Scaling relations in the Lyapunov exponents of one dimensional maps

We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map. where the scaling index is found to be different.

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

Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal

The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.

Bifurcation structure and Lyapunov exponents of a modulated logistic map

We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

Studies on Rubber Composition as Passive Acoustic Materials in Underwater Electro Acoustic Tranducer Technology and Their aging Characteristic

The research work has been in the area of compounding and characterization of rubbers for use in under water electro acoustic transducers. The study also covers specific material system such as encapsulation materials, baffle material, seal material, etc. Life prediction techniques of under water rubbers in general have been established with reference to more than one functional property. Ranges of passive materials, besides the active sensing material go into the construction of underwater electro acoustic transducers. Reliability of the transducer is critically dependent on these passive materials. Rubbers are a major class of passive materials. The present work concentrates on these materials. Conventional rubbers are inadequate to meet many of the stringent function specific requirements. There exists a large gap of information in the rubber technology of underwater rubbers, particularly relating to underwater electro acoustic transducers. This study is towards filling up the gaps of information in this crucial area. Water intake into rubber is considered as the single most important issue for the long-term performance of rubbers, especially Neoprene. In this study, the cause and effects of a range of parameters affecting the water absorption by diffusion and permeation have been investigated.

STUDIES ON THE STRESS FLUCTUATIONS IN SHEARED STOKESIAN SUSPENSIONS USING CHAOS THEORY AND NONLINEAR DYNAMICS

The thesis report results obtained from a detailed analysis of the fluctuations of the rheological parameters viz. shear and normal stresses, simulated by means of the Stokesian Dynamics method, of a macroscopically homogeneous sheared suspension of neutrally buoyant non-Brownian suspension of identical spheres in the Couette gap between two parallel walls in the limit of vanishingly small Reynolds numbers using the tools of non-linear dynamics and chaos theory for a range of particle concentration and Couette gaps. The thesis used the tools of nonlinear dynamics and chaos theory viz. average mutual information, space-time separation plots, visual recurrence analysis, principal component analysis, false nearest-neighbor technique, correlation integrals, computation of Lyapunov exponents for a range of area fraction of particles and for different Couette gaps. The thesis observed that one stress component can be predicted using another stress component at the same area fraction. This implies a type of synchronization of one stress component with another stress component. This finding suggests us to further analysis of the synchronization of stress components with another stress component at the same or different area fraction of particles. The different model equations of stress components for different area fraction of particles hints at the possible existence a general formula for stress fluctuations with area fraction of particle as a parameter

The Steady-State and Transient Characteristic Analysis of Thermal Fixing a Photorefractive Hologram Grating in Lithium Niobate

The transient interaction between a refraction index grating and light beams during simultaneous writing and thermal fixing of a photorefractive hologram is investigated. With a diffusion- and photovoltaic-dominated carrier transport mechanism and carrier thermal activation (temperature dependent) considered in Fe:LiNbO3 crystal, from the standpoint of field-material coupling, the theoretical thermal fixing time and the space-charge field buildup, spatial distribution, and temperature dependence are given numerically by combining the band transport model with mobile ions with the coupled-wave equation

Unusual autofluorescence characteristic of cultured red-rain cells

The red cells found in the red rain in Kerala, India are now considered as a possible case of extraterrestrial life form. These cells can undergo rapid replication even at an extreme high temperature of 300 deg C. They can also be cultured in diverse unconventional chemical substrates. The molecular composition of these cells is yet to be identified. This paper reports the unusual autofluorescence characteristic of the cultured red rain cells. A spectrofluorimetric study has been performed to investigate this, which shows a systematic shift of the fluorescence emission peak wavelength as the excitation wavelength is increased. Conventional biomolecules are not known to have this property. Details of this investigation and the results are discussed.

Nonlinear Dynamics of Multiple Quantum Well Lasers: Chaos and Multistability

This thesis presents analytical and numerical results from studies based on the multiple quantum well laser rate equation model. We address the problem of controlling chaos produced by direct modulation of laser diodes. We consider the delay feedback control methods for this purpose and study their performance using numerical simulation. Besides the control of chaos, control of other nonlinear effects such as quasiperiodicity and bistability using delay feedback methods are also investigated.A number of secure communication schemes based on synchronization of chaos semiconductor lasers have been successfully demonstrated theoretically and experimentally. The current investigations in these field include the study of practical issues on the implementations of such encryption schemes. We theoretically study the issues such as channel delay, phase mismatch and frequency detuning on the synchronization of chaos in directly modulated laser diodes. It would be helpful for designing and implementing chaotic encryption schemes using synchronization of chaos in modulated semiconductor lasers.

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.

Suppression of chaos through reverse period doubling in coupled directly modulated semiconductor lasers

The effect of coupling on two high frequency modulated semiconductor lasers is numerically studied. The phase diagrams and bifurcatio.n diagrams are drawn. As the coupling constant is increased the system goes from chaotic to periodic behavior through a reverse period doubling sequence. The Lyapunov exponent is calculated to characterize chaotic and periodic regions.

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.

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.

Phase effects on synchronization by dynamical relaying in delay-coupled systems

Synchronization in an array of mutually coupled systems with a finite time delay in coupling is studied using the Josephson junction as a model system. The sum of the transverse Lyapunov exponents is evaluated as a function of the parameters by linearizing the equation about the synchronization manifold. The dependence of synchronization on damping parameter, coupling constant, and time delay is studied numerically. The change in the dynamics of the system due to time delay and phase difference between the applied fields is studied. The case where a small frequency detuning between the applied fields is also discussed.

Characteristic Study of the Boundary Layer Parameters over the Arabian Sea and the Bay of Bengal Using the QuikSCAT Dataset

The marine atmospheric boundary layer (MABL) plays a vital role in the transport of momentum and heat from the surface of the ocean into the atmosphere. A detailed study on the MABL characteristics was carried out using high-resolution surface-wind data as measured by the QuikSCAT (Quick scatterometer) satellite. Spatial variations in the surface wind, frictional velocity, roughness parameter and drag coe±cient for the di®erent seasons were studied. The surface wind was strong during the southwest monsoon season due to the modulation induced by the Low Level Jetstream. The drag coe±cient was larger during this season, due to the strong winds and was lower during the winter months. The spatial variations in the frictional velocity over the seas was small during the post-monsoon season (»0.2 m s¡1). The maximum spatial variation in the frictional velocity was found over the south Arabian Sea (0.3 to 0.5 m s¡1) during the southwest monsoon period, followed by the pre-monsoon over the Bay of Bengal (0.1 to 0.25 m s¡1). The mean wind-stress curl during the winter was positive over the equatorial region, with a maximum value of 1.5£10¡7 N m¡3, but on either side of the equatorial belt, a negative wind-stress curl dominated. The area average of the frictional velocity and drag coe±cient over the Arabian Sea and Bay of Bengal were also studied. The values of frictional velocity shows a variability that is similar to the intraseasonal oscillation (ISO) and this was con¯rmed via wavelet analysis. In the case of the drag coe±cient, the prominent oscillations were ISO and quasi-biweekly mode (QBM). The interrelationship between the drag coe±cient and the frictional velocity with wind speed in both the Arabian Sea and the Bay of Bengal was also studied.