The three dimensional Monte Carlo radiation transport model McArtim is extended to account for the simulation of the propagation of polarized radiation and the inelastic rotational Raman scattering which is the cause of the so called Ring effect. From the achieved and now sufficient precision of the calculated Ring effect new opportunities in optical absorption spectroscopy arise. In the calculation the method of importance sampling (IS) is applied. Thereby one obtains from an ensemble of Monte Carlo photon trajectories an intensity accounting for the elastic aerosol particle-, Cabannes- and the inelastic rotational Raman scattering (RRS) and simultaneously an intensity, for which Rayleigh scattering is treated as an elastic scattering process. By combining both intensities one obtains the so called filling-in (FI, which quantifies the filling-in of Fraunhofer lines) as a measure for the strength of the Ring effect with the same relative precision as the intensities. The validation of the polarized radiometric quantities and the Ring effect is made by comparison with partially published results of other radiation transport models. Furthermore the concept of discretisation of the optical domain into grid cells is extended by making grid cells arbitrarily joining into so called clusters, i.e. grid cell aggregates. Therewith the program is able to calculate derivatives of radiometrically or spectroscopically accessible quantities, namely the intensities at certain locations in the atmospheric radiation field and the light path integrals of trace gas concentrations associated thereto, i.e. the product of the DOAS (differential optical absorption spectroscopy) method, with respect to optical properties of aerosols and gases in connected spatial regions. The first and second order derivatives are validated through so called self-consistency tests. These derivatives allow the inversion of three dimensional tracegas and aerosol concentration profiles and pave the way down to 3D optical scattered light tomography. If such tomographic inversion scheme is based solely on spectral intensitites the available second order derivatives allows the consideration of the curvature in the cost function and therefore allows implementation of efficient optimisation algorithms. The influence of the instrument function on the spectra is analysed in order to mathematically assess the potential of DOAS to a sufficient degree. It turns out that the detailed knowledge of the instrument function is required for an advanced spectral analysis. Concludingly the mathematical separability of narrow band signatures of absorption and the Ring effect from the relatively broad band influence of the elastic scattering processes on the spectra is demonstrated which corresponds exactly to the DOAS principle. In that procedure the differential signal is obtained by approximately 4 orders of magnitude faster then by the separate modelling with and without narrow band structures. Thereby the fusion of the separated steps DOAS spectral analysis and subsequent radiation transport modeling becomes computationally feasible.:1.1. Radiation Transport Modeling and Atmospheric State Inversion 1.2. Vector RTE Solution Methods 1.3. Scope of the Thesis 1.4. Outline of the Thesis 2.1. General Structure 2.1.1. Chemical Composition of the Gas Phase 2.1.2. The Troposphere, Temperature and Pressure Vertical Structure 2.1.3. The Stratosphere 2.2. Aerosols and Clouds 2.2.1. Classification and Morphology 2.2.2. Water Related Particle Growth and Shrinking Processes 2.2.3. Size Spectra and Modes 3.1. Electromagnetic Waves 3.1.1. Maxwell\''s Equations 3.1.2. Measurement of Electromagnetic Waves 3.1.3. Polarization State of EM Waves 3.1.4. Stokes Vectors 3.2. Scattering and Absorption of EM Waves by Molecules and Particles 3.2.1. General Description of Scattering and Coordinate Systems 3.2.2. Molecular Scattering 3.2.3. Molecular Absorption Processes and Electronic Molecular States 3.2.4. Scattering On Spherical Particles - Mie Theory 3.3. Mathematical Description of Radiation Transport 3.3.1. Radiance and Irradiance 3.3.2. Absorption, Scattering and Extinction Coefficients 3.3.3. Optical Thickness and Transmission 3.3.4. Scattering 3.3.5. Incident (Ir)Radiance 3.3.6. The Black Surface Single Scattering Approximation 3.3.7. Radiative Transfer Equations 4.1. General Monte Carlo Methods 4.1.1. Numerical Integration 4.1.2. Importance Sampling and Zero Variance Estimates 4.1.3. Optimal Sampling 4.1.4. Sampling from Arbitrary Distributions 4.2. Path Generation or Collision Density Estimation 4.2.1. Discretization of the Optical Domain into Cells and Clusters 4.2.2. RTE Integral Form 4.2.3. Formal Solution of the