Essays on numerically efficient inference in nonlinear and non-Gaussian state space models, and commodity market analysis.

The first two articles build procedures to simulate vector of univariate states and estimate parameters in nonlinear and non Gaussian state space models. We propose state space speci fications that offer more flexibility in modeling dynamic relationship with latent variables. Our procedures are extension of the HESSIAN method of McCausland[2012]. Thus, they use approximation of the posterior density of the vector of states that allow to : simulate directly from the state vector posterior distribution, to simulate the states vector in one bloc and jointly with the vector of parameters, and to not allow data augmentation. These properties allow to build posterior simulators with very high relative numerical efficiency. Generic, they open a new path in nonlinear and non Gaussian state space analysis with limited contribution of the modeler. The third article is an essay in commodity market analysis. Private firms coexist with farmers' cooperatives in commodity markets in subsaharan african countries. The private firms have the biggest market share while some theoretical models predict they disappearance once confronted to farmers cooperatives. Elsewhere, some empirical studies and observations link cooperative incidence in a region with interpersonal trust, and thus to farmers trust toward cooperatives. We propose a model that sustain these empirical facts. A model where the cooperative reputation is a leading factor determining the market equilibrium of a price competition between a cooperative and a private firm

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

Plasma Polymerised Organic Thin Films-A Study on the Structural, Electrical and Nonlinear Optical Properties for Possible Applications

This proposed thesis is entitled “Plasma Polymerised Organic Thin Films: A study on the Structural, Electrical, and Nonlinear Optical Properties for Possible Applications. Polymers and polymer based materials find enormous applications in the realm of electronics and optoelectronics. They are employed as both active and passive components in making various devices. Enormous research activities are going on in this area for the last three decades or so, and many useful contributions are made quite accidentally. Conducting polymers is such a discovery, and eversince the discovery of conducting polyacetylene, a new branch of science itself has emerged in the form of synthetic metals. Conducting polymers are useful materials for many applications like polymer displays, high density data storage, polymer FETs, polymer LEDs, photo voltaic devices and electrochemical cells. With the emergence of molecular electronics and its potential in finding useful applications, organic thin films are receiving an unusual attention by scientists and engineers alike. This is evident from the vast literature pertaining to this field appearing in various journals. Recently, computer aided design of organic molecules have added further impetus to the ongoing research activities in this area. Polymers, especially, conducting polymers can be prepared both in the bulk and in the thinfilm form. However, many applications necessitate that they are grown in the thin film form either as free standing or on appropriate substrates. As far as their bulk counterparts are concerned, they can be prepared by various polymerisation techniques such as chemical routes and electrochemical means. A survey of the literature reveals that polymers like polyaniline, polypyrrole, polythiophene, have been investigated with a view to studying their structural electrical and optical properties. Among the various alternate techniques employed for the preparation of polymer thin films, the method of plasma polymerisation needs special attention in this context. The technique of plasma polymerisation is an inexpensive method and often requires very less infra structure. This method includes the employment of ac, rf, dc, microwave and pulsed sources. They produce pinhole free homogeneous films on appropriate substrates under controlled conditions. In conventional plasma polymerisation set up, the monomer is fed into an evacuated chamber and an ac/rf/dc/ w/pulsed discharge is created which enables the monomer species to dissociate, leading to the formation of polymer thin films. However, it has been found that the structure and hence the properties exhibited by plasma polymerized thin films are quite different from that of their counterparts produced by other thin film preparation techniques such as electrochemical deposition or spin coating. The properties of these thin films can be tuned only if the interrelationship between the structure and other properties are understood from a fundamental point of view. So very often, a through evaluation of the various properties is a pre-requisite for tailoring the properties of the thin films for applications. It has been found that conjugation is a necessary condition for enhancing the conductivity of polymer thin films. RF technique of plasma polymerisation is an excellent tool to induce conjugation and this modifies the electrical properties too. Both oxidative and reductive doping can be employed to modify the electrical properties of the polymer thin films for various applications. This is where organic thin films based on polymers scored over inorganic thin films, where in large area devices can be fabricated with organic semiconductors which is difficult to achieve by inorganic materials. For such applications, a variety of polymers have been synthesized such as polyaniline, polythiophene, polypyrrole etc. There are newer polymers added to this family every now and then. There are many virgin areas where plasma polymers are yet to make a foray namely low-k dielectrics or as potential nonlinear optical materials such as optical limiters. There are also many materials which are not been prepared by the method of plasma polymerisation. Some of the materials which are not been dealt with are phenyl hydrazine and tea tree oil. The advantage of employing organic extracts like tea tree oil monomers as precursors for making plasma polymers is that there can be value addition to the already existing uses and possibility exists in converting them to electronic grade materials, especially semiconductors and optically active materials for photonic applications. One of the major motivations of this study is to synthesize plasma polymer thin films based on aniline, phenyl hydrazine, pyrrole, tea tree oil and eucalyptus oil by employing both rf and ac plasma polymerisation techniques. This will be carried out with the objective of growing thin films on various substrates such as glass, quartz and indium tin oxide (ITO) coated glass. There are various properties namely structural, electrical, dielectric permittivity, nonlinear optical properties which are to be evaluated to establish the relationship with the structure and the other properties. Special emphasis will be laid in evaluating the optical parameters like refractive index (n), extinction coefficient (k), the real and imaginary components of dielectric constant and the optical transition energies of the polymer thin films from the spectroscopic ellipsometric studies. Apart from evaluating these physical constants, it is also possible to predict whether a material exhibit nonlinear optical properties by ellipsometric investigations. So further studies using open aperture z-scan technique in order to evaluate the nonlinear optical properties of a few selected samples which are potential nonlinear optical materials is another objective of the present study. It will be another endeavour to offer an appropriate explanation for the nonlinear optical properties displayed by these films. Doping of plasma polymers is found to modify both the electrical conductivity and optical properties. Iodine is found to modify the properties of the polymer thin films. However insitu iodine doping is tricky and the film often looses its stability because of the escape of iodine. An appropriate insitu technique of doping will be developed to dope iodine in to the plasma polymerized thin films. Doping of polymer thin films with iodine results in improved and modified optical and electrical properties. However it requires tools like FTIR and UV-Vis-NIR spectroscopy to elucidate the structural and optical modifications imparted to the polymer films. This will be attempted here to establish the role of iodine in the modification of the properties exhibited by the films

