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.

Filamentation in Air and Water and Nonlinear Optical Characterization of Biopolymer Using Ultrashort Laser Pulses

Important issues related to femtosecond (fs) pulses and its relevance to this thesis are discussed. A fundamental characteristic, like the timebandwidth product for fs pulses is decribed in detail. A brief review of generation of ultrashort pulses and its propagation through an optically transparent media are presented. Interaction of strong pulses with matter and different ionization processes are also described. An overview of the thesis is presented at the end

Desorption/ionization Efficiencies Of Triacylglycerols And Phospholipids Via Easi-ms.

Knowledge of the major effects governing desorption/ionization efficiency is required for the development and application of ambient mass spectrometry. Although all triacylglycerols (TAG) have the same favorable protonation and cationization sites, their desorption/ionization efficiencies can vary dramatically during easy ambient sonic-spray ionization because of structural differences in the carbon chain. To quantify this somewhat surprising and drastic effect, we have performed a systematic investigation of desorption/ionization efficiencies as a function of unsaturation and length for TAG as well as for diacylglycerols, monoacylglycerols and several phospholipids (PL). Affinities for Na(+) as a function of unsaturation level have also been assayed via comprehensive metadynamics calculations to understand the influence of this phenomenon on the ionization efficiency. The results suggest that dipole-dipole interactions within a carbon chain tuned by unsaturation sites govern ionization efficiency of TAG and PL.

Effect Of Platform Connection And Abutment Material On Stress Distribution In Single Anterior Implant-supported Restorations: A Nonlinear 3-dimensional Finite Element Analysis.

Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections.

Petroleomics By Electrospray Ionization Ft-icr Mass Spectrometry Coupled To Partial Least Squares With Variable Selection Methods: Prediction Of The Total Acid Number Of Crude Oils.

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

Identification Of Corynebacterium Spp. Isolated From Bovine Intramammary Infections By Matrix-assisted Laser Desorption Ionization-time Of Flight Mass Spectrometry.

Corynebacterium species (spp.) are among the most frequently isolated pathogens associated with subclinical mastitis in dairy cows. However, simple, fast, and reliable methods for the identification of species of the genus Corynebacterium are not currently available. This study aimed to evaluate the usefulness of matrix-assisted laser desorption ionization/mass spectrometry (MALDI-TOF MS) for identifying Corynebacterium spp. isolated from the mammary glands of dairy cows. Corynebacterium spp. were isolated from milk samples via microbiological culture (n=180) and were analyzed by MALDI-TOF MS and 16S rRNA gene sequencing. Using MALDI-TOF MS methodology, 161 Corynebacterium spp. isolates (89.4%) were correctly identified at the species level, whereas 12 isolates (6.7%) were identified at the genus level. Most isolates that were identified at the species level with 16 S rRNA gene sequencing were identified as Corynebacterium bovis (n=156; 86.7%) were also identified as C. bovis with MALDI-TOF MS. Five Corynebacterium spp. isolates (2.8%) were not correctly identified at the species level with MALDI-TOF MS and 2 isolates (1.1%) were considered unidentified because despite having MALDI-TOF MS scores >2, only the genus level was correctly identified. Therefore, MALDI-TOF MS could serve as an alternative method for species-level diagnoses of bovine intramammary infections caused by Corynebacterium spp.

Direct And Non-destructive Proof Of Authenticity For The 2nd Generation Of Brazilian Real Banknotes Via Easy Ambient Sonic Spray Ionization Mass Spectrometry.

Using a desorption/ionization technique, easy ambient sonic-spray ionization coupled to mass spectrometry (EASI-MS), documents related to the 2nd generation of Brazilian Real currency (R$) were screened in the positive ion mode for authenticity based on chemical profiles obtained directly from the banknote surface. Characteristic profiles were observed for authentic, seized suspect counterfeit and counterfeited homemade banknotes from inkjet and laserjet printers. The chemicals in the authentic banknotes' surface were detected via a few minor sets of ions, namely from the plasticizers bis(2-ethylhexyl)phthalate (DEHP) and dibutyl phthalate (DBP), most likely related to the official offset printing process, and other common quaternary ammonium cations, presenting a similar chemical profile to 1st-generation R$. The seized suspect counterfeit banknotes, however, displayed abundant diagnostic ions in the m/z 400-800 range due to the presence of oligomers. High-accuracy FT-ICR MS analysis enabled molecular formula assignment for each ion. The ions were separated by 44 m/z, which enabled their characterization as Surfynol® 4XX (S4XX, XX=40, 65, and 85), wherein increasing XX values indicate increasing amounts of ethoxylation on a backbone of 2,4,7,9-tetramethyl-5-decyne-4,7-diol (Surfynol® 104). Sodiated triethylene glycol monobutyl ether (TBG) of m/z 229 (C10H22O4Na) was also identified in the seized counterfeit banknotes via EASI(+) FT-ICR MS. Surfynol® and TBG are constituents of inks used for inkjet printing.

