Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

Raman and infrared spectral analysis of thallium niobyl phosphates: Tl2NbO2PO4, Tl3NaNb4O9(PO4)2 and TlNbOP2O7

Raman and infrared spectra of Tl2NbO2PO4, Tl3NaNb4O9(PO4)2 and TlNbOP2O7 are reported. The observed bands are assigned in terms of vibrations of NbO6 octahedra and PO4 tetrahedra in the first two compounds and in terms of NbO6 octahedra and P2O7 4− anion in the third compound. The NbO6 octahedra in all the title compounds are found to be corner-shared and distorted. The higher wavenumber values of the ν1 (NbO6) mode and other stretching modes indicate that the NbO6 octahedra in them are distorted in the order TlNbOP2O7 > Tl2NbO2PO4 > Tl3NaNb4O9(PO4)2. The splitting of the ν3 (PO4) mode indicates that PO4 tetrahedra is distorted more in Tl2NbO2PO4 than in Tl3NaNb4O9(PO4)2. The symmetry of P2O7 4− anion in TlNbOP2O7 is lowered. Bands indicate that the P–O–P bridge in the above compound has a bent P–O–P bridge configuration

Implementation of a Neural Network Classifier for Noise Sources in the Ocean

The paper investigates the feasibility of implementing an intelligent classifier for noise sources in the ocean, with the help of artificial neural networks, using higher order spectral features. Non-linear interactions between the component frequencies of the noise data can give rise to certain phase relations called Quadratic Phase Coupling (QPC), which cannot be characterized by power spectral analysis. However, bispectral analysis, which is a higher order estimation technique, can reveal the presence of such phase couplings and provide a measure to quantify such couplings. A feed forward neural network has been trained and validated with higher order spectral features

Design, Fabrication and Characterization of Passive and Active Polymer Photonic Devices

The rapid developments in fields such as fibre optic communication engineering and integrated optical electronics have expanded the interest and have increased the expectations about guided wave optics, in which optical waveguides and optical fibres play a central role. The technology of guided wave photonics now plays a role in generating information (guided-wave sensors) and processing information (spectral analysis, analog-to-digital conversion and other optical communication schemes) in addition to its original application of transmitting information (fibre optic communication). Passive and active polymer devices have generated much research interest recently because of the versatility of the fabrication techniques and the potential applications in two important areas – short distant communication network and special functionality optical devices such as amplifiers, switches and sensors. Polymer optical waveguides and fibres are often designed to have large cores with 10-1000 micrometer diameter to facilitate easy connection and splicing. Large diameter polymer optical fibres being less fragile and vastly easier to work with than glass fibres, are attractive in sensing applications. Sensors using commercial plastic optical fibres are based on ideas already used in silica glass sensors, but exploiting the flexible and cost effective nature of the plastic optical fibre for harsh environments and throw-away sensors. In the field of Photonics, considerable attention is centering on the use of polymer waveguides and fibres, as they have a great potential to create all-optical devices. By attaching organic dyes to the polymer system we can incorporate a variety of optical functions. Organic dye doped polymer waveguides and fibres are potential candidates for solid state gain media. High power and high gain optical amplification in organic dye-doped polymer waveguide amplifier is possible due to extremely large emission cross sections of dyes. Also, an extensive choice of organic dye dopants is possible resulting in amplification covering a wide range in the visible region.

Investigations on Photoconductivity and Electrical Switiching in Selected Chalcogenide Glasses

