Studies on magnetic monopole solutions of non-abelian gauge theories and related problems

In 1931 Dirac studied the motion of an electron in the field of a magnetic monopole and found that the quantization of electric charge can be explained by postulating the mere existence of a magnetic monopole. Since 1974 there has been a resurgence of interest in magnetic monopole due to the work of ‘t’ Hooft and Polyakov who independently observed that monopoles can exist as finite energy topologically stable solutions to certain spontaneously broken gauge theories. The thesis, “Studies on Magnetic Monopole Solutions of Non-abelian Gauge Theories and Related Problems”, reports a systematic investigation of classical solutions of non-abelian gauge theories with special emphasis on magnetic monopoles and dyons which possess both electric and magnetic charges. The formation of bound states of a dyon with fermions and bosons is also studied in detail. The thesis opens with an account of a new derivation of a relationship between the magnetic charge of a dyon and the topology of the gauge fields associated with it. Although this formula has been reported earlier in the literature, the present method has two distinct advantages. In the first place, it does not depend either on the mechanism of symmetry breaking or on the nature of the residual symmetry group. Secondly, the results can be generalized to finite temperature monopoles.

On Szegö’s Type Theorems

This study is to look the effect of change in the ordering of the Fourier system on Szegö’s classical observations of asymptotic distribution of eigenvalues of finite Toeplitz forms.This is done by checking proofs and Szegö’s properties in the new set up.The Fourier system is unconditional [19], any arbitrary ordering of the Fourier system forms a basis for the Hilbert space L2 [-Π, Π].Here study about the classical Szegö’s theorem.Szegö’s type theorem for operators in L2(R+) and check its validity for certain multiplication operators.Since the trigonometric basis is not available in L2(R+) or in L2(R) .This study discussed about the classes of orderings of Haar System in L2 (R+) and in L2(R) in which Szegö’s Type TheoreT Am is valid for certain multiplication operators.It is divided into two sections. In the first section there is an ordering to Haar system in L2(R+) and prove that with respect to this ordering, Szegö’s Type theorem holds for general class of multiplication operators Tƒ with multiplier ƒ ε L2(R+), subject to some conditions on ƒ.Finally in second section more general classes of ordering of Haar system in L2(R+) and in L2(R) are identified in such a way that for certain classes of multiplication operators the asymptotic distribution of eigenvalues exists.

Photoacoustic study of the effect of doping concentration on the transport properties of GaAs epitaxial layers

We report a photoacoustic (PA) study of the thermal and transport properties of a GaAs epitaxial layer doped with Si at varying doping concentration, grown on GaAs substrate by molecular beam epitaxy. The data are analyzed on the basis of Rosencwaig and Gersho’s theory of the PA effect. The amplitude of the PA signal gives information about various heat generation mechanisms in semiconductors. The experimental data obtained from the measurement of the PA signal as a function of modulation frequency in a heat transmission configuration were fitted with the phase of PA signal obtained from the theoretical model evaluated by considering four parameters—viz., thermal diffusivity, diffusion coefficient, nonradiative recombination time, and surface recombination velocity—as adjustable parameters. It is seen from the analysis that the photoacoustic technique is sensitive to the changes in the surface states depend on the doping concentration. The study demonstrates the effectiveness of the photoacoustic technique as a noninvasive and nondestructive method to measure and evaluate the thermal and transport properties of epitaxial layers.

Synthesis, Characterization and Catalytic Activity of Nanocrystalline Ceria Modified With Zirconia

The use of catalysts in chemical and refining processes has increased rapidly since 1945, when oil began to replace coal as the most important industrial raw material. Catalysis has a major impact on the quality of human life as well as economic development. The demand for catalysts is still increasing since catalysis is looked up as a solution to eliminate or replace polluting processes. Metal oxides represent one of the most important and widely employed classes of solid catalysts. Much effort has been spent in the preparation, characterization and application of metal oxides. Recently, great interest has been devoted to the cerium dioxide (CeO2) containing materials due to their broad range of applications in various fields, ranging from catalysis to ceramics, fuel cell technologies, gas sensors, solid state electrolytes, ceramic biomaterials, etc., in addition to the classical application of CeO2 as an additive in the so-called three way catalysts (TWC) for automotive exhaust treatment. Moreover, it can promote water gas shift and steam reforming reactions, favours catalytic activity at the interfacial metal-support sites. The solid solutions of ceria with Group IV transitional-metals deserve particular attention for their applicability in various technologically important catalytic processes. Mesoporous CeO2−ZrO2 solid solutions have been reported to be employed in various reactions which include CO oxidation, soot oxidation, water-gas shift reaction, and so on. Inspired by the unique and promising characteristics of ceria based mixed oxides and solid solutions for various applications, we have selected ceria-zirconia oxides for our studies. The focus of the work is the synthesis and investigation of the structural and catalytic properties of modified and pure ceria-zirconia mixed oxide.

Analysis of Stochastic Volatility Sequences Generated by Product Autoregressive Models

The classical methods of analysing time series by Box-Jenkins approach assume that the observed series uctuates around changing levels with constant variance. That is, the time series is assumed to be of homoscedastic nature. However, the nancial time series exhibits the presence of heteroscedasticity in the sense that, it possesses non-constant conditional variance given the past observations. So, the analysis of nancial time series, requires the modelling of such variances, which may depend on some time dependent factors or its own past values. This lead to introduction of several classes of models to study the behaviour of nancial time series. See Taylor (1986), Tsay (2005), Rachev et al. (2007). The class of models, used to describe the evolution of conditional variances is referred to as stochastic volatility modelsThe stochastic models available to analyse the conditional variances, are based on either normal or log-normal distributions. One of the objectives of the present study is to explore the possibility of employing some non-Gaussian distributions to model the volatility sequences and then study the behaviour of the resulting return series. This lead us to work on the related problem of statistical inference, which is the main contribution of the thesis