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.

Strategies for Inverse Profiling of Two Dimensional Dielectric Scatterers Using Electromagnetic Illumination

Electromagnetic tomography has been applied to problems in nondestructive evolution, ground-penetrating radar, synthetic aperture radar, target identification, electrical well logging, medical imaging etc. The problem of electromagnetic tomography involves the estimation of cross sectional distribution dielectric permittivity, conductivity etc based on measurement of the scattered fields. The inverse scattering problem of electromagnetic imaging is highly non linear and ill posed, and is liable to get trapped in local minima. The iterative solution techniques employed for computing the inverse scattering problem of electromagnetic imaging are highly computation intensive. Thus the solution to electromagnetic imaging problem is beset with convergence and computational issues. The attempt of this thesis is to develop methods suitable for improving the convergence and reduce the total computations for tomographic imaging of two dimensional dielectric cylinders illuminated by TM polarized waves, where the scattering problem is defmed using scalar equations. A multi resolution frequency hopping approach was proposed as opposed to the conventional frequency hopping approach employed to image large inhomogeneous scatterers. The strategy was tested on both synthetic and experimental data and gave results that were better localized and also accelerated the iterative procedure employed for the imaging. A Degree of Symmetry formulation was introduced to locate the scatterer in the investigation domain when the scatterer cross section was circular. The investigation domain could thus be reduced which reduced the degrees of freedom of the inverse scattering process. Thus the entire measured scattered data was available for the optimization of fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of Symmetry formulation could also be applied to the practical problem of limited angle tomography, as in the case of a buried pipeline, where the ill posedness is much larger. The formulation was also tested using experimental data generated from an experimental setup that was designed. The experimental results confirmed the practical applicability of the formulation.

Two Dimensional Large Amplitude Quasi Solitons in Thin Helium Films

Large amplitude local density fluctuations in a thin superfluid He film is considered. It is shown that these large amplitude fluctuations travel and behave like "quasi-solitons" under collision, even when the full nonlinearity arising from the Van der Waals potential is taken into account.

Solitons and their resonances on two-dimensional superfluid films

The dynamics of saturated two-dimensional superfluid4He films is shown to be governed by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the lowest order nonlinearity, such resonance would happen only if two dimensional effects are taken into account. The amplitude and velocity of the resonant soliton are obtained.

Evidence for the existence of Sarkovskii ordering in a two-dimensional map

We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.

Two-dimensional Microwave Tomographic Imaging of Breast Tissues

Despite its recognized value in detecting and characterizing breast disease, X-ray mammography has important limitations that motivate the quest for alternatives to augment the diagnostic tools that are currently available to the radiologist. The rationale for pursuing electromagnetic methods are based on the significant dielectric contrast between normal and cancerous breast tissues, when exposed to microwaves. The present study analyzes two-dimensional microwave tomographic imaging on normal and malignant breast tissue samples extracted by mastectomy, to assess the suitability of the technique for early detection ofbreast cancer. The tissue samples are immersed in matching coupling medium and are illuminated by 3 GHz signal. 2-D tomographic images ofthe breast tissue samples are reconstructed from the collected scattered data using distorted Born iterative method. Variations of dielectric permittivity in breast samples are distinguishable from the obtained permittivity profiles, which is a clear indication of the presence of malignancy. Hence microwave tomographic imaging is proposed as an alternate imaging modality for early detection ofbreast cancer.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

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

Theory Division Department of Physics