Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

We present the analytical investigations on a logistic map with a discontinuity at the centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also shows the presence of multiple attractors. Our results are verified by numerical experiments as well.

Investigations on the Radiation Characteristics of Broadband Strip Loaded Slotted Microstrip Antennas

With the recent progress and rapid increase in mobile terminals, the design of antennas for small mobile terminals is acquiring great importance. In view of this situation, several design concepts are already been addressed by the scientists and engineers. Compactness and efficiency are the major criteria for mobile terminal antennas. The challenging task of the microwave scientists and engineers is to device compact printed radiating systems having broadband behavior, together with good efficiency. Printed antenna technology has received popularity among antenna scientists after the introduction of microstrip antenna in 1970s. The successors in this kind such as printed monopoles and planar inverted F are also equally important. Scientists and Engineers are trying to explore this technology as a viable coast effective solution for forthcoming microwave revolution. The transmission line perspectives of antennas are very interesting. The concept behind any electromagnetic radiator is simple. Any electromagnetic system with a discontinuity is radiating electromagnetic energy. The size, shape and the orientation of the discontinuities controls the radiation characteristics of the system such as radiation pattern, gain, polarization etc. It can be either resonant or non resonant structure. Microstrip antennas are suitable for wireless applications due to their low cost, high gain and ease of fabrication. But the major disadvantage of micro strip antennas is their inherent narrow bandwidth. A lot of techniques are introduced by the researchers all over the world to enhance the bandwidth of micro strip patch antennas. The thesis addresses an attempt to enhance the bandwidth of micro strip patch antennas by incorporating impedance matching strip as a part of the micro strip patch antenna. The first part of the thesis deals with the broadband operation of the tilted square slot and polygonal slot loaded square micro strip patch antennas. The resonant mechanisms are clearly mentioned using the simulation and experimental studies. The bandwidth of the polygonal slotted broadband patch antenna is again enhanced by implementing an Lstrip feed mechanism. In the second major part of the thesis, a novel gain enhancement technique for single band and broadband square micro strip patch antennas is achieved by implementing offset stacked configurations.

Investigations on the radiation characteristics of new hollow dielectric horn antennas

Investigations on the design and development of certain new hollow dielectric hom antennas of rectangular cross section have been carried out. The main shortcoming of the existing ordinary hollow dielectric hom antenna (HDH) is the abrupt discontinuity at the feed-end. A new launching technique using a dielectric rod is introduced to overcome this limitation. Also a strip loading technique is employed for further modification of the antenna. Radiation parameters of new I-IDH antennas of Eplane sectoral, H-plane sectoral and pyramidal types were studied and are found to be very attractive. Theoretical approach based on Marcatili’s principle and two aperture theory along with diffraction theory and image theory is used to support the experimental findings. The HDH is considered as solid horn of effective dielectric constant and the aperture field is evaluated. The antenna is excited by the open waveguide in the dominant TE1o mode and so the existence of any hybrid mode is mled-out. The theoretical results are observed to be in good agreement with the experimental results.

“Design and Development of Coplanar Strip Fed Planar Antennas”

With the recent progress and rapid increase in the field of communication, the designs of antennas for small mobile terminals with enhanced radiation characteristics are acquiring great importance. Compactness, efficiency, high data rate capacity etc. are the major criteria for the new generation antennas. The challenging task of the microwave scientists and engineers is to design a compact printed radiating structure having broadband behavior along with good efficiency and enhanced gain. Printed antenna technology has received popularity among antenna scientists after the introduction of planar transmission lines in mid-seventies. When we view the antenna through a transmission line concept, the mechanism behind any electromagnetic radiator is quite simple and interesting. Any electromagnetic system with a discontinuity is radiating electromagnetic energy. The size, shape and orientation of the discontinuities control the radiation characteristics of the system such as radiation pattern, gain, polarization etc. It can be either resonant or non-resonant. This thesis deals with antennas that are developed from a class of transmission lines known as coplanar strip-CPS, a planar analogy of parallel pair transmission line. The specialty of CPS is its symmetric structure compared to other transmission lines, which makes the antenna structures developed from CPS quite simple for design and fabrication. The structural modifications on either metallic strip of CPS results in different antennas. The first part of the thesis discusses a single band and dual band design derived from open ended slot lines which are very much suitable for 2.4 and 5.2 GHz WLAN applications. The second section of the study is vectored into the development of enhanced gain dipoles. A single band dipole and a wide band enhanced gain dipole suitable for 5.2/5.8 GHZ band and imaging applications are developed and discussed. Last part of the thesis discusses the development of directional UWBs. Three different types of ultra-compact UWBs are developed and almost all the frequency domain and time domain analysis of the structures are discussed.

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.

Investigations on the Radiation Characteristics of Broadband Strip Loaded Slotted Microstrip Antennas

With the recent progress and rapid increase in mobile terminals, the design of antennas for small mobile terminals is acquiring great importance. In view of this situation, several design concepts are already been addressed by the scientists and engineers. Compactness and efficiency are the major criteria for mobile terminal antennas. The challenging task of the microwave scientists and engineers is to device compact printed radiating systems having broadband behavior, together with good efficiency. Printed antenna technology has received popularity among antenna scientists after the introduction of microstrip antenna in 1970s. The successors in this kind such as printed monopoles and planar inverted F are also equally important. Scientists and Engineers are trying to explore this technology as a viable coast effective solution for forthcoming microwave revolution. The transmission line perspectives of antennas are very interesting. The concept behind any electromagnetic radiator is simple. Any electromagnetic system with a discontinuity is radiating electromagnetic energy. The size, shape and the orientation of the discontinuities controls the radiation characteristics of the system such as radiation pattern, gain, polarization etc. It can be either resonant or non resonant structure.