IRTE 4.2.4. Overview on Monte Carlo RTE Solution Algorithms 4.2.5. Crude Monte Carlo 4.2.6. Sequential Importance Sampling (SIS) or Path Generation 4.3. Importance Sampling in Monte Carlo SIS Radiative Transfer 4.3.1. Weights for Alternate Kernels 4.3.2. Weights in the Calculation of RTE Functional Estimates 4.3.3. Application of IS to Mie Phase Functions Scatter Angle Sampling 5.1. Radiances, Intensities and the Reciprocity Theorem 5.1.1. Scalar Radiance Estimates 5.1.2. Backward Monte Carlo Scalar Radiance 5.1.3. Vector Radiances 5.2. Radiance Derivatives 5.2.1. Variables for Radiance Derivatives 5.3. Validation of Functionals 5.3.1. Validation of Vector Radiances 5.3.2. Validation of Radiance Derivatives 6.1. A Simply Structured Instrument Forward Model 6.2. Pure Atmospheric Spectra and Absorption 6.2.1. Direct Light Spectra 6.2.2. Scattered Sun Light Spectra 6.3. (D)OAS from the Perspective of Radiative Transfer Modeling 6.3.1. (Rest) Signatures of Weakly Absorbing Gases 6.3.2. Spectroscopic Measurements and Standard DOAS 6.4. DOAS Analysis Summary 6.4.1. DSCD Retrieval 6.4.2. Inversion 7.1. RRS-Modified RTE 7.1.1. RRS Cross Sections for Scattering out and into a Wavelength 7.1.2. Modification of the RTE Loss and Source Terms 7.2. Intensity Estimates Considering Rotational Raman Scattering 7.2.1. RRS in the Path Sampling Procedure 7.2.2. Adjoint RRS Correction Weights 7.2.3. Local Estimates of Intensities with RRS 7.2.4. Intensity Estimates 7.3. Ring Spectra 7.3.1. Elastic Biasing of the Local Estimates 7.3.2. Cumulative Weights and Local Estimates 7.3.3. Test of the Elastic Biasing 7.4. Validation 7.4.1. Comparison to an Analytic Single Scattering Code 7.4.2. Single Scattering Model Including Rotational Raman Scattering 7.4.3. Multiple Scattering Model Comparison 7.4.4. Comparison with A Measurement 7.4.5. Validation of Approximate Methods For Ring Effect Modeling 7.5. Summary and Discussion 8.1. Status and Summary 8.1.1. Ring-Effect and Absorption Corrected Radiances 8.1.2. Derivatives of Radiometric Quantities Accessible Through Spectroscopy 8.1.3. Polarization 8.1.4. Time Integrated Sensitivities for 3D UV/vis/NIR Remote Sensing 8.2. Outlook A.1. Zero Variance Estimates A.2. Free Path Length Sampling in a Homogeneous Medium A.3. Cumulative Differential Scatter Cross Sections A.3.1. Cardanic formulas A.3.2. Rayleigh and Raman Phase Functions A.3.3. Henyey-Greenstein Model A.3.4. Legendre Polynomial Phase Function Model A.3.5. Table Methods A.4. Greens Function in the Derivation of the IRTE A.5. Source Code For Stokes Vector Transformation Plot B.1. 1st Order Derivatives B.2. 2nd Order Derivatives B.3. Hessian of Integrals Depending on Many Variables C.1. Slit Function f Derivatives C.2. Signal Sn Derivatives C.3. Chi Square Spline Fitting C.3.1. Constrained Non-Linear Least Square Problem C.3.2. Spline Fitting C.3.3. Jacobians and Hessian

Knowledge of the properties of single molecule diffusion is important for controlling dynamic self-assembly of molecular structures. A powerful experimental technique for determining diffusion coefficients is the recording of diffusion-induced signal fluctuations by a locally fixed point-like probe. Here, the signal becomes modified, whenever a molecule enters a certain detection area on the surface under the probe. The technique is minimal invasive and has a very good time resolution, enabling the investigation of highly mobile molecules. Theories are necessary for the analysis of the fluctuations and the extraction of diffusion properties. In this thesis, three methods are presented, which are based on the autocorrelation function, the distribution of peak widths and the distribution of interpeak intervals. Analytical expressions are derived for the distributions and the autocorrelation function in case of molecules, which can be described by circular or rectangular shapes. For rectangular shaped molecules, rotational diffusion can influence the recorded fluctuations. To allow for a simultaneous determination of rotational and translational diffusion coefficients the analytical treatment is extended. Furthermore, new methods are developed to determine the diffusion tensor for anisotropic stochastic molecular motion, using either one linearly extended probe or two individual probes. Coarse-graining the signal recorded by a point-like probe, which repeatedly moves on a line or a circle, is suggested for experimental implementation. All facets of the evaluation methods are verified against kinetic Monte Carlo simulations. Applications to experimental data, recorded by a locally fixed scanning tunneling microscope tip, are demonstrated for copperphthalocyanine and PTCDA molecules diffusing on Ag(100).

