different surfaces of constant radius . Chapter 5is dedicated to the study of the evolution of massless fields around the black hole geometry in the HL gravity.

Grain refinement studies on Mg and Mg-Al based alloys

Demand on magnesium and its alloys is increased significantly in the automotive industry because of their great potential in reducing the weight of components, thus resulting in improvement in fuel efficiency of the vehicle. To date, most of Mg products have been fabricated by casting, especially, by die-casting because of its high productivity, suitable strength, acceptable quality & dimensional accuracy and the components produced through sand, gravity and low pressure die casting are small extent. In fact, higher solidification rate is possible only in high pressure die casting, which results in finer grain size. However, achieving high cooling rate in gravity casting using sand and permanent moulds is a difficult task, which ends with a coarser grain nature and exhibit poor mechanical properties, which is an important aspect of the performance in industrial applications. Grain refinement is technologically attractive because it generally does not adversely affect ductility and toughness, contrary to most other strengthening methods. Therefore formation of fine grain structure in these castings is crucial, in order to improve the mechanical properties of these cast components. Therefore, the present investigation is “GRAIN REFINEMENT STUDIES ON Mg AND Mg-Al BASED ALLOYS”. The primary objective of this present investigation is to study the effect of various grain refining inoculants (Al-4B, Al- 5TiB2 master alloys, Al4C3, Charcoal particles) on Pure Mg and Mg-Al alloys such as AZ31, AZ91 and study their grain refining mechanisms. The second objective of this work is to study the effect of superheating process on the grain size of AZ31, AZ91 Mg alloys with and without inoculants addition. In addition, to study the effect of grain refinement on the mechanical properties of Mg and Mg-Al alloys. The thesis is well organized with seven chapters and the details of the studies are given below in detail.

Numerical Modelling of Tsunami Propagation in the South East Arabian Sea (SEAS) and Inundation along the Kerala Coast

Tsunamis are water waves generated by a sudden vertical displacement of the water surface. They are waves generated in the ocean by the disturbance associated with seismic activity, under sea volcanic eruptions, submarine landslides, nuclear explosion or meteorite impacts with the ocean. These waves are generated in the ocean and travel into coastal bays, gulfs, estuaries and rivers. These waves travel as gravity waves with a velocity dependent on water depth. The term tsunami is Japanese and means harbour (tsu) and wave (nami). It has been named so because such waves often develop resonant phenomena in harbours after offshore earthquakes.

Modelling of Ultraviolet and Vissible Emissions in Comets

Comets are the spectacular objects in the night sky since the dawn of mankind. Due to their giant apparitions and enigmatic behavior, followed by coincidental calamities, they were termed as notorious and called as `bad omens'. With a systematic study of these objects modern scienti c community understood that these objects are part of our solar system. Comets are believed to be remnant bodies of at the end of evolution of solar system and possess the material of solar nebula. Hence, these are considered as most pristine objects which can provide the information about the conditions of solar nebula. These are small bodies of our solar system, with a typical size of about a kilometer to a few tens of kilometers orbiting the Sun in highly elliptical orbits. The solid body of a comet is nucleus which is a conglomerated mixture of water ice, dust and some other gases. When the cometary nucleus advances towards the Sun in its orbit the ices sublimates and produces the gaseous envelope around the nucleus which is called coma. The gravity of cometary nucleus is very small and hence can not in uence the motion of gases in the cometary coma. Though the cometary nucleus is a few kilometers in size they can produce a transient, extensive, and expanding atmosphere with size several orders of magnitude larger in space. By ejecting gas and dust into space comets became the most active members of the solar system. The solar radiation and the solar wind in uences the motion of dust and ions and produces dust and ion tails, respectively. Comets have been observed in di erent spectral regions from rocket, ground and space borne optical instruments. The observed emission intensities are used to quantify the chemical abundances of di erent species in the comets. The study of various physical and chemical processes that govern these emissions is essential before estimating chemical abundances in the coma. Cameron band emission of CO molecule has been used to derive CO2 abundance in the comets based on the assumption that photodissociation of CO2 mainly produces these emissions. Similarly, the atomic oxygen visible emissions have been used to probe H2O in the cometary coma. The observed green ([OI] 5577 A) to red-doublet emission ([OI] 6300 and 6364 A) ratio has been used to con rm H2O as the parent species of these emissions. In this thesis a model is developed to understand the photochemistry of these emissions and applied to several comets. The model calculated emission intensities are compared with the observations done by space borne instruments like International Ultraviolet Explorer (IUE) and Hubble Space Telescope (HST) and also by various ground based telescopes.