In this thesis, we present the results of our investigations on the photoconducting and electrical switching properties of selected chalcogenide glass systems. We have used XRD and X-ray photoelectron spectroscopy (XPS) analysis for confinuing the amorphous nature of these materials and for confirming their constituents respectively.Photoconductivity is the enhancement in electrical conductivity of materials brought about by the motion of charge carriers excited by absorbed radiation. The phenomenon involves absorption, photogeneration, recombination and transport processes and it gives good insight into the density of states in the energy gap of solids due to the presence of impurities and lattice defects. Photoconductivity measurements lead to the determination of such important parameters as quantum efficiency, photosensiti\'ity, spectral sensitivity and carrier lifetime. Extensive research work on photoconducting properties of amorphous semiconductors has resulted in the development of a variety of very sensitive photodetectors. Photoconductors are finding newer and newer uses eyery day. CdS, CdSe. Sb2S3, Se, ZnO etc, are typical photoconducting materials which are used in devices like vidicons, light amplifiers, xerography equipment etc.Electrical switching is another interesting and important property possessed by several Te based chalcogenides. Switching is the rapid and reversible transition between a highly resistive OFF state, driven by an external electric field and characterized by a threshold voltage, and a low resistivity ON state, Switching can be either threshold type or memory type. The phenomenon of switching could find applications in areas like infonnation storage, electrical power control etc. Investigations on electrical switching in chalcogenide glasses help in understanding the mechanism of switching which is necessary to select and modify materials for specific switching applications.Analysis of XRD pattern gives no further infonuation about amorphous materials than revealing their disordered structure whereas x-ray photoelectron spectroscopy,XPS) provides information about the different constituents present in the material. Also it gives binding energies (b.e.) of an element in different compounds and hence b.e. shift from the elemental form.Our investigations have been concentrated on the bulk glasses, Ge-In-Se, Ge-Bi-Se and As-Sb-Se for photoconductivity measurements and In-Te for electrical switching. The photoconducting properties of Ge-Sb-Se thin films prepared by sputtering technique have also been studied. The bulk glasses for the present investigations are prepared by the melt quenching technique and are annealed for half an hour at temperatures just below their respective glass transition temperatures. The dependence of photoconducting propenies on composition and temperature are investigated in each system. The electrical switching characteristics of In-Te system are also studied with different compositions and by varying the temperature.

Identification of spectral lines of elements using artificial neural networks

Artificial neural networks (ANNs) are relatively new computational tools that have found extensive utilization in solving many complex real-world problems. This paper describes how an ANN can be used to identify the spectral lines of elements. The spectral lines of Cadmium (Cd), Calcium (Ca), Iron (Fe), Lithium (Li), Mercury (Hg), Potassium (K) and Strontium (Sr) in the visible range are chosen for the investigation. One of the unique features of this technique is that it uses the whole spectrum in the visible range instead of individual spectral lines. The spectrum of a sample taken with a spectrometer contains both original peaks and spurious peaks. It is a tedious task to identify these peaks to determine the elements present in the sample. ANNs capability of retrieving original data from noisy spectrum is also explored in this paper. The importance of the need of sufficient data for training ANNs to get accurate results is also emphasized. Two networks are examined: one trained in all spectral lines and other with the persistent lines only. The network trained in all spectral lines is found to be superior in analyzing the spectrum even in a noisy environment.

Swift heavy ion induced surface and microstructural evolution in metallic glass thin films

Swift heavy ion induced changes in microstructure and surface morphology of vapor deposited Fe–Ni based metallic glass thin films have been investigated by using atomic force microscopy, X-ray diffraction and transmission electron microscopy. Ion beam irradiation was carried out at room temperature with 103 MeV Au9+ beam with fluences ranging from 3 1011 to 3 1013 ions/cm2. The atomic force microscopy images were subjected to power spectral density analysis and roughness analysis using an image analysis software. Clusters were found in the image of as-deposited samples, which indicates that the film growth is dominated by the island growth mode. As-deposited films were amorphous as evidenced from X-ray diffraction; however, high resolution transmission electron microscopy measurements revealed a short range atomic order in the samples with crystallites of size around 3 nm embedded in an amorphous matrix. X-ray diffraction pattern of the as-deposited films after irradiation does not show any appreciable changes, indicating that the passage of swift heavy ions stabilizes the short range atomic ordering, or even creates further amorphization. The crystallinity of the as-deposited Fe–Ni based films was improved by thermal annealing, and diffraction results indicated that ion beam irradiation on annealed samples results in grain fragmentation. On bombarding annealed films, the surface roughness of the films decreased initially, then, at higher fluences it increased. The observed change in surface morphology of the irradiated films is attributed to the interplay between ion induced sputtering, volume diffusion and surface diffusion

Magnetic and topographical modifications of amorphous Co–Fe thin films induced by high energy Ag7+ ion irradiation