Cette thèse porte sur le rotomoulage réactif de polyamide 6. Ce procédé a la particularité de présenter des cycles thermiques relativement réduit et de fabriquer des polymères sur mesure contrairement à son homologue conventionnelle. La voie envisagée pour la synthèse in situ de PA6 est la polymérisation anionique de l’ε-caprolactame par ouverture de cycle. Le Caprolactamate de sodium et le bromure de caprolactame-magnésium ont été utilisés comme catalyseurs, et l’hexaméthylène dicarbamoyl dicaprolactame a été employé comme activateur. L’étude rhéocinétique de deux systèmes réactifs lactames qui ont été utilisé à différentes compositions et températures a permis de déterminer une formulation appropriée aux exigences du procédé (faible viscosité initiale du système réactif, temps de polymérisation court...). La simultanéité des phénomènes de polymérisation et de cristallisation aux faibles températures à été observé à l’aide des résultats du suivi cinétique par DSC. La mise en forme par la technique de rotomoulage a été réalisée sur une installation pilote de rotomoulage associée à un système d’acquisition de température par télémesure radio. La comparaison des propriétés des articles en PA 6 obtenus par voie réactive par rapport a ceux obtenus par voie fondue, a montré un gain au niveau du temps de cycle et une amélioration des propriétés mécaniques du matériau notamment dans le domaine des faibles déformations. Le rotomoulage de la bicouche PA6/PE-GMA a été ainsi étudié, le contrôle des mécanismes réactionnels mis en jeu à l’interface par rhéologie, durant la formation de la couche de polymère PA6 par voie anionique sur une couche de PE-GMA a été effectué dans un rhéomètre, une bonne adhésion à l’interface a été observé. La faisabilité d’élaboration de nanocomposite PA 6/argile par le procède de rotomoulage réactif a été testé, les caractérisations physico-chimiques et les observations morphologiques ont été étudiés afin d’évaluer l’état de dispersion et la nature des interactions. Durant cette étude, nous avons mesurés la faisabilité de l’intercalation et le gonflement de l’argile dans le monomère ε- caprolactame et estimer la possibilité d’avoir une morphologie exfolié des nanocomposites élaborés par le procédé de rotomoulage réactif. / A reactive rotational molding (RRM) process was developed to obtain a PA6 by activated anionic ring-opening polymerization of epsilon-caprolactam (APA6). Sodium caprolactamate (C10) and caprolactam magnesium bromide (C1) were employed as catalysts, and difunctional hexamethylene-1,6-dicarbamoylcaprolactam (C20) was used as an activator. The kinetics of the anionic polymerization of ε-caprolactam into polyamide 6 was monitored through dynamic rheology and differential scanning calorimetry measurements. The effect of the processing parameters, such as the polymerization temperature, different catalyst/activator combinations and concentrations, on the kinetics of polymerization is discussed. A temperature of 150°C was demonstrated to be the most appropriate. It was also found that crystallization may occur during PA6 polymerization and that the combination C1/C20 was well suited as it permitted a suitable induction time. Isoviscosity curves were drawn in order to determine the available processing window for RRM. The properties of the obtained APA6 were compared with those of a conventionally rotomolded PA6. Results pointed at lower cycle times and increased tensile properties at weak deformation. Additionally, rotational molding of the bilayer PA6/PE-GMA has been studied, the control of the reactions mechanisms involved in the interface by rheology , during formation of the anionically PA6 polymer layer on a PE- GMA layer was carried out in a rheometer , a good adhesion at the interface was observed. The feasibility of developing nanocomposite PA 6/clay by reactive rotational molding process has been tested; the physico-chemical characterization and morphological observations were studied to assess the state of dispersion and the nature of interactions. During this study, we measured the feasibility of intercalation and swelling the clay in the ε-caprolactam monomer and estimate the possibility of having morphology of exfoliated nanocomposites prepared by reactive rotational molding process.