Dual-frequency dual-polarized slot -coupled compact microstrip antenna for communication system

A new design of' a dual-frequency dual-polarized square microsh'ip antenna fed along the diagonal, embedded with a square slot having three extended stubs for frequency tuning, is introduced. The proposed antenna was fabricated using a standard photolithographic method and the antenna was tested using the HP 3510(:; Vector Network Analyser. The antenna is capable of generating dual resonant frequencies with mutually perpendicular polarizations and broad radiation pattern characteristics. Such dual-frequency designs find wide applications in personal mobile handsets combining GSM and CDS 1800 modes, and applications in which different frequencies are used for emission and reception such as personal satellite communications and cellular network systems.

INVESTIGATIONS ON SLOT-LOADED SQUARE MICROSTRIP PATCH ANTENNAS FOR COMPACT DUAL FREQUENCY DUAL POLARIZED OPERATIONS

The thesis is the outcome of the experimental and theoretical investigations carried out on a novel slotted microstrip antenna.The antenna excites two resonance frequencies and provides orthogonal polarization. The radiation characteristics of the antenna are studied in detail. The antenna design is optimized using IE3D electromagnetic simulation tool. The frequency-Difference Time-Domain (FDTD) method is employed for the analysis of the antenna.The antenna can be used for personal and satellite communication applications.

Study on the determination of molecular distance in organic dye mixtures using dual beam thermal lens technique

A sensitive method based on the principle of photothermal phenomena to study the energy transfer processes in organic dye mixtures is presented. A dual beam thermal lens method can be very effectively used as an alternate technique to determine the molecular distance between donor and acceptor in fluorescein–rhodamine B mixture using optical parametric oscillator.

