Studies on the universal parameters and onset of chaos in dissipative systems

It has become clear over the last few years that many deterministic dynamical systems described by simple but nonlinear equations with only a few variables can behave in an irregular or random fashion. This phenomenon, commonly called deterministic chaos, is essentially due to the fact that we cannot deal with infinitely precise numbers. In these systems trajectories emerging from nearby initial conditions diverge exponentially as time evolves)and therefore)any small error in the initial measurement spreads with time considerably, leading to unpredictable and chaotic behaviour The thesis work is mainly centered on the asymptotic behaviour of nonlinear and nonintegrable dissipative dynamical systems. It is found that completely deterministic nonlinear differential equations describing such systems can exhibit random or chaotic behaviour. Theoretical studies on this chaotic behaviour can enhance our understanding of various phenomena such as turbulence, nonlinear electronic circuits, erratic behaviour of heart and brain, fundamental molecular reactions involving DNA, meteorological phenomena, fluctuations in the cost of materials and so on. Chaos is studied mainly under two different approaches - the nature of the onset of chaos and the statistical description of the chaotic state.

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

" Nonlinear Signal Processing of Electroencephalogram .' Application in the Study of Neurodynamics. "

Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.

”Nonlinear optical properties of polymers containing azomesogens and chiral molecules: theoretical and experimental evaluations."

The present work emphasizes the use of chirality as an efficient tool to synthesize new types of second order nonlinear materials. Second harmonic generation efficiency (SHG) is used as a measure of second order nonlinear response. Nonlinear optical properties of polymers have been studied theoretically and experimentally. Polymers were designed theoretically by ab initio and semiempirical calculations. All the polymeric systems have been synthesized by condensation polymerization. Second harmonic generation efficiency of the synthesized systems has been measured experimentally by Kurtz and Perry powder method

Investigations on Nonlinear and Radiative Properties of Certain Phatonic Materials

Light in its physical and philosophical sense has captured the imagination of human mind right from the dawn of civilization. The invention of lasers in the 60’s caused a renaissance in the field of optics. This intense, monochromatic, highly directional radiation created new frontiers in science and technology. The strong oscillating electric field of laser radiation creates a. polarisation response that is nonlinear in character in the medium through which it passes and the medium acts as a new source of optical field with alternate properties. It was in this context, that the field of optoelectronics which encompasses the generation, modulation, transmission etc. of optical radiation has gained tremendous importance. Organic molecules and polymeric systems have emerged as a class of promising materials of optoelectronics because they offer the flexibility, both at the molecular and bulk levels, to optimize the nonlinearity and other suitable properties for device applications. Organic nonlinear optical media, which yield large third-order nonlinearities, have been widely studied to develop optical devices like high speed switches, optical limiters etc. Transparent polymeric materials have found one of their most promising applicationsin lasers, in which they can be used as active elements with suitable laser dyes doped in it. The solid-matrix dye lasers make possible combination of the advantages of solid state lasers with the possibility of tuning the radiation over a broad spectral range. The polymeric matrices impregnated with organic dyes have not yet widely used because of the low resistance of the polymeric matrices to laser damage, their low dye photostability, and low dye stability over longer time of operation and storage. In this thesis we investigate the nonlinear and radiative properties of certain organic materials and doped polymeric matrix and their possible role in device development