Effect of Concentration of DYE on the Storage Life of Plane Wave Gratings on Photopolymer Film

Holographic grating with good storage life in poly(vinyl alcohol) based photopolymer film, prepared by gravity settling method, with reduced concentration of the dye was found to give good diffraction efficiency without crosslinking. The material was found to show good diffraction efficiency and sensitivity (75% diffraction efficiency at exposure energy of 80 mJ/cm2). The shelf life of the photopolymer solution could be improved by storage at a temperature 4 C in refrigerator

Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

Sedimentology and Geochemistry of core sediments from the Ashtamudi estuary and the adjoining coastal plain,central Kerala,India

The evolution of coast through geological time scale is dependent on the transgression-regression event subsequent to the rise or fall of sea level. This event is accounted by investigation of the vertical sediment deposition patterns and their interrelationship for paleo-enviornmental reconstruction. Different methods like sedimentological (grain size and micro-morphological) and geochemical (elemental relationship) analyses as well as radiocarbon dating are generally used to decipher the sea level changes and paleoclimatic conditions of the Quaternary sediment sequence. For the Indian coast with a coastline length of about 7500 km, studies on geological and geomorphological signatures of sea level changes during the Quaternary were reported in general by researchers during the last two decades. However, for the southwest coast of India particularily Kerala which is famous for its coastal landforms comprising of estuaries, lagoons, backwaters, coastal plains, cliffs and barrier beaches, studies pertaining to the marine transgression-regression events in the southern region are limited. The Neendakara-Kayamkulam coastal stretch in central Kerala where the coast is manifested with shore parallel Kayamkulam Lagoon on one side and shore perpendicular Ashtamudi Estuary on the other side indicating existence of an uplifted prograded coastal margin followed by barrier beaches, backwater channels, ridge and runnel topography is an ideal site for studying such events. Hence the present study has been taken up in this context to address the gap area. The location for collection of core samples representing coastal plain, estuarylagoon and offshore regions have been identified based on published literature and available sedimentary records. The objectives of the research work are:  To study the lithological variations and depositional environments of sediment cores along the coastal plain, estuary-lagoon and offshore regions between Kollam and Kayamkulam in the central Kerala coast  To study the transportation and diagenetic history of sediments in the area  To investigate the geochemical characterization of sediments and to elucidate the source-sink relationship  To understand the marine transgression-regression events and to propose a conceptual model for the region The thesis comprises of 8 chapters. The first chapter embodies the preamble for the selection and significance of this research work. The study area is introduced with details on its physiographical, geological, geomorphological, rainfall and climate information. A review of literature, compiling the research on different aspects such as physico-chemical, geomorphological, tectonics, transgression-regression events are presented in the second chapter and they are broadly classified into three viz:- International, National and Kerala. The field data collection and laboratory analyses adopted in the research work are discussed in the third chapter. For collection of sediment core samples from the coastal plains, rotary drilling method was employed whereas for the estuary-lagoon and offshore locations the gravity/piston corer method was adopted. The collected subsurficial samples were analysed for texture, surface micro-texture, elemental analysis, XRD and radiocarbon dating techniques for age determination. The fourth chapter deals with the textural analysis of the core samples collected from various predefined locations of the study area. The result reveals that the Ashtamudi Estuary is composed of silty clay to clayey type of sediments whereas offshore cores are carpeted with silty clay to relict sand. Investigation of the source of sediments deposited in the coastal plain located on either side of the estuary indicates the dominance of terrigenous to marine origin in the southern region whereas it is predominantly of marine origin towards the north. Further the hydrodynamic conditions as well as the depositional enviornment of the sediment cores are elucidated based on statistical parameters that decipher the deposition pattern at various locations viz., coastal plain (open to closed basin), Ashtamudi Estuary (partially open to restricted estuary to closed basin) and offshore (open channel). The intensity of clay minerals is also discussed. From the results of radiocarbon dating the sediment depositional environments were deciphered.The results of the microtextural study of sediment samples (quartz grains) using Scanning Electron Microscope (SEM) are presented in the fifth chapter. These results throw light on the processes of transport and diagenetic history of the detrital sediments. Based on the lithological variations, selected quartz grains of different environments were also analysed. The study indicates that the southern coastal plain sediments were transported and deposited mechanically under fluvial environment followed by diagenesis under prolonged marine incursion. But in the case of the northern coastal plain, the sediments were transported and deposited under littoral environment indicating the dominance of marine incursion through mechanical as well as chemical processes. The quartz grains of the Ashtamudi Estuary indicate fluvial origin. The surface texture features of the offshore sediments suggest that the quartz grains are of littoral origin and represent the relict beach deposits. The geochemical characterisation of sediment cores based on geochemical classification, sediment maturity, palaeo-weathering and provenance in different environments are discussed in the sixth chapter. In the seventh chapter the integration of multiproxies data along with radiocarbon dates are presented and finally evolution and depositional history based on transgression–regression events is deciphered. The eighth chapter summarizes the major findings and conclusions of the study with recommendation for future work.