We have investigated the effects of swift heavy ion irradiation on thermally evaporated 44 nm thick, amorphous Co77Fe23 thin films on silicon substrates using 100 MeV Ag7+ ions fluences of 1 1011 ions/ cm2, 1 1012 ions/cm2, 1 1013 ions/cm2, and 3 1013 ions/cm2. The structural modifications upon swift heavy irradiation were investigated using glancing angle X-ray diffraction. The surface morphological evolution of thin film with irradiation was studied using Atomic Force Microscopy. Power spectral density analysis was used to correlate the roughness variation with structural modifications investigated using X-ray diffraction. Magnetic measurements were carried out using vibrating sample magnetometry and the observed variation in coercivity of the irradiated films is explained on the basis of stress relaxation. Magnetic force microscopy images are subjected to analysis using the scanning probe image processor software. These results are in agreement with the results obtained using vibrating sample magnetometry. The magnetic and structural properties are correlated

Structural, topographical and magnetic evolution of RF-sputtered Fe-Ni alloy based thin films with thermal annealing

Metglas 2826 MB having a nominal composition of Fe40Ni38Mo4B18 is an excellent soft magnetic material and finds application in sensors and memory heads. However, the thin-film forms of Fe40Ni38Mo4B18 are seldom studied, although they are important in micro-electro-mechanical systems/nano-electromechanical systems devices. The stoichiometry of the film plays a vital role in determining the structural and magnetic properties of Fe40Ni38Mo4B18 thin films: retaining the composition in thin films is a challenge. Thin films of 52 nm thickness were fabricated by RF sputtering technique on silicon substrate from a target of nominal composition of Fe40Ni38Mo4B18. The films were annealed at temperatures of 400 °C and 600 °C. The micro-structural studies of films using glancing x-ray diffractometer (GXRD) and transmission electron microscope (TEM) revealed that pristine films are crystalline with (FeNiMo)23B6 phase. Atomic force microscope (AFM) images were subjected to power spectral density analysis to understand the probable surface evolution mechanism during sputtering and annealing. X-ray photoelectron spectroscopy (XPS) was employed to determine the film composition. The sluggish growth of crystallites with annealing is attributed to the presence of molybdenum in the thin film. The observed changes in magnetic properties were correlated with annealing induced structural, compositional and morphological changes

Inertial oscillation forced by the September 1997 cyclone in the Bay of Bengal

Time-series measurements from a moored data buoy located in the Bay of Bengal captured signals of inertial oscillation forced by the September 1997 cyclone. The progressive vector diagram showed mean northeastward current with well-defined clockwise circulation. Spectral analysis exhibited inertial peak at 0.67 cpd with blue shift and high rotary coefficient of –0.99, which signifies strong circular inertial oscillation. The wind and SST also exhibited spectral peak at inertial band (0.69 cpd) with higher blue shift. The inertial amplitude of 148.8 cm/s corresponding to a wind stress of 0.99 N/m2 and spectral peak near the local inertial frequency (0.653 cpd) indicate that the transfer of momentum was high.

Synthesis, characterization and benzylation activity of nanocrystalline chromia loaded sulfated titania prepared via sol–gel route

Chromia loaded sulfated titania has been synthesized via sol–gel route with different chromia loadings. These catalysts are characterized using conventional techniques such as XRD analysis, FTIR analysis, surface area and pore volume measurements, EDX, SEM and UV–Vis diffuse reflectance spectral analysis. Acidity is measured using spectrophotometric monitoring of adsorption of perylene, thermogravimetric desorption of 2,6-dimethylpyridine and temperature programmed desorption of ammonia. Activity studies are done in the liquid phase. It has been concluded that Lewis acid sites are responsible for the benzylation of arenes with benzyl chloride.

Influence of residual cations (Na+, K+ and Mg2+) in the alkylation activity of benzene with 1-octene over rare earth metal ion exchanged FAU–Y zeolite

The effect of residual cations in rare earth metal modified faujasite–Y zeolite has been monitored using magic angle spinning NMR spectral analysis and catalytic activity studies. The second metal ions being used are Na+, K+ and Mg+. From a comparison of the spectra of different samples, it is concluded that potassium and magnesium exchange causes a greater downfield shift in the 29Si NMR peaks. Also, lanthanum exchanged samples show migration behavior from large cages to small cages, which causes the redistribution of second counter cations. It is also observed that Mg2+ causes the most effective migration of lanthanum ions due to its greater charge. The prepared systems were effectively employed for the alkylation of benzene with 1-octene in the vapor phase. From the deactivation studies it is observed that the as-exchanged zeolites possess better stability towards reaction condition over the pure HFAU zeolite.