Synthesis, Characterization and Applications of Modified TiO2 Systems

This thesis is divided in to 9 chapters and deals with the modification of TiO2 for various applications include photocatalysis, thermal reaction, photovoltaics and non-linear optics. Chapter 1 involves a brief introduction of the topic of study. An introduction to the applications of modified titania systems in various fields are discussed concisely. Scope and objectives of the present work are also discussed in this chapter. Chapter 2 explains the strategy adopted for the synthesis of metal, nonmetal co-doped TiO2 systems. Hydrothermal technique was employed for the preparation of the co-doped TiO2 system, where Ti[OCH(CH3)2]4, urea and metal nitrates were used as the sources for TiO2, N and metals respectively. In all the co-doped systems, urea to Ti[OCH(CH3)2]4 was taken in a 1:1 molar ratio and varied the concentration of metals. Five different co-doped catalytic systems and for each catalysts, three versions were prepared by varying the concentration of metals. A brief explanation of physico-chemical techniques used for the characterization of the material was also presented in this chapter. This includes X-ray Diffraction (XRD), Raman Spectroscopy, FTIR analysis, Thermo Gravimetric Analysis, Energy Dispersive X-ray Analysis (EDX), Scanning Electron Microscopy(SEM), UV-Visible Diffuse Reflectance Spectroscopy (UV-Vis DRS), Transmission Electron Microscopy (TEM), BET Surface Area Measurements and X-ray Photoelectron Spectroscopy (XPS). Chapter 3 contains the results and discussion of characterization techniques used for analyzing the prepared systems. Characterization is an inevitable part of materials research. Determination of physico-chemical properties of the prepared materials using suitable characterization techniques is very crucial to find its exact field of application. It is clear from the XRD pattern that photocatalytically active anatase phase dominates in the calcined samples with peaks at 2θ values around 25.4°, 38°, 48.1°, 55.2° and 62.7° corresponding to (101), (004), (200), (211) and (204) crystal planes (JCPDS 21-1272) respectively. But in the case of Pr-N-Ti sample, a new peak was observed at 2θ = 30.8° corresponding to the (121) plane of the polymorph brookite. There are no visible peaks corresponding to dopants, which may be due to their low concentration or it is an indication of the better dispersion of impurities in the TiO2. Crystallite size of the sample was calculated from Scherrer equation byusing full width at half maximum (FWHM) of the (101) peak of the anatase phase. Crystallite size of all the co-doped TiO2 was found to be lower than that of bare TiO2 which indicates that the doping of metal ions having higher ionic radius into the lattice of TiO2 causes some lattice distortion which suppress the growth of TiO2 nanoparticles. The structural identity of the prepared system obtained from XRD pattern is further confirmed by Raman spectra measurements. Anatase has six Raman active modes. Band gap of the co-doped system was calculated using Kubelka-Munk equation and that was found to be lower than pure TiO2. Stability of the prepared systems was understood from thermo gravimetric analysis. FT-IR was performed to understand the functional groups as well as to study the surface changes occurred during modification. EDX was used to determine the impurities present in the system. The EDX spectra of all the co-doped samples show signals directly related to the dopants. Spectra of all the co-doped systems contain O and Ti as the main components with low concentrations of doped elements. Morphologies of the prepared systems were obtained from SEM and TEM analysis. Average particle size of the systems was drawn from histogram data. Electronic structures of the samples were identified perfectly from XPS measurements. Chapter 4 describes the photocatalytic degradation of herbicides Atrazine and Metolachlor using metal, non-metal co-doped titania systems. The percentage of degradation was analyzed by HPLC technique. Parameters such as effect of different catalysts, effect of time, effect of catalysts amount and reusability studies were discussed. Chapter 5 deals with the photo-oxidation of some anthracene derivatives by co-doped catalytic systems. These anthracene derivatives come underthe category of polycyclic aromatic hydrocarbons (PAH). Due to the presence of stable benzene rings, most of the PAH show strong inhibition towards biological degradation and the common methods employed for their removal. According to environmental protection agency, most of the PAH are highly toxic in nature. TiO2 photochemistry has been extensively investigated as a method for the catalytic conversion of such organic compounds, highlighting the potential of thereof in the green