A Metabolomic Protocol For Plant Systematics By Matrix-assisted Laser-desorption/ionization Time-of Flight Mass Spectrometry.

Matrix-assisted laser desorption/ionization time-of flight mass spectrometry (MALDI-TOF MS) has been widely used for the identification and classification of microorganisms based on their proteomic fingerprints. However, the use of MALDI-TOF MS in plant research has been very limited. In the present study, a first protocol is proposed for metabolic fingerprinting by MALDI-TOF MS using three different MALDI matrices with subsequent multivariate data analysis by in-house algorithms implemented in the R environment for the taxonomic classification of plants from different genera, families and orders. By merging the data acquired with different matrices, different ionization modes and using careful algorithms and parameter selection, we demonstrate that a close taxonomic classification can be achieved based on plant metabolic fingerprints, with 92% similarity to the taxonomic classifications found in literature. The present work therefore highlights the great potential of applying MALDI-TOF MS for the taxonomic classification of plants and, furthermore, provides a preliminary foundation for future research.

Interaction Between Fiscal And Monetary Policy In A Dynamic Nonlinear Model.

The objective of this study is to verify the dynamics between fiscal policy, measured by public debt, and monetary policy, measured by a reaction function of a central bank. Changes in monetary policies due to deviations from their targets always generate fiscal impacts. We examine two policy reaction functions: the first related to inflation targets and the second related to economic growth targets. We find that the condition for stable equilibrium is more restrictive in the first case than in the second. We then apply our simulation model to Brazil and United Kingdom and find that the equilibrium is unstable in the Brazilian case but stable in the UK case.

Unconstrained Finite Element for Geometrical Nonlinear Dynamics of Shells

This paper presents a positional FEM formulation to deal with geometrical nonlinear dynamics of shells. The main objective is to develop a new FEM methodology based on the minimum potential energy theorem written regarding nodal positions and generalized unconstrained vectors not displacements and rotations. These characteristics are the novelty of the present work and avoid the use of large rotation approximations. A nondimensional auxiliary coordinate system is created, and the change of configuration function is written following two independent mappings from which the strain energy function is derived. This methodology is called positional and, as far as the authors' knowledge goes, is a new procedure to approximated geometrical nonlinear structures. In this paper a proof for the linear and angular momentum conservation property of the Newmark beta algorithm is provided for total Lagrangian description. The proposed shell element is locking free for elastic stress-strain relations due to the presence of linear strain variation along the shell thickness. The curved, high-order element together with an implicit procedure to solve nonlinear equations guarantees precision in calculations. The momentum conserving, the locking free behavior, and the frame invariance of the adopted mapping are numerically confirmed by examples. Copyright (C) 2009 H. B. Coda and R. R. Paccola.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems

This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials. An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm. This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available. The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.

A frequency approach to identifying asteroid families II. Families interacting with nonlinear secular resonances and low-order mean-motion resonances

Aims. In an earlier paper we introduced a new method for determining asteroid families where families were identified in the proper frequency domain (n, g, g + s) ( where n is the mean-motion, and g and s are the secular frequencies of the longitude of pericenter and nodes, respectively), rather than in the proper element domain (a, e, sin(i)) (semi-major axis, eccentricity, and inclination). Here we improve our techniques for reliably identifying members of families that interact with nonlinear secular resonances of argument other than g or g + s and for asteroids near or in mean-motion resonant configurations. Methods. We introduce several new distance metrics in the frequency space optimal for determining the diffusion in secular resonances of argument 2g - s, 3g - s, g - s, s, and 2s. We also regularize the dependence of the g frequency as a function of the n frequency (Vesta family) or of the eccentricity e (Hansa family). Results. Our new approaches allow us to recognize as family members objects that were lost with previous methods, while keeping the advantages of the Carruba & Michtchenko (2007, A& A, 475, 1145) approach. More important, an analysis in the frequency domain permits a deeper understanding of the dynamical evolution of asteroid families not always obtainable with an analysis in the proper element domain.