Multipole Theory Analysis of Cutoff Wavenumbers of Waveguides Partially Filled with Dielectric

A new approach, the multipole theory (MT) method, is presented for the computation of cutoff wavenumbers of waveguides partially filled with dielectric. The MT formulation of the eigenvalue problem of an inhomogeneous waveguide is derived. Representative computational examples, including dielectric-rod-loaded rectangular and double-ridged waveguides, are given to validate the theory, and to demonstrate the degree of its efficiency

Use of photoacoustic effect for the detection of phase transitions in liquid crystal mixtures

We report on a laser induced photoacoustic study of the nematic-to-isotropic transition in certain commercial nematic liquid crystal mixtures, namely BL001, BL002, BL032 and BL035. A simple analysis of the experimental data using the Rosencwaig–Gersho theory shows that the heat capacities of all these compounds exhibit a sharp peak as the temperature of the sample is varied across the transition region. Also, substantial differences in the photoacoustic signal amplitudes in nematic and isotropic phases have been noticed for all the mixtures. The increased light scattering property of the nematic phase may be the reason for the enhanced photoacoustic signal amplitude in this phase.

Use of photoacoustic effect for the detection of phase transitions in liquid crystal mixtures

We report on a laser induced photoacoustic study of the nematic-to-isotropic transition in certain commercial nematic liquid crystal mixtures, namely BL001, BL002, BL032 and BL035. A simple analysis of the experimental data using the Rosencwaig–Gersho theory shows that the heat capacities of all these compounds exhibit a sharp peak as the temperature of the sample is varied across the transition region. Also, substantial differences in the photoacoustic signal amplitudes in nematic and isotropic phases have been noticed for all the mixtures. The increased light scattering property of the nematic phase may be the reason for the enhanced photoacoustic signal amplitude in this phase

Use of photoacoustic effect for the detection of phase transitions in liquid crystal mixtures

We report on a laser induced photoacoustic study of the nematic-to-isotropic transition in certain commercial nematic liquid crystal mixtures, namely BL001, BL002, BL032 and BL035. A simple analysis of the experimental data using the Rosencwaig–Gersho theory shows that the heat capacities of all these compounds exhibit a sharp peak as the temperature of the sample is varied across the transition region. Also, substantial differences in the photoacoustic signal amplitudes in nematic and isotropic phases have been noticed for all the mixtures. The increased light scattering property of the nematic phase may be the reason for the enhanced photoacoustic signal amplitude in this phase.

Studies on the propagation of errors in physical oceanographic computations

The results of an investigation on the limits of the random errors contained in the basic data of Physical Oceanography and their propagation through the computational procedures are presented in this thesis. It also suggest a method which increases the reliability of the derived results. The thesis is presented in eight chapters including the introductory chapter. Chapter 2 discusses the general theory of errors that are relevant in the context of the propagation of errors in Physical Oceanographic computations. The error components contained in the independent oceanographic variables namely, temperature, salinity and depth are deliniated and quantified in chapter 3. Chapter 4 discusses and derives the magnitude of errors in the computation of the dependent oceanographic variables, density in situ, gt, specific volume and specific volume anomaly, due to the propagation of errors contained in the independent oceanographic variables. The errors propagated into the computed values of the derived quantities namely, dynamic depth and relative currents, have been estimated and presented chapter 5. Chapter 6 reviews the existing methods for the identification of level of no motion and suggests a method for the identification of a reliable zero reference level. Chapter 7 discusses the available methods for the extension of the zero reference level into shallow regions of the oceans and suggests a new method which is more reliable. A procedure of graphical smoothening of dynamic topographies between the error limits to provide more reliable results is also suggested in this chapter. Chapter 8 deals with the computation of the geostrophic current from these smoothened values of dynamic heights, with reference to the selected zero reference level. The summary and conclusion are also presented in this chapter.

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.