The doctoral thesis focuses on problem of stability of steel thin-walled beams with lateral and torsional restraints along the spans. Theoretical background of lateral-torsional buckling of an ideal beam with and without restraints preventing out-of-plane buckling is briefly described. In the following chapters the problem of stabilization of steel thin-walled beams by planar members is dealt with. The state of the art in this field is summarized and some open questions are identified. The research in this field could bring new findings about actual behavior of these structural systems. The rate of stabilization can be quantified using values of shear and rotational stiffness provided to a thin-walled member by a planar member. In the frame of the thesis the problem of torsional restraint given to steel cold-formed members by sandwich panels under load is discussed. In case of the uplift load applied on the sandwich panels the torsional restraint should be verified by experimental analysis. To contribute to this field, experimental verification of rotational stiffness provided to steel cold-formed beams by sandwich panels was proposed and performed. Torsional restraint under no external load as well as under uplift load applied on the panels was investigated. The purpose was to obtain the values of the rotational stiffness provided by planar members. The performed tests indicate significant and practically applicable rate of the torsional restraint even in case of the uplift load on the surfaces of the panels. Utilization of the values of the rotational stiffness might result in more economical, effective and reliable structural design. Selected problems were investigated using numerical modeling in a finite element method based software.

One of the current testing method (the Dry Flow test) to qualify resin for use in production in the rotomolding process has been shown to have many flaws in both equipment and procedure. Research was done here to investigate a possible alternative that could eliminate some of these testing deficiencies. By reducing equipment and operator errors, the testing of materials becomes more valuable of an exercise. The Angular Flow test developed in this research can increase repeatability. By coming to understand the rotational molding process better, an evaluation that can give more valid information was devised.

[pt] Vigas flexíveis são encontradas com cada vez mais frequência em diferentes indústrias, uma vez que novos projetos têm buscado por estruturas mais longas e leves. Isso pode ser uma consequência direta das novas demandas estruturais nos projetos, ou uma simples consequência do engajamento das indústrias em programas de redução de custo (utilização de menos materiais). Em geral, vigas flexíveis são modeladas sob hipóteses de grandes deslocamentos, grandes rotações, mas com pequenas deformações. Essas hipóteses permitem que o equacionamento da dinâmica de vigas flexíveis seja feito através de elementos finitos co-rotacionais. A formulação co-rotacional decompõe o movimento das estruturas flexíveis em duas partes: uma contendo o movimento de corpo rígido e outra com uma (pequena) deformação elástica. Dessa forma, a não-linearidade geométrica causada pelos grandes deslocamentos e rotações das seções transversais das vigas podem ser computadas de forma eficiente. Uma das inovações dessa tese é o uso direto das equações de movimentos geradas pelos elementos finitos co-rotacionais no cálculo dos modos normais não-lineares (MNNs). Até agora, a maioria das análises dinâmicas com elementos finitos co-rotacionais foram restritas à integração das equações de movimento. O conhecimento de MNNs é útil na análise de sistemas não-lineares pois permitem um detalhado entendimento das vibrações nos regimes não-lineares. Com eles, pode-se, por exemplo, prever comportamentos de enrijecimento/relaxamento, localização de respostas, interação entre modos, existência de isolas, etc. A definição de Rosenberg sobre MNNs como sendo soluções periódicas (não necessariamente síncronas) do sistema é adotado na tese. Os métodos do Balanço Harmônico e do Tiro são apresentados e utilizados no cálculo de soluções periódicas de sistemas não-lineares. Um procedimento de continuação numérica é implementado para computar os MNN eficientemente para diferentes níveis de energia. Exemplos numéricos mostram a capacidade do método proposto quando aplicado aos elementos finitos co-rotacionais. / [en] Flexible beams are becoming ubiquitous in several industrial applications, as new projects often aim for lighter and longer structures. This fact is directly related to the new challenging demands on structural performances, or it is a simple consequence of the engagement of industries in cost reduction programs (usage of less material). Flexible beams are usually modeled under the assumption of large displacements, finite rotations, but with small strains. Such hypotheses allow the equation of motion to be built using co-rotational finite elements. The co-rotational formulation decomposes the total motion of a flexible structure into two parts: a rigid body displacement and an elastic (small) deformation. This way, the geometric nonlinearity caused by the large displacements and rotations of the beam s cross sections can be efficiently computed. One of the novelties of this thesis is the direct usage of the equation of motion generated by a co-rotational finite element formulation in the computation of nonlinear normal modes (NNM). So far, most of the dynamic analyses with co-rotation finite element models were restricted to numerical integrations of the equation of motion. The knowledge of NNMs can be beneficial in the analysis of any nonlinear structure since it allows a thoroughly understanding of the vibratory response in the nonlinear regime. They can be used, for example, to predict a hardening/softening behavior, a localization of the responses, the interactions between modes, the existence of isolas, etc. The Rosenberg s definition of NNM as periodic solutions (non-necessarily synchronous motion) is adopted here. The Harmonic Balance method and the Shooting methods are presented and used to compute periodic solutions of nonlinear systems. A numerical path continuation scheme is implemented to efficiently compute NNMs at different energy levels. Numerical examples show the capability of the proposed method when applied to co-rotational beam elements.

