The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities. The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified. The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated. / eSSENCE

Since the introduction of modern computers, numerical methods for atmospheric simulations have routinely been applied for weather prediction, and in the last fifty years, there has been a steady improvement in the accuracy of forecasts. Accurate numerical models of the atmosphere are also becoming more important as researchers rely on global climate simulations to assess and understand the impact of global warming. The choice of grid in a numerical model is an important design decision and no obvious optimal choice exists for computations in spherical geometry. Despite this disadvantage, grid-based methods are found in all current circulation models. A different approach to the issue of discretizing the surface of the sphere is given by meshless methods, of which radial basis function (RBF) methods are becoming prevalent. In this thesis, RBF methods for simulation of atmospheric flows are explored. Several techniques are introduced to increase the efficiency of the methods. By utilizing a novel algorithm for adaptively placing the node points, accuracy is shown to improve by over one order of magnitude for two relevant test problems. The computational cost can also be reduced by using a local finite difference-like RBF scheme. However, this requires a stabilization mechanism for the hyperbolic problems of interest here. A hyper-viscosity scheme is introduced to address this issue. Another stability issue arising from the ill-conditioning of the RBF basis for almost-flat basis functions is also discussed in the thesis, and two algorithms are proposed for dealing with this stability problem. The algorithms are specifically tailored for the task of creating finite difference weights using RBFs and are expected to overcome the issue of stationary error in local RBF collocation.

In numerical simulations, problems stemming from aerodynamics pose many challenges for the method used. Some of these are addressed in this thesis, such as the fluid interacting with objects, the presence of shocks, and various types of boundary conditions. Scenarios of the kind mentioned above are described mathematically by initial boundary value problems (IBVPs). We discretize the IBVPs using high order accurate finite difference schemes on summation by parts form (SBP), combined with weakly imposed boundary conditions, a technique called simultaneous approximation term (SAT). By using the energy method, stability can be shown. The weak implementation is compared to the more commonly used strong implementation, and it is shown that the weak technique enhances the rate of convergence to steady state for problems with solid wall boundary conditions. The analysis is carried out for a linear problem and supported numerically by simulations of the fully non-linear Navier–Stokes equations. Another aspect of the boundary treatment is observed for fluid structure interaction problems. When exposed to eigenfrequencies, the coupled system starts oscillating, a phenomenon called flutter. We show that the strong implementation sometimes cause instabilities that can be mistaken for flutter. Most numerical schemes dealing with flows including shocks are first order accurate to avoid spurious oscillations in the solution. By modifying the SBP-SAT technique, a conservative and energy stable scheme is derived where the order of accuracy can be lowered locally. The new scheme is coupled to a shock-capturing scheme and it retains the high accuracy in smooth regions. For problems with complicated geometry, one strategy is to couple the finite difference method to the finite volume method. We analyze the accuracy of the latter on unstructured grids. For grids of bad quality the truncation error can be of zeroth order, indicating that the method is inconsistent, but we show that some of the accuracy is recovered. We also consider artificial boundary closures on unbounded domains. Non-reflecting boundary conditions for an incompletely parabolic problem are derived, and it is shown that they yield well-posedness. The SBP-SAT methodology is employed, and we prove that the discretized problem is stable.

Stochastic di®erential equations (SDEs) are　central to much of modern finance theory and have been widely used to model the behaviour of key variables such as the　instantaneous short-term interest rate, asset prices, asset returns and their volatility.　The explanatory and/or predictive power of these models depends crucially on the particularisation of the model SDE(s) to real data through the choice of values for their parameters. In econometrics, optimal parameter estimates are generally considered to　be those that maximise the likelihood of the sample. In the context of the estimation of the parameters of SDEs, however, a closed-form expression for the likelihood　function is rarely available and hence exact maximum-likelihood (EML) estimation is usually infeasible. The key research problem examined in this thesis is the development of generic, accurate and computationally feasible estimation procedures based on the　ML principle, that can be implemented in the absence of a closed-form expression for　the likelihood function. The overall recommendation to come out of the thesis is that　an estimation procedure based on the finite-element solution of a reformulation of the Fokker-Planck equation in terms of the transitional cumulative distribution function(CDF) provides the best balance across all of the desired characteristics. The recommended approach involves the use of an interpolation technique proposed in this thesis which greatly reduces the required computational effort.

