Studies on Fluxon Dynamics in Coupled Josephson Junctions

The thesis deals with detailed theoretical analysis of fluxon dynamics in single and in coupled Josephson junctions of different geometries under various internal and external conditions. The main objective of the present work is to investigate the properties of narrow Long Josephson junctions (LJJs) and to discuss the intriguing physics. In this thesis, Josephson junctions of three types of geometries, viz, rectangular, semiannular and quarter annular geometries in single and coupled format are studied to implement various fluxon based devices. Studies presented in this thesis reveal that mulistacked junctions are extremely useful in the fabrication of various super conducting electronic devices. The stability of the dynamical mode and therefore the operational stability of the proposed devices depend on parameters such as coupling strength, external magnetic fields, damping parameters etc. Stacked junctions offer a promising way to construct high-TC superconducting electronic components. Exploring the complex dynamics of fluxons in coupled junctions is a challenging and important task for the future experimental and theoretical investigations

Studies on the Effect of Randomness on the Synchronization of Coupled Systems and on the Dynamics of Intermittently driven systems

Nonlinear dynamics has emerged into a prominent area of research in the past few Decades.Turbulence, Pattern formation,Multistability etc are some of the important areas of research in nonlinear dynamics apart from the study of chaos.Chaos refers to the complex evolution of a deterministic system, which is highly sensitive to initial conditions. The study of chaos theory started in the modern sense with the investigations of Edward Lorentz in mid 60's. Later developments in this subject provided systematic development of chaos theory as a science of deterministic but complex and unpredictable dynamical systems. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. Here we introduce the concept of noise, and two familiar types of noise are discussed. The classifications and representation of white and colored noise are introduced. Based on this we introduce the concept of randomness that we deal with as a variant of the familiar concept of noise. The dynamical systems introduced are the Rossler system, directly modulated semiconductor lasers and the Harmonic oscillator. The directly modulated semiconductor laser being not a much familiar dynamical system, we have included a detailed introduction to its relevance in Chaotic encryption based cryptography in communication. We show that the effect of a fluctuating parameter mismatch on synchronization is to destroy the synchronization. Further we show that the relation between synchronization error and timescales can be found empirically but there are also cases where this is not possible. Studies show that under the variation of the parameters, the system becomes chaotic, which appears to be the period doubling route to chaos.

Dynamical aspects of coupled Rossler systems: effects of noise

Nonlinear time series analysis is employed to study the complex behaviour exhibited by a coupled pair of Rossler systems. Dimensional analysis with emphasis on the topological correlation dimension and the Kolmogorov entropy of the system is carried out in the coupling parameter space. The regime of phase synchronization is identified and the extent of synchronization between the systems constituting the coupled system is quantified by the phase synchronization index. The effect of noise on the coupling between the systems is also investigated. An exhaustive study of the topological, dynamical and synchronization properties of the nonlinear system under consideration in its characteristic parameter space is attempted.

Permutation Entropy Based Analysis of Complex Signals for Characterising Change in System Dynamics

Timely detection of sudden change in dynamics that adversely affect the performance of systems and quality of products has great scientific relevance. This work focuses on effective detection of dynamical changes of real time signals from mechanical as well as biological systems using a fast and robust technique of permutation entropy (PE). The results are used in detecting chatter onset in machine turning and identifying vocal disorders from speech signal.Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. Here we propose the use of permutation entropy (PE), to detect the dynamical changes in two non linear processes, turning under mechanical system and speech under biological system.Effectiveness of PE in detecting the change in dynamics in turning process from the time series generated with samples of audio and current signals is studied. Experiments are carried out on a lathe machine for sudden increase in depth of cut and continuous increase in depth of cut on mild steel work pieces keeping the speed and feed rate constant. The results are applied to detect chatter onset in machining. These results are verified using frequency spectra of the signals and the non linear measure, normalized coarse-grained information rate (NCIR).PE analysis is carried out to investigate the variation in surface texture caused by chatter on the machined work piece. Statistical parameter from the optical grey level intensity histogram of laser speckle pattern recorded using a charge coupled device (CCD) camera is used to generate the time series required for PE analysis. Standard optical roughness parameter is used to confirm the results.Application of PE in identifying the vocal disorders is studied from speech signal recorded using microphone. Here analysis is carried out using speech signals of subjects with different pathological conditions and normal subjects, and the results are used for identifying vocal disorders. Standard linear technique of FFT is used to substantiate thc results.The results of PE analysis in all three cases clearly indicate that this complexity measure is sensitive to change in regularity of a signal and hence can suitably be used for detection of dynamical changes in real world systems. This work establishes the application of the simple, inexpensive and fast algorithm of PE for the benefit of advanced manufacturing process as well as clinical diagnosis in vocal disorders.