Studies on collective excitations of quasi-two-dimensional Bose-Einstein condensate

Theory Division Department of Physics

Numerical Simulation of Flows at Low Mach Numbers with Heat Sources

This work is concerned with finite volume methods for flows at low mach numbers which are under buoyancy and heat sources. As a particular application, fires in car tunnels will be considered. To extend the scheme for compressible flow into the low Mach number regime, a preconditioning technique is used and a stability result on this is proven. The source terms for gravity and heat are incorporated using operator splitting and the resulting method is analyzed.

A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

Structural Dynamics Model of a Cartesian Robot

Methods are developed for predicting vibration response characteristics of systems which change configuration during operation. A cartesian robot, an example of such a position-dependent system, served as a test case for these methods and was studied in detail. The chosen system model was formulated using the technique of Component Mode Synthesis (CMS). The model assumes that he system is slowly varying, and connects the carriages to each other and to the robot structure at the slowly varying connection points. The modal data required for each component is obtained experimentally in order to get a realistic model. The analysis results in prediction of vibrations that are produced by the inertia forces as well as gravity and friction forces which arise when the robot carriages move with some prescribed motion. Computer simulations and experimental determinations are conducted in order to calculate the vibrations at the robot end-effector. Comparisons are shown to validate the model in two ways: for fixed configuration the mode shapes and natural frequencies are examined, and then for changing configuration the residual vibration at the end of the mode is evaluated. A preliminary study was done on a geometrically nonlinear system which also has position-dependency. The system consisted of a flexible four-bar linkage with elastic input and output shafts. The behavior of the rocker-beam is analyzed for different boundary conditions to show how some limiting cases are obtained. A dimensional analysis leads to an evaluation of the consequences of dynamic similarity on the resulting vibration.

Corner Flows in Free Liquid Films

A lubrication-flow model for a free film in a corner is presented. The model, written in the hyperbolic coordinate system ξ = x² – y², η = 2xy, applies to films that are thin in the η direction. The lubrication approximation yields two coupled evolution equations for the film thickness and the velocity field which, to lowest order, describes plug flow in the hyperbolic coordinates. A free film in a corner evolving under surface tension and gravity is investigated. The rate of thinning of a free film is compared to that of a film evolving over a solid substrate. Viscous shear and normal stresses are both captured in the model and are computed for the entire flow domain. It is shown that normal stress dominates over shear stress in the far field, while shear stress dominates close to the corner.

Determinantes del comercio para países en desarrollo

El documento intenta identificar factores que influyen y afectan el incremento de los niveles de exportaciones de una muestra de países en desarrollo, y porqué el desempeño de algunos países es mejor que otros. La muestra está compuesta por países que para 1991 mostraban niveles similares tanto de exportaciones como de ingresos. Usando una ecuación gravitacional, se realiza la evaluación basada en datos de COMTRADE, y se analizan con respecto a los países de origen y de destino de las exportaciones. A este análisis se incluyen variables económicas como ingreso, demográficas como población e idioma en común, geográficas como distancia, contigüidad, y acceso al mar. Así mismo, se introducen variables que capten el efecto de las políticas de los países como acuerdos comerciales, productividad y educación. El análisis de resultados se realiza tanto para la muestra de países, como para cada país individual; encontrando que la relación bilateral entre países de destino y de origen de exportaciones es determinante del nivel de exportaciones. Así mismo, esta relación está establecida por los niveles de ingresos y variables bilaterales.

Factors that have shaped the eEvolution of bilateral trade between Canada and Colombia in the long run (1953-2003)

Currently bilateral trade between Canada and Colombia is low. In 2003, this trade amounted to US $489 million, with Co­lombian imports from Canada totaling US $ 213 million (DOTS, 2004). Canada supplied approximately 4.0% of Colombia’s total trade (total imports and total ex­ports), in contrast Colombia supplied only around 0.1% of the Canadian total trade. In 2005, Colombia was the third largest Canadian partner in South America after Brazil and Venezuela. The objective of this paper is to analyze the trade performance between Canada and Colombia using a modified gravity equation to identify the most relevant historical factors that have shaped the evo­lution of this bilateral trade in the long run (during the period from 1953 to 2003). The analysis includes traditional economic va­riables (such as population and income of the importing and exporting countries). In order to understand the qualitative nature of the evolution of this bilateral trade the second objective is to review the evolving nature of trade including commodity com­position and trade characteristics.  

Inserción de América Latina en la región de Asia-Pacífico: estrategias unilaterales y multilaterales. Estudio de caso: Alianza del Pacífico

La investigación aborda el tema de la inserción de América Latina en la región de Asia Pacífico, en el caso de la Alianza del Pacífico. A partir de la revisión de las estrategias unilaterales de inserción de Chile, Colombia, México y Perú, y de la estrategia multilateral de la Alianza, se analiza la articulación entre ambas. Al respecto se sostiene que el bloque en cuestión cuenta con un bajo grado de articulación, sin desconocer su potencial para convertirse en puente entre sus Estados miembros y Asia Pacífico.