Σκοπός της παρούσας εργασίας είναι να παράσχει χρήσιμες πληροφορίες για την πρακτική κατασκευή συσκευών αορατότητας. Αρχικά, παρουσιάζονται οι διαφορετικοί τύποι των δισδιάστατων μέσων μετασχηματισμού (συσκευών αορατότητας) και διαπιστώνεται η υπεροχή του δισδιάστατου μανδύα αορατότητας επιπέδου από διηλεκτρικό. Προκειμένου να διερευνήσουμε αριθμητικά την οπτική συμπεριφορά αυτού του τύπου μανδύα, χρησιμοποιούμε τις εξισώσεις που εξάγονται από τη θεωρία της οπτικής μετασχηματισμών, και μέσω της μεθόδου F.D.T.D υπολογίζουμε το ηλεκτρομαγνητικό πεδίο σε όλα τα σημεία του υπολογιστικού πλέγματος. Στα όρια του πλέγματος αυτού τοποθετείται ένα στρώμα τέλειας προσαρμογής , έτσι ώστε να ελαχιστοποιούνται οι ανακλάσεις στα όρια αυτά, σε αναλογία με το πραγματικό πείραμα. Υλοποιώντας έναν κώδικα σε Μatlab, υπολογίζουμε την ένταση της σκεδαζόμενης ακτινοβολίας, για εγκάρσια μαγνητικά επίπεδα κύματα που προσπίπτουν υπό γωνία σε ένα αντικείμενο που περιβάλλεται από έναν μανδύα από διηλεκτρικό και είναι τοποθετημένο σε επίπεδο. Συγκεκριμένα, μελετάμε: την επίδοση της συσκευής συναρτήσει του βαθμού διακριτοποίησης του αριθμητικού πλέγματος, την επίδραση της απορρόφησης και της τυχαίας διαταραχής της επιτρεπτότητας των δομικών υλικών του μανδύα, καθώς και την επίδοση για πρόσπτωση υπό διαφορετικές γωνίες. Τέλος, εκτιμάμε τις ιδιότητες των στρώσεων από διηλεκτρικά που θα μπορούσαν να περιβάλουν τον μανδύα και να βελτιώσουν την αποδοτικότητά του στο ορατό φάσμα. / This work aims to provide useful information for the fabrication of practical cloaking devices. Initially, different types of two dimensional transformation media (invisibility devices) are presented and it is concluded that the all dielectric, two dimensional electromagnetic ground plane cloak dominates. In order to perform a numerical study of the sensitivity of this type of cloak, we use the equations deduced from the transformation optics via finite difference time domain method, for the electromagnetic wave, at every single point of the numerical domain. In the boundaries of this domain, we place a perfectly matched layer in order to minimize the reflections in those boundaries. That would replicate the real experiment with our simulations. By the application of a code written in Matlab, we calculate the scattering signature of an object surrounded by an all dielectric cloak and placed on a ground plane. Transverse magnetic plane waves are launched at an angle towards the object. In particular, we study the performance of the system as a function of the number of distinct components the cloak is divided into, the effects of lossy elements, the angle of incidence, as well as typical random variations of the permittivity of the building materials. Finally, we evaluate impedance matching layers that can surround the cloak and improve its effectiveness in the visible spectrum.

Made available in DSpace on 2014-10-09T12:37:04Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:37Z (GMT). No. of bitstreams: 1 04489.pdf: 3207506 bytes, checksum: 72ff1580741242388f8d1d69c5c3ef6d (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

This work is concerned with the numerical simulation of percussion instruments based on physical principles. Three novel modular environments for sound synthesis are presented: a system composed of various plates vibrating under nonlinear conditions, a model for a nonlinear double membrane drum and a snare drum. All are embedded in a 3D acoustic environment. The approach adopted is based on the finite difference method, and extends recent results in the field. Starting from simple models, the modular instruments can be created by combining different components in order to obtain virtual environments with increasing complexity. The resulting numerical codes can be used by composers and musicians to create music by specifying the parameters and a score for the systems. Stability is a major concern in numerical simulation. In this work, energy techniques are employed in order to guarantee the stability of the numerical schemes for the virtual instruments, by imposing suitable coupling conditions between the various components of the system. Before presenting the virtual instruments, the various components are individually analysed. Plates are the main elements of the multiple plate system, and they represent the first approximation to the simulation of gongs and cymbals. Similarly to plates, membranes are important in the simulation of drums. Linear and nonlinear plate/membrane vibration is thus the starting point of this work. An important aspect of percussion instruments is the modelling of collisions. A novel approach based on penalty methods is adopted here to describe lumped collisions with a mallet and distributed collisions with a string in the case of a membrane. Another point discussed in the present work is the coupling between 2D structures like plates and membranes with the 3D acoustic field, in order to obtain an integrated system. It is demonstrated how the air coupling can be implemented when nonlinearities and collisions are present. Finally, some attention is devoted to the experimental validation of the numerical simulation in the case of tom tom drums. Preliminary results comparing different types of nonlinear models for membrane vibration are presented.

