In this thesis, I develop a novel time-domain approach for nonlinear scattering theory (NLST), a previously frequency domain method for estimating the nonlinear generation from a nanostructure. Due to a gap in literature, I then perform a full comparison of this novel time domain approach to the existing one in the frequency domain. Using the example scenario of third harmonic generation from various media in 1D and 3D, I compare - quantitatively - the NLST estimated nonlinear spectra to two types of direct nonlinear simulations: one using an experimental value for the nonlinear optical susceptibility, and, for plasmonic systems, another using a hydrodynamics model for the nonlinear plasmonic response. Through testing differing NLST approaches on these systems, I demonstrate the effectiveness of the novel time-domain NLST and assess the use cases for this method as well as the pre-existing ones. Lastly, I discuss the applicability of NLST in future works involving the inverse design process, and high-order harmonic generation.

Many complexities arise when writing software for computational physics. The choice of underlying data structures, physics model representation, and numerical methods used for the solver all add to the overall complexity of a code and significantly affect the simulation speed and accuracy of the solution. This work has integrated multiple recently developed software tools into a unified framework called ELEMENTS. ELEMENTS contains tools to address the complexities of data representation and numerical methods implementation for computational physics applications. ELEMENTS consists of multiple software packages: Elements, MATAR, Swage, Geometry, and SLAM. MATAR is a performance portability and productivity implementation of data-oriented design that leverages KOKKOS for multi-architecture portability. MATAR's data-oriented design allows for highly efficient memory use through the use of contiguous memory allocation and access for optimal performance. The elements library contains the requisite mathematical functions for a wide range of numerical methods and high order field representation, including the Serendipity basis set that allows for a higher-order solution with fewer degrees of freedom than the more standard tensor product elements. Swage is a novel mesh class capable of representing all of the geometric entities required to implement low and high-order continuous and discontinuous Galerkin methods on unstructured hexahedral meshes as well as connectivity structures between the disparate index spaces. SLAM is a library for linear algebra solvers and tools for linking to external solver packages. Combining these tools allows for the research and development of novel methods for solving problems in computational physics. This work discusses the ELEMENTS package and reviews multiple numerical methods built using ELEMENTS.

<p>This thesis presents briefly the application of quantum mechanics on systems ofchemical interest, i.e., the field of quantum chemistry and computational chemistry.The molecules of the ten-electron series, hydrogen fluoride, water, ammonia,methane and neon, are taken as computational examples. Some applications ofquantum chemistry are then shown on these systems, with emphasis on the natureof the molecular bonds. Conceptual methods of chemistry and theoreticalchemistry for these systems are shown to be valid with some restrictions, as theseinterpretations does not represent physically measurable entities.The orbitals and orbital energies of neon is studied, the binding van der Waalsinteractionresulting in a Ne2 molecule is studied with a theoretical bond lengthof 3.23 °A and dissociation energy of 81.75 μEh. The equilibrium geometries ofFH, H2O, NH3 and CH4 are studied and the strength and character of the bondsinvolved evaluated using bond order, dipole moment, Mulliken population analysisand L¨owdin population analysis. The concept of electronegativity is studied in thecontext of electron transfer. Lastly, the barrier of inversion for NH3 is studied, withan obtained barrier height of 8.46 mEh and relatively constant electron transfer.</p>

This thesis presents briefly the application of quantum mechanics on systems ofchemical interest, i.e., the field of quantum chemistry and computational chemistry.The molecules of the ten-electron series, hydrogen fluoride, water, ammonia,methane and neon, are taken as computational examples. Some applications ofquantum chemistry are then shown on these systems, with emphasis on the natureof the molecular bonds. Conceptual methods of chemistry and theoreticalchemistry for these systems are shown to be valid with some restrictions, as theseinterpretations does not represent physically measurable entities.The orbitals and orbital energies of neon is studied, the binding van der Waalsinteractionresulting in a Ne2 molecule is studied with a theoretical bond lengthof 3.23 °A and dissociation energy of 81.75 μEh. The equilibrium geometries ofFH, H2O, NH3 and CH4 are studied and the strength and character of the bondsinvolved evaluated using bond order, dipole moment, Mulliken population analysisand L¨owdin population analysis. The concept of electronegativity is studied in thecontext of electron transfer. Lastly, the barrier of inversion for NH3 is studied, withan obtained barrier height of 8.46 mEh and relatively constant electron transfer.

<p>  </p> <p>In 2011, the Materials Genome Initiative (MGI) was founded as an effort to unite and drive materials design at an unprecedented pace. By linking computational tools with experimental data, and aligning their data structures to match and interact, scientists across the world have been able to change the way they do science at a fundamental level.</p> <p>The 3 Mission Statements of the Materials Genome Initiative include: 1) Developing a Materials Innovation Infrastructure 2) Achieving National Goals with Advanced Materials 3) Equipping the Next-Generation Materials Workforce. Since the inception of the MGI the Materials Engineering community has developed numerous cyberinfrastructure repositories for experimental, and varied levels of computational data. This practice aligns with a separate initiative for Findable, Accessible, Interoperable, and Reproducible (F.A.I.R.) principles for data handling and science. By integrating the cyberinfrastructure efforts with continued collaboration from experimental and computational scientists we push the field to evolve improved workflows for research.</p> <p>This thesis is a collection of applied solutions for materials design with atomistic modeling, and machine learning (ML). In Part 1, we will discuss bridges for the gaps between atomistic simulation and experiment, and what it means for material solutions. A showcase of combining experimental information with ab initio electronic transport calculations will be discussed, as well as the principles of density functional theory (DFT) and molecular dynamics (MD) simulations. In Part 2, our focus will shift to applications of machine learning and the use of composition and chemical featurizers for materials design. Here we leverage cyberinfrastructure efforts with APIs and ML with transfer and active learning for efficient high-dimensional space exploration. In Part 3 local atomic environments and configurations, associative fingerprinting solutions, and workflows for designing deep learning (DL) interatomic potentials for MD are discussed. Finally, a brief section will conclude with efforts made to align with F.A.I.R. principles for Materials Engineering research, and educational development for Mission Statement 3 of the MGI.</p>

In the aerospace industry, gas discharges have gained importance with the exploration of their performance and capabilities for flow control and combustion. Tunable properties of plasma make gas discharges efficient tools for various purposes. Since the scales of plasma and the available technology limit the knowledge gained from experimental studies, computational studies are essential to understand the results of experimental studies. The temporal and spatial scales of plasma also restrict the numerical studies. It is a necessity to use an idealized model, in which enough physics is captured, while the computational costs are acceptable.<br><br>In this work, numerical simulations of different low-pressure gas discharges are presented with a detailed analysis of the numerical approach. A one moment model is employed for DC glow discharges and nanosecond-pulse discharges. The cheap-est method regarding the modeling and simulation costs is chosen by checking the requirements of the fundamental processes of gas discharges. The verification of one-moment 1-D glow discharges with constant electron temperature variation is achieved by comparing other computational results.<br><br>The one moment model for pulse discharge simulation aims to capture the information from the experimental data for low-pressure argon discharges. Since the constant temperature assumption is crude, the local field approximation is investigated to obtain the data for electron temperature. It was observed that experimental data and computational data do not match because of the stagnant decay of electron number densities and temperatures. At the suggestion of the experimental group, water vapor was added as an impurity to the plasma chemistry. Although there was an improvement with the addition of water vapor, the results were still not in good agreement with experiment.<br><br>The applicability of the local field approximation was investigated, and non-local effects were included in the context of an averaged energy equation. A 0