Studies on Fluorescence Efficiency and Photodegradation of Rhodamine 6G Doped PMMA Using a Dual Beam Thermal Lens Technique

In this paper we report the use of the dual beam thermal lens technique as a quantitative method to determine absolute fluorescence quantum efficiency and concentration quenching of fluorescence emission from rhodamine 6G doped Poly(methyl methacrylate) (PMMA), prepared with different concentrations of the dye. A comparison of the present data with that reported in the literature indicates that the observed variation of fluorescence quantum yield with respect to the dye concentration follows a similar profile as in the earlier reported observations on rhodamine 6G in solution. The photodegradation of the dye molecules under cw laser excitation is also studied using the present method.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Development and Analysis of a Compact Dual-Band Coplanar Antenna

The coplanar wave guide is an attractive device in microwave integrated circuits due to its uniplanar nature, ease of fabrication and low production cost. Several attempts are already done to explore the radiating modes in coplanar wave guide transmission lines. Usually coplanar wave guides are excited by an SMA connector with its centre conductor connected to the exact middle of the centre strip and the outer ground conductor to the two ground strips. The mode excited on it is purely a bound mode. The E-field distribution in the two slots are out of phase and there for cancels at the far field. This thesis addresses an attempt to excite an in phase E-field distribution in the two slots of the co planar wave guide by employing a feed asymmetry, in order to get radiation from the two large slot discontinuities of the coplanar waveguide. The omni directional distribution of the radiating energy can be achieved by widening the centre strip.The first part of the thesis deals with the investigations on the resonance phenomena of conventional coplanar waveguides at higher frequency bands. Then an offset fed open circuited coplanar waveguide supporting resonance/radiation phenomena is analyzed. Finally, a novel compact co planar antenna geometry with dual band characteristics, suitable for mobile terminal applications is designed and characterized using the inferences from the above study.

Development and Evaluation of Blind Identification Techniques for Nonlinear Systems

Identification and Control of Non‐linear dynamical systems are challenging problems to the control engineers.The topic is equally relevant in communication,weather prediction ,bio medical systems and even in social systems,where nonlinearity is an integral part of the system behavior.Most of the real world systems are nonlinear in nature and wide applications are there for nonlinear system identification/modeling.The basic approach in analyzing the nonlinear systems is to build a model from known behavior manifest in the form of system output.The problem of modeling boils down to computing a suitably parameterized model,representing the process.The parameters of the model are adjusted to optimize a performanace function,based on error between the given process output and identified process/model output.While the linear system identification is well established with many classical approaches,most of those methods cannot be directly applied for nonlinear system identification.The problem becomes more complex if the system is completely unknown but only the output time series is available.Blind recognition problem is the direct consequence of such a situation.The thesis concentrates on such problems.Capability of Artificial Neural Networks to approximate many nonlinear input-output maps makes it predominantly suitable for building a function for the identification of nonlinear systems,where only the time series is available.The literature is rich with a variety of algorithms to train the Neural Network model.A comprehensive study of the computation of the model parameters,using the different algorithms and the comparison among them to choose the best technique is still a demanding requirement from practical system designers,which is not available in a concise form in the literature.The thesis is thus an attempt to develop and evaluate some of the well known algorithms and propose some new techniques,in the context of Blind recognition of nonlinear systems.It also attempts to establish the relative merits and demerits of the different approaches.comprehensiveness is achieved in utilizing the benefits of well known evaluation techniques from statistics. The study concludes by providing the results of implementation of the currently available and modified versions and newly introduced techniques for nonlinear blind system modeling followed by a comparison of their performance.It is expected that,such comprehensive study and the comparison process can be of great relevance in many fields including chemical,electrical,biological,financial and weather data analysis.Further the results reported would be of immense help for practical system designers and analysts in selecting the most appropriate method based on the goodness of the model for the particular context.

