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.

Studies on the effect of randoniness on the synchronization of coupled systems and on the dynamics of intermittently driven systems

It has been shown recently that systems driven with random pulses show the signature of chaos ,even without non linear dynamics.This shows that the relation between randomness and chaos is much closer than it was understood earlier .The effect of random perturbations on synchronization can be also different. In some cases identical random perturbations acting on two different chaotic systems induce synchronizations. However most commonly ,the effect of random fluctuations on the synchronizations of chaotic system is to destroy synchronization. This thesis deals with the effect of random fluctuations with its associated characteristic timescales on chaos and synchronization. The author tries to unearth yet another manifestation of randomness on chaos and sychroniztion. This thesis is organized into six chapters.

Studies on the dynamics and rheology of dilute suspensions of Brownian particles in simple shear flow under the action of an external force

We present a novel approach to computing the orientation moments and rheological properties of a dilute suspension of spheroids in a simple shear flow at arbitrary Peclct number based on a generalised Langevin equation method. This method differs from the diffusion equation method which is commonly used to model similar systems in that the actual equations of motion for the orientations of the individual particles are used in the computations, instead of a solution of the diffusion equation of the system. It also differs from the method of 'Brownian dynamics simulations' in that the equations used for the simulations are deterministic differential equations even in the presence of noise, and not stochastic differential equations as in Brownian dynamics simulations. One advantage of the present approach over the Fokker-Planck equation formalism is that it employs a common strategy that can be applied across a wide range of shear and diffusion parameters. Also, since deterministic differential equations are easier to simulate than stochastic differential equations, the Langevin equation method presented in this work is more efficient and less computationally intensive than Brownian dynamics simulations.We derive the Langevin equations governing the orientations of the particles in the suspension and evolve a procedure for obtaining the equation of motion for any orientation moment. A computational technique is described for simulating the orientation moments dynamically from a set of time-averaged Langevin equations, which can be used to obtain the moments when the governing equations are harder to solve analytically. The results obtained using this method are in good agreement with those available in the literature.The above computational method is also used to investigate the effect of rotational Brownian motion on the rheology of the suspension under the action of an external force field. The force field is assumed to be either constant or periodic. In the case of con- I stant external fields earlier results in the literature are reproduced, while for the case of periodic forcing certain parametric regimes corresponding to weak Brownian diffusion are identified where the rheological parameters evolve chaotically and settle onto a low dimensional attractor. The response of the system to variations in the magnitude and orientation of the force field and strength of diffusion is also analyzed through numerical experiments. It is also demonstrated that the aperiodic behaviour exhibited by the system could not have been picked up by the diffusion equation approach as presently used in the literature.The main contributions of this work include the preparation of the basic framework for applying the Langevin method to standard flow problems, quantification of rotary Brownian effects by using the new method, the paired-moment scheme for computing the moments and its use in solving an otherwise intractable problem especially in the limit of small Brownian motion where the problem becomes singular, and a demonstration of how systems governed by a Fokker-Planck equation can be explored for possible chaotic behaviour.

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

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

Solvent Effect on Absolute Fluorescence Quantum Yield of Rhodamine 6G Determined Using Transient Thermal Lens Technique

Dual beam thermal lens tecbnique is successfully employed for the determination of absolute Fluorescence quantum yield of rhodamine 6G lnser dye in different solvents. A 532 nm radiation from a Q-switched Nd:YAG laser was used for the excitation purpose. The fluorescence quantum yield values are found to be strongly influenced by environmental effects. It has been observed that fluorescence yield is greater for rhodamine 6G in ethylene glycol system than in water or in methanol. Our results also indicate that parameters like concentration of the dye solution, aggregate formation and excited state absorption affect the absolute values of fluorescence yield significantly.

Performance characteristics of positive and negative delayed feedback on chaotic dynamics of directly modulated InGaAsP semiconductor lasers

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.

Studies on the Dynamics of Cochin Estuary

The thesis entitled Studies on the Dynamics of Cochin Estuary. This thesis is addressed to an investigation on the tidal, seasonal and spatial variations of the hydrographic parameters, circulation and mixing processes of the Cochin estuary. The present programme of study is aimed at obtaining a comprehensive picture of the tidal characteristics, hydrography, circulation and mixing present in this estuarine system during different seasons. The studies have been carried out through field collection of data on salinity, temperature and water currents to get a picture of their spatial and temporal variations. The hydrographic data have been analysed in relation to tide, rainfall and river discharges. From the findings it is seen that at the Cochin inlet, the estuarine features vary annually. During July and August, the estuary is characterised as almost saltwedge type; during June, September, October, December and January it shows appreciabie stratification, and during the rest of the months the estuary shows almost well mixed nature. Seasonal variations are well reflected in water temperature in the Cochin estuary, where the temperature reaches its maximum during the dry pre monsoon period with very weak thermal gradients indicating strong vertical mixing

Studies on nonlinear dynamics of certain reaction systems

The nonlinear dynamics of certain important reaction systems are discussed and analysed in this thesis. The interest in the theoretical and the experimental studies of chemical reactions showing oscillatory dynamics and associated properties is increasing very rapidly. An attempt is made to study some nonlinear phenomena exhibited by the well known chemical oscillator, the BelousovZhabotinskii reaction whose mathematical properties are much in common with the properties of biological oscillators. While extremely complex, this reaction is still much simpler than biological systems at least from the modelling point of view. A suitable model [19] for the system is analysed and the researcher has studied the limit cycle behaviour of the system, for different values of the stoichiometric parameter f, by keeping the value of the reaction rate (k6) fixed at k6 = l. The more complicated three-variable model is stiff in nature.

Studies On The Dynamics And Water Quality Of The Muvattupuzha River In Relation To Effluent Discharge

The present study aims at the investigation of the 1ysico—chemical features of a tropical tidal river viz. we Muvattupuzha river. This river is expected to receive Jderate to heavy pollution loads in years to come, from we lone industrial unit, already set up on its bank. ilike other rivers, the geographical disposition of this Lver attains unique importance as regards its dynamics for 3) availability of natural runoff water from catchment :eas, which becomes very heavy during the monsoon season 3) regular steady availability of tail race water from a /dro—electric power station throughout the yearThe study also aims at arriving at the balancing forces of inherent self~purification of the river verses pollution loads from the factory effluents. The investigation period falls ahead of actual pollution occurrence and so the ambient conditions for a period of nearly one-and-a—half years were investigated, the analyses of which providflz to formulate the inter-relations of parameters varying with seasons. Tracer experiments were carried out which revealed the dispersion and dilution characteristics of the river in the vicinity of effluent outfall. The studv covers the trial—cum-capacity production periods of the factory during which effluents of various strength and quantity were discharged into the river; a few computed values arQ’cjmpgrQdl ... with the observed values. The base data along with the profiles of Oxygen sag equation have been utilized fb develop a mathematical model of the river with regard to its water quality