Applications of Fractal Based Structures in Radar Cross Section Reduction

This thesis presents the Radar Cross Section measurements of different geometric structures such as flat plate,cylinder, corner reflector and circular cone loaded with fractal based metallo dielectric structures.Use of different fractal geometris,metallizations of different shapes as well as the frequency tanability is investigated for TE and TM polarization of the incident electromagnetic field.Application of fractal based metallo-dielectric structures results in RCS reduction over a wide range of frequency bands.RCS enhancement of dihedral corner is observed at certain acute and obtuse corner angles.The experimental results are validated using electromagnetic simulation softwares.

Scattering Behaviour of fractal based metallo-dielectric structures

The scattering behaviour of fractal based metallodielectric structures loaded over metallic targets of different shapes such as flat plate, cylinder and dihedral corner reflector are investigated for both TE and TM polarizations of the incident wave. Out of the various fractal structures studied,square Sierpinski carpet structure is found to give backscattering reduction for an appreciable range of frequencies. The frequency of minimum backscattering depends on the geometry of the structure as well as on the thickness of the substrate. This structure when loaded over a dihedral corner reflector is showing an enhancement in RCS for corner angles other than 90◦.

Radar cross-section enhancement of dihedral corner reflector using fractal-based metallo-dielectric structures

Effective use of fractal-based metallo-dielectric structures for enhancing the radar cross-section (RCS) of dihedral corner reflectors is reported. RCS enhancement of about 30 dBsm is obtained for corner reflectors with corner angles other than 90deg. This may find application in remote sensing and synthetic aperture radar.

Fractal based techniques for classification of mammograms and identification of microcalcifications

After skin cancer, breast cancer accounts for the second greatest number of cancer diagnoses in women. Currently the etiologies of breast cancer are unknown, and there is no generally accepted therapy for preventing it. Therefore, the best way to improve the prognosis for breast cancer is early detection and treatment. Computer aided detection systems (CAD) for detecting masses or micro-calcifications in mammograms have already been used and proven to be a potentially powerful tool , so the radiologists are attracted by the effectiveness of clinical application of CAD systems. Fractal geometry is well suited for describing the complex physiological structures that defy the traditional Euclidean geometry, which is based on smooth shapes. The major contribution of this research include the development of • A new fractal feature to accurately classify mammograms into normal and normal (i)With masses (benign or malignant) (ii) with microcalcifications (benign or malignant) • A novel fast fractal modeling method to identify the presence of microcalcifications by fractal modeling of mammograms and then subtracting the modeled image from the original mammogram. The performances of these methods were evaluated using different standard statistical analysis methods. The results obtained indicate that the developed methods are highly beneficial for assisting radiologists in making diagnostic decisions. The mammograms for the study were obtained from the two online databases namely, MIAS (Mammographic Image Analysis Society) and DDSM (Digital Database for Screening Mammography.

A Novel Planar Fractal Antenna with CPW-Feed for Multiband Applications

In this paper, a multiband antenna using a novel fractal design is presented. The antenna structure is formed by inscribing a hexagonal slot within a circle. This base structure is then scaled and arranged within the hexagon along its sides without touching the outer structure. The proposed CPW fed, low profile antenna offers good performance in the 1.65 – 2.59 GHz, 4.16 – 4.52 GHz and 5.54 – 6.42 GHz bands and is suitable for GSM 1800/1900, Bluetooth, IMT advanced systems and upper WLAN applications. The antenna has been fabricated on a substrate of height 1.6 mm and εr = 4.4 and simulation and experimental results are found to be in good agreement

Fast Fractal Coding Method for the Detection of Microcalcification in Mammograms

The presence of microcalcifications in mammograms can be considered as an early indication of breast cancer. A fastfractal block coding method to model the mammograms fordetecting the presence of microcalcifications is presented in this paper. The conventional fractal image coding method takes enormous amount of time during the fractal block encoding.procedure. In the proposed method, the image is divided intoshade and non shade blocks based on the dynamic range, andonly non shade blocks are encoded using the fractal encodingtechnique. Since the number of image blocks is considerablyreduced in the matching domain search pool, a saving of97.996% of the encoding time is obtained as compared to theconventional fractal coding method, for modeling mammograms.The above developed mammograms are used for detectingmicrocalcifications and a diagnostic efficiency of 85.7% isobtained for the 28 mammograms used.

A New Fast Fractal Modeling Approach for the Detection of Microcalcifications in Mammograms

In this paper, a novel fast method for modeling mammograms by deterministic fractal coding approach to detect the presence of microcalcifications, which are early signs of breast cancer, is presented. The modeled mammogram obtained using fractal encoding method is visually similar to the original image containing microcalcifications, and therefore, when it is taken out from the original mammogram, the presence of microcalcifications can be enhanced. The limitation of fractal image modeling is the tremendous time required for encoding. In the present work, instead of searching for a matching domain in the entire domain pool of the image, three methods based on mean and variance, dynamic range of the image blocks, and mass center features are used. This reduced the encoding time by a factor of 3, 89, and 13, respectively, in the three methods with respect to the conventional fractal image coding method with quad tree partitioning. The mammograms obtained from The Mammographic Image Analysis Society database (ground truth available) gave a total detection score of 87.6%, 87.6%, 90.5%, and 87.6%, for the conventional and the proposed three methods, respectively.