chemistry. There are actually two methods for the removal of pollutants from the ecosystem. Complete mineralization is the one way to remove pollutants. Conversion of toxic compounds to another compound having toxicity less than the initial starting compound is the second way. Here in this chapter, we are concentrating on the second aspect. The catalysts used were Gd(1wt%)-N-Ti, Pd(1wt%)-N-Ti and Ag(1wt%)-N-Ti. Here we were very successfully converted all the PAH to anthraquinone, a compound having diverse applications in industrial as well as medical fields. Substitution of 10th position of desired PAH by phenyl ring reduces the feasibility of photo reaction and produced 9-hydroxy 9-phenyl anthrone (9H9PA) as an intermediate species. The products were separated and purified by column chromatography using 70:30 hexane/DCM mixtures as the mobile phase and the resultant products were characterized thoroughly by 1H NMR, IR spectroscopy and GCMS analysis. Chapter 6 elucidates the heterogeneous Suzuki coupling reaction by Cu/Pd bimetallic supported on TiO2. Sol-Gel followed by impregnation method was adopted for the synthesis of Cu/Pd-TiO2. The prepared system was characterized by XRD, TG-DTG, SEM, EDX, BET Surface area and XPS. The product was separated and purified by column chromatography using hexane as the mobile phase. Maximum isolated yield of biphenyl of around72% was obtained in DMF using Cu(2wt%)-Pd(4wt%)-Ti as the catalyst. In this reaction, effective solvent, base and catalyst were found to be DMF, K2CO3 and Cu(2wt%)-Pd(4wt%)-Ti respectively. Chapter 7 gives an idea about the photovoltaic (PV) applications of TiO2 based thin films. Due to energy crisis, the whole world is looking for a new sustainable energy source. Harnessing solar energy is one of the most promising ways to tackle this issue. The present dominant photovoltaic (PV) technologies are based on inorganic materials. But the high material, low power conversion efficiency and manufacturing cost limits its popularization. A lot of research has been conducted towards the development of low-cost PV technologies, of which organic photovoltaic (OPV) devices are one of the promising. Here two TiO2 thin films having different thickness were prepared by spin coating technique. The prepared films were characterized by XRD, AFM and conductivity measurements. The thickness of the films was measured by Stylus Profiler. This chapter mainly concentrated on the fabrication of an inverted hetero junction solar cell using conducting polymer MEH-PPV as photo active layer. Here TiO2 was used as the electron transport layer. Thin films of MEH-PPV were also prepared using spin coating technique. Two fullerene derivatives such as PCBM and ICBA were introduced into the device in order to improve the power conversion efficiency. Effective charge transfer between the conducting polymer and ICBA were understood from fluorescence quenching studies. The fabricated Inverted hetero junction exhibited maximum power conversion efficiency of 0.22% with ICBA as the acceptor molecule. Chapter 8 narrates the third order order nonlinear optical properties of bare and noble metal modified TiO2 thin films. Thin films were fabricatedby spray pyrolysis technique. Sol-Gel derived Ti[OCH(CH3)2]4 in CH3CH2OH/CH3COOH was used as the precursor for TiO2. The precursors used for Au, Ag and Pd were the aqueous solutions of HAuCl4, AgNO3 and Pd(NO3)2 respectively. The prepared films were characterized by XRD, SEM and EDX. The nonlinear optical properties of the prepared materials were investigated by Z-Scan technique comprising of Nd-YAG laser (532 nm,7 ns and10 Hz). The non-linear coefficients were obtained by fitting the experimental Z-Scan plot with the theoretical plots. Nonlinear absorption is a phenomenon defined as a nonlinear change (increase or decrease) in absorption with increasing of intensity. This can be mainly divided into two types: saturable absorption (SA) and reverse saturable absorption (RSA). Depending on the pump intensity and on the absorption cross- section at the excitation wavelength, most molecules show non- linear absorption. With increasing intensity, if the excited states show saturation owing to their long lifetimes, the transmission will show SA characteristics. Here absorption decreases with increase of intensity. If, however, the excited state has strong absorption compared with that of the ground state, the transmission will show RSA characteristics. Here in our work most of the materials show SA behavior and some materials exhibited RSA behavior. Both these properties purely depend on the nature of the materials and alignment of energy states within them. Both these SA and RSA have got immense applications in electronic devices. The important results obtained from various studies are presented in chapter 9.