<p dir="ltr">The objective of this research is to advance the development and application of laser diagnostics in gas phase medium, which ranges from atmospheric non-reacting flows to turbulent reacting flows in high-pressure, high-temperature environments. Laser diagnostic techniques are powerful tools for non-intrusive and in-situ measurements of important chemical parameters, such as temperature, pressure, and species mole fractions, in harsh environments. These measurements significantly advance the knowledge across various research disciplines, such as combustion dynamics, chemical kinetics, and molecular spectroscopy. In this thesis, detailed theoretical models and experimental analysis are presented for three different techniques: 1. Chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs CARS); 2. Two-color polarization spectroscopy (TCPS); 3. Ultrafast-laser-absorption-spectroscopy (ULAS). The first chapter provides a brief survey of laser diagnostics, including both linear and nonlinear methods. The motivations behind the three studies covered in this dissertation are also discussed. </p><p dir="ltr">In the second chapter, single-shot CPP fs CARS thermometry is developed for the hydrogen molecule at 5 kHz. The results are divided into two parts. The first part concentrates on the development of H₂ CPP fs CARS thermometry for high-pressure and high-temperature conditions. The second part demonstrates the application of H₂ CPP fs CARS in a model rocket combustor at pressures up to 70 bar. In the first part, H₂ fs CARS thermometry was performed in Hencken burner flames up to 2300 K, as well as in a heated gas-cell at temperatures up to 1000 K. It was observed that the H₂ fs CARS spectra are highly sensitive to the pump and Stokes chirp. Chirp typically originates from optical components such as windows and polarizers. As a result, the pump delay is modeled to provide a shift to the Raman excitation efficiency curve. With the updated theoretical model, excellent agreement was found between the simulated and experimental spectra. The averaged error and precision are 2.8% and 2.3%, respectively. In addition, the spectral phase and pump delay determined from the experimental spectra closely align with the theoretical predictions. It is also found that pressure does not have significant effects on the H₂ fs CARS spectra up to 50 bar at 1000 K. The collision model provides excellent agreement with the experiment. This allows the use of low-pressure laser parameters for high-pressure thermometry measurements. In the second part, spatially resolved H₂ temperature was measured in a rocket chamber at pressures up to 70 bar. This is the first demonstration of fs CARS thermometry inside a high-pressure rocket combustor. These results highlight the potential of using H₂ CPP fs CARS thermometry to provide quantitative data in high-pressure experiments for the study of combustion dynamics and model validation efforts at application relevant operating conditions.</p><p dir="ltr">The third chapter presents the development of a TCPS system for the study of the NO (<i>A</i>²Σ⁺-<i>X</i>²Π) state-to-state collision dynamics with He, Ar, and N₂. Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295 K and 1 atm, were obtained with the pump beam tuned to the R₁₁(11.5) and ^OP₁₂(1.5) transitions. The probe was scanned while the pump beam was tuned to the line center. Collision induced transitions were observed in the spectra as the probe scanned over transitions that were not coupled with the pump frequency. The strength and structure of the collision induced transitions in the TCPS spectra were compared between the three colliding partners. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. An unique aspect of this work is that the collisional transfer from an initial to a final Zeeman state was modeled based on the difference in the cosine of the rotational quantum number <i>J</i> projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the <i>A</i>²Σ⁺ level of NO is almost zero for rotational quantum numbers ≥ 8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra. </p><p dir="ltr">The fourth chapter presents the development and application of a broadband ULAS technique operating in the mid-infrared for simultaneous measurements of temperature, methane (CH₄), and propane (C₃H₈) mole fractions. Single-shot measurements targeting the C-H stretch fundamental vibration bands of CH₄ and C₃H₈ near 3.3 μm were acquired in both a heated gas cell up to ~650 K and laminar diffusion flames at 5 kHz. The average temperature error is 0.6%. The average species mole fraction error are 5.4% for CH₄, and 9.9% for C₃H₈. This demonstrates that ULAS is capable of providing high-fidelity hydrocarbon-based thermometry and simultaneous measurements of both large and small hydrocarbons in combustion gases. </p>

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