Vanadia supported on ceria: Characterization and activity in liquid-phase oxidation of ethylbenzene

Vanadia/ceria catalysts (2–10 wt% of V2O5) were prepared by wet impregnation of ammonium metavanadate in oxalic acid solution. Structural characterization was done with energy dispersive X-ray analysis (EDX), powder X-ray diffraction (XRD), BET surface area measurements, FT-IR spectroscopy and nuclear magnetic spectral analysis (51V MASNMR). XRD and 51V MASNMR results show highly dispersed vanadia species at lower loadings and the formation of CeVO4 phase at higher V2O5 loading. The catalytic activity of catalysts was conducted in liquid phase oxidation of ethylbenzene with H2O2 as oxidant. The oxidation activity is increased with loading up to 8 wt% V2O5 and then decreased with further increase in V2O5 content to 10 wt%. Different vanadia species evidenced by various techniques were found to be selective towards ethylbenzene oxidation. The CeVO4 formation associated with increased concentration of vanadia on ceria results the production of acetophenone along with 2-hydroxyacetophenone.

Techniques for Enhancing Wind Energy Generation - A CFD Based Multibody Dynamics Approach in Horizontal Axis Wind Turbines

Wind energy has emerged as a major sustainable source of energy.The efficiency of wind power generation by wind mills has improved a lot during the last three decades.There is still further scope for maximising the conversion of wind energy into mechanical energy.In this context,the wind turbine rotor dynamics has great significance.The present work aims at a comprehensive study of the Horizontal Axis Wind Turbine (HAWT) aerodynamics by numerically solving the fluid dynamic equations with the help of a finite-volume Navier-Stokes CFD solver.As a more general goal,the study aims at providing the capabilities of modern numerical techniques for the complex fluid dynamic problems of HAWT.The main purpose is hence to maximize the physics of power extraction by wind turbines.This research demonstrates the potential of an incompressible Navier-Stokes CFD method for the aerodynamic power performance analysis of horizontal axis wind turbine.The National Renewable Energy Laboratory USA-NREL (Technical Report NREL/Cp-500-28589) had carried out an experimental work aimed at the real time performance prediction of horizontal axis wind turbine.In addition to a comparison between the results reported by NREL made and CFD simulations,comparisons are made for the local flow angle at several stations ahead of the wind turbine blades.The comparison has shown that fairly good predictions can be made for pressure distribution and torque.Subsequently, the wind-field effects on the blade aerodynamics,as well as the blade/tower interaction,were investigated.The selected case corresponded to a 12.5 m/s up-wind HAWT at zero degree of yaw angle and a rotational speed of 25 rpm.The results obtained suggest that the present can cope well with the flows encountered around wind turbines.The areodynamic performance of the turbine and the flow details near and off the turbine blades and tower can be analysed using theses results.The aerodynamic performance of airfoils differs from one another.The performance mainly depends on co-efficient of performnace,co-efficient of lift,co-efficient of drag, velocity of fluid and angle of attack.This study shows that the velocity is not constant for all angles of attack of different airfoils.The performance parameters are calculated analytically and are compared with the standardized performance tests.For different angles of ,the velocity stall is determined for the better performance of a system with respect to velocity.The research addresses the effect of surface roughness factor on the blade surface at various sections.The numerical results were found to be in agreement with the experimental data.A relative advantage of the theoretical aerofoil design method is that it allows many different concepts to be explored economically.Such efforts are generally impractical in wind tunnels because of time and money constraints.Thus, the need for a theoretical aerofoil design method is threefold:first for the design of aerofoil that fall outside the range of applicability of existing calalogs:second,for the design of aerofoil that more exactly match the requirements of the intended application:and third,for the economic exploration of many aerofoil concepts.From the results obtained for the different aerofoils,the velocity is not constant for all angles of attack.The results obtained for the aerofoil mainly depend on angle of attack and velocity.The vortex generator technique was meticulously studies with the formulation of the specification for the right angle shaped vortex generators-VG.The results were validated in accordance with the primary analysis phase.The results were found to be in good agreement with the power curve.The introduction of correct size VGs at appropriate locations over the blades of the selected HAWT was found to increase the power generation by about 4%