Frequency tunable metallo–dielectric structure for backscattering reduction

Electromagnetic scattering behaviour of a superstrate loaded metallo– dielectric structure based on Sierpinski carpet fractal geometry is reported. The results indicate that the frequency at which backscattering is minimum can be tuned by varying the thickness of the superstrate. A reduction in backscattered power of 44 dB is obtained simultaneously for both TE and TM polarisations of the incident field.

Low backscattered dual-polarised metallo-dielectric structure based on sierpinski carpet

A novel technique for backscattering reduction for both TE and TM polarisation, employing a metallo-dielectric structure based on Sierpinski carpet fractal geometry, is reported. A reduction in backscattered power of --30 dB is obtained for normal incidence in the X-band for the structure using the third iterated stage of the fractal geometry

Secret Sharing Schemes Using Visual Cryptography

Secret sharing schemes allow a secret to be shared among a group of participants so that only qualified subsets of participants can recover the secret. A visual cryptography scheme (VCS) is a special kind of secret sharing scheme in which the secret to share consists of an image and the shares consist of xeroxed transparencies which are stacked to recover the shared image. In this thesis we have given the theoretical background of Secret Sharing Schemes and the historical development of the subject. We have included a few examples to improve the readability of the thesis. We have tried to maintain the rigor of the treatment of the subject. The limitations and disadvantages of the various forms secret sharing schemes are brought out. Several new schemes for both dealing and combining are included in the thesis. We have introduced a new number system, called, POB number system. Representation using POB number system has been presented. Algorithms for finding the POB number and POB value are given.We have also proved that the representation using POB number system is unique and is more efficient. Being a new system, there is much scope for further development in this area.

Investigations on broadband planar monopole and slot radiators and their suitability for UWB applications

In recent years, there is a visible trend for products/services which demand seamless integration of cellular networks, WLANs and WPANs. This is a strong indication for the inclusion of high speed short range wireless technology in future applications. In this context UWB radio has a significant role to play as an extension/complement to existing cellular/access technology. In the present work, we have investigated two major types of wide band planar antennas: Monopole and Slot. Four novel compact broadband antennas, suitable for poratble applications, are designed and characterized, namely 1. Elliptical monopole 2. Inverted cone monopole 3. Koch fractal slot 4. Wide band slot The performance of these designs have been studied using standard simulation tools used in industry/academia and they have been experimentally verified. Antenna design guidelines are also deduced by accounting the resonances in each structure. In addition to having compact sized, high efficiency and broad bandwidth antennas, one of the major criterion in the design of impulse-UWB systems have been the transmission of narrow band pulses with minimum distortion. The key challenge is not only to design a broad band antenna with constant and stable gain but to maintain a flat group delay or linear phase response in the frequency domain or excellent transient response in time domain. One of the major contributions of the thesis lies in the analysis of the frequency and time-domain response of the designed UWB antennas to confirm their suitability for portable pulsed-UWB systems. Techniques to avoid narrowband interference by engraving narrow slot resonators on the antenna is also proposed and their effect on a nano-second pulse have been investigated.

Dynamics of the logistic map under discrete parametric perturbation

By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

An analogue of the logistic map in two dimensions

This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.

Analysis of Fluctuations in the Early Universe Using Fokker-Planck Formalism

The thesis begins with a review of basic elements of general theory of relativity (GTR) which forms the basis for the theoretical interpretation of the observations in cosmology. The first chapter also discusses the standard model in cosmology, namely the Friedmann model, its predictions and problems. We have also made a brief discussion on fractals and inflation of the early universe in the first chapter. In the second chapter we discuss the formulation of a new approach to cosmology namely a stochastic approach. In this model, the dynam ics of the early universe is described by a set of non-deterministic, Langevin type equations and we derive the solutions using the Fokker—Planck formalism. Here we demonstrate how the problems with the standard model, can be eliminated by introducing the idea of stochastic fluctuations in the early universe. Many recent observations indicate that the present universe may be approximated by a many component fluid and we assume that only the total energy density is conserved. This, in turn, leads to energy transfer between different components of the cosmic fluid and fluctuations in such energy transfer can certainly induce fluctuations in the mean to factor in the equation of state p = wp, resulting in a fluctuating expansion rate for the universe. The third chapter discusses the stochastic evolution of the cosmological parameters in the early universe, using the new approach. The penultimate chapter is about the refinements to be made in the present model, by means of a new deterministic model The concluding chapter presents a discussion on other problems with the conventional cosmology, like fractal correlation of galactic distribution. The author attempts an explanation for this problem using the stochastic approach.

DNA Sequence Representation methods

DNA sequence representation methods are used to denote a gene structure effectively and help in similarities/dissimilarities analysis of coding sequences. Many different kinds of representations have been proposed in the literature. They can be broadly classified into Numerical, Graphical, Geometrical and Hybrid representation methods. DNA structure and function analysis are made easy with graphical and geometrical representation methods since it gives visual representation of a DNA structure. In numerical method, numerical values are assigned to a sequence and digital signal processing methods are used to analyze the sequence. Hybrid approaches are also reported in the literature to analyze DNA sequences. This paper reviews the latest developments in DNA Sequence representation methods. We also present a taxonomy of various methods. A comparison of these methods where ever possible is also done