Nonlinear Optical Properties of Organic and Polymer Systems

Present thesis has discussed the design and synthesis of polymers suitable for nonlinear optics. Most of the molecules that were studied have shown good nonlinear optical activity. The second order nonlinear optical activity of the polymers was measured experimentally by Kurtz and Perry powder technique. The thesis comprises of eight chapters.The theory of NLO phenomenon and a review about the various nonlinear optical polymers has been discussed in chapter 1. The review has provided a survey of NLO active polymeric materials with a general introduction, which included the principles and the origin of nonlinear optics, and has given emphasis to polymeric materials for nonlinear optics, including guest-host systems, side chain polymers, main chain polymers, crosslinked polymers, chiral polymers etc.Chapter 2 has discussed the stability of the metal incorporated tetrapyrrole molecules, porphyrin, chlorin and bacteriochlorin.Chapter 3 has provided the NLO properties of certain organic molecules by computational tools. The chapter is divided into four parts. The first part has described the nonlinear optical properties of chromophore (D-n-A) and bichromophore (D-n-A-A-n-D) systems, which were separated by methylene spacer, by making use of DPT and semiempirical calculations.Chapter 4: A series of polyurethanes was prepared from cardanol, a renewable resource and a waste of the cashew industry by previously designed bifunctional and multifunctional polymers using quantum theoretical approach.Chapter 5: A series of chiral polyurethanes with main chain bis azo diol groups in the polymer backbone was designed and NLO activity was predicted by ZlNDO/ CV methods.In Chapter 7, polyurethanes were first designed by computational methods and the NLO properties were predicted by correction vector method. The designed bifunctional and multifunctional polyurethanes were synthesized by varying the chiral-achiral diol compositions

Analysis of System Signals Based on Cross Recurrence Method for System Dynamics Characterization

Natural systems are inherently non linear. Recurrent behaviours are typical of natural systems. Recurrence is a fundamental property of non linear dynamical systems which can be exploited to characterize the system behaviour effectively. Cross recurrence based analysis of sensor signals from non linear dynamical system is presented in this thesis. The mutual dependency among relatively independent components of a system is referred as coupling. The analysis is done for a mechanically coupled system specifically designed for conducting experiment. Further, cross recurrence method is extended to the actual machining process in a lathe to characterize the chatter during turning. The result is verified by permutation entropy method. Conventional linear methods or models are incapable of capturing the critical and strange behaviours associated with the dynamical process. Hence any effective feature extraction methodologies should invariably gather information thorough nonlinear time series analysis. The sensor signals from the dynamical system normally contain noise and non stationarity. In an effort to get over these two issues to the maximum possible extent, this work adopts the cross recurrence quantification analysis (CRQA) methodology since it is found to be robust against noise and stationarity in the signals. The study reveals that the CRQA is capable of characterizing even weak coupling among system signals. It also divulges the dependence of certain CRQA variables like percent determinism, percent recurrence and entropy to chatter unambiguously. The surrogate data test shows that the results obtained by CRQA are the true properties of the temporal evolution of the dynamics and contain a degree of deterministic structure. The results are verified using permutation entropy (PE) to detect the onset of chatter from the time series. The present study ascertains that this CRP based methodology is capable of recognizing the transition from regular cutting to the chatter cutting irrespective of the machining parameters or work piece material. The results establish this methodology to be feasible for detection of chatter in metal cutting operation in a lathe.

Theory of differential inequalities with appliciations to singular perturbiation problems and method of lines

During recent years, the theory of differential inequalities has been extensively used to discuss singular perturbation problems and method of lines to partial differential equations. The present thesis deals with some differential inequality theorems and their applications to singularly perturbed initial value problems, boundary value problems for ordinary differential equations in Banach space and initial boundary value problems for parabolic differential equations. The method of lines to parabolic and elliptic differential equations are also dealt The thesis is organised into nine chapters

Studies on some aspects of wave propagation through nonlinear media

Nonlinearity is a charming element of nature and Nonlinear Science has now become one of the most important tools for the fundamental understanding of the nature. Solitons— solutions of a class of nonlinear partial differential equations — which propagate without spreading and having particle— like properties represent one of the most striking aspects of nonlinear phenomena. The study of wave propagation through nonlinear media has wide applications in different branches of physics.Different mathematical techniques have been introduced to study nonlinear systems. The thesis deals with the study of some of the aspects of electromagnetic wave propagation through nonlinear media, viz, plasma and ferromagnets, using reductive perturbation method. The thesis contains 6 chapters