Submitted by Raniere Barreto (raniere.barros@ufvjm.edu.br) on 2018-05-10T17:24:21Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) altamiro_junio_mendes_silva.pdf: 4294935 bytes, checksum: fa3eca4f34d0f388a736e8026703da56 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-05-14T14:40:09Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) altamiro_junio_mendes_silva.pdf: 4294935 bytes, checksum: fa3eca4f34d0f388a736e8026703da56 (MD5) / Made available in DSpace on 2018-05-14T14:40:09Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) altamiro_junio_mendes_silva.pdf: 4294935 bytes, checksum: fa3eca4f34d0f388a736e8026703da56 (MD5) Previous issue date: 2016 / O presente trabalho apresenta a aplica??o do M?todo das Diferen?as Finitas Energ?ticas para an?lise do comportamento de placas delgadas. Este ? semelhante ao m?todo cl?ssico das diferen?as finitas, por?m as derivadas envolvidas nas equa??es diferenciais s?o de menor ordem. A an?lise e projeto de placas, cascas e chapas constituem uma importante ?rea na engenharia estrutural, por possuir uma participa??o significativa na composi??o do custo da estrutura e nos requisitos relacionados a sua seguran?a. Neste contexto, o estudo de placas ? um tema relevante na an?lise estrutural, pois permite uma interpreta??o cada vez mais pr?xima da realidade dos fen?menos f?sicos. A resolu??o anal?tica deste tipo de estrutura pode ser uma tarefa complexa, at? mesmo imposs?vel, pois depende de v?rios fatores, sendo necess?rio recorrer ? utiliza??o de m?todos num?ricos que sejam capazes de fornecer resultados aproximados e com precis?o satisfat?ria. Neste sentido, foi implementada uma rotina por meio do software M?XIMA, de modo a automatizar os procedimentos da formula??o desenvolvida para an?lise de placas delgadas. Para validar a metodologia aplicada, os resultados foram comparados com outros obtidos por solu??es anal?ticas, na literatura e pela an?lise realizada por outros programas. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Tecnologia, Sa?de e Sociedade, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2016. / This paper presents the application of energy finite difference method for determining the major efforts on thin plates. This is similar to the classic finite differences method, but the derivatives involved in the differential equations are of a lesser order. The analysis and design of plates and shells are an important area within the structural engineering, because it has a significant participation in the cost of the composition of the structure and requirements related to their safety. In this context, the study of plates is a relevant issue in the structural analysis, because allows an interpretation ever closer to the reality of physical phenomena. The analytical resolution of this type of structure can be a complex task, even impossible, it depends on various factors, being necessary to resort to the use of numerical methods that are able to provide approximate results and satisfactory precision. In this sense, it was implemented a routine through MAXIMA, in order to automate procedures to be carried out during the analysis of thin plates. The results were compared with other obtained by analytical solutions, in the literature, and the analysis by other programs, to validate the methodology applied.

Orientador: Luis Vicente de Andrade Scalvi / Banca: Valdemir Garcia Ferreira / Banca: Julio Ricardo Sambrano / Banca: Carlos José Leopoldo Constantino / Banca: Carlos Antonio Ruggiero / O Programa de Pós-Graduação em Ciência e Tecnologia de Materiais, PosMat, tem caráter institucional e integra as atividades de pesquisa em materiais de diversos campi da Unesp / Resumo: Neste trabalho foi realizada a simulação numérica da fase líquida no processo de deposição de filmes finos pela técnica de molhamento (dip-coating), via sol-gel, utilizando como aplicação soluções precursoras de dióxido de estanho (Sn'IND. 2'). Dióxido de estanho é um semicondutor transparente de gap largo, amplamente utilizado em muitos tipos de dispositivos. Além da técnica convencional, o trabalho analisa uma nova proposta da técnica de deposição dip-coating onde a solução se encontra em uma temperatura diferente da ambiente. Para ambas as técnicas foram realizadas a modelagem matemática dos problemas e desenvolveu-se um método numérico apropriado baseado no método MAC (Marker and Cell). O problema foi resolvido em coordenadas cartesianas bidimensionais e as equações foram discretizadas pela técnica de diferenças finitas. Os resultados numéricos são visualizados por meio da distribuição de temperatura e vetores velocidade da solução precursora, que fornecem subsídios para investigação da influência dos vetores velocidade na obtenção de filmes com boas propriedades, em relação à uniformidade e homogeneidade. Verifica-se que estas características refletem diretamente na qualidade óptica dos filmes investigados, tornando-se parâmetros importantes para aplicações em dispositivos opto-eletrônicos. Através dos resultados numéricos verificou-se que nas regiões do fluido próximas ao substrato, os módulos dos vetores velocidade são maiores, há uma maior quantidade de material sendo depositado. Notou-se também, através da distribuição de velocidades em direção ao substrato que o filme tem uma melhor uniformidade na sua espessura quando os vetores velocidade possuem os valores de seus módulos mais próximos uns dos outros. Portanto, mudando os parâmetros iniciais de viscosidade, densidade, velocidade de imersão/emersão do substrato ou temperatura no fluido pode-se estudar o comportamento. / Abstract: In this work, the numerical simulation of liquid phase in the thin film deposition, by the sol-gel-dip-coating technique, was carried out. The method was applied to tin dioxide (Sn'IND. 2') solutions. Tin dioxide is a transparent semiconductor of wide bandgap, extensively used in many types of devices. Besides the conventional procedure, this work analyses a new proposal for the deposition technique, where the solution is heated above room temperature. In both cases, the mathematical modeling was done and the appropriated numerical method was developed, based on MAC (Marker and Cell) approach. The problem was solved in two-dimensional Cartesian coordinates and the equations were discretized by the finite difference technique. The numerical results are visualized through temperature and vector velocity distributions in the precursos solution, yielding subsides to the investigation of the influence of vectors velocity in the deposition of good property films, concerning uniformity and homogeneity. It was verified that these characteristics point directly toward the optical quality of investigated films, becoming important parameters for application in optoelectronic devices. The numerical results allow verifying that in the fluid regions close to the substrate, where the velocity modulus is highter, there is a larger amount of material being deposited. It was also noticed, through the velocity distribution towards the substrate, that the film has a better thickness uniformity when the vectors velocity have modulus values closer to each other. Therefore, changing initial parameters such as viscosity, density, substrate dipping rate or fluid temperature, it is possible to evaluate the fluid behavior during the thin film deposition. / Doutor

abstract: In sub transmission systems, many more raptor deaths have been recorded near metal poles rather than wood poles. The metal pole, which is reliable in structure but also grounded, may increase the risk of electrocution when raptors perch on the insulator. This thesis focuses on evaluating the effectiveness of the raptor guard to prevent both debilitating and lethal electrocutions to local wildlife in 69 kV sub transmission systems. First, the two-dimensional (2D) finite difference methods (FDM) were proposed to solve the Poisson and Laplace equations, which describe the electric field. Second, the verification of the FDM algorithm was made based on a parallel-plate capacitor model. Then, the potential and the electric field were simulated by the raptor-insulator model to evaluate the possibility of flashover and leakage current under various conceivable scenarios. Third, several dielectric performance experiments were implemented to gain insight into the physical property of the raptor guard developed by the Salt River Project (SRP) as an example. The proposed initial-tracking-voltage and time-to-track experiments tested the ability of the guard, which is designed to prevent the tracking phenomenon under a contaminated situation such as rain, fog, and snow. A data acquisition also collected the leakage current data for the comparison of maximum raptor tolerance. Furthermore, the puncture voltage of this guard material was performed by the dielectric breakdown voltage experiment in an oil-covered container. With the combination of the model simulation and the experiments in this research, the raptor guard was proven to be practical and beneficial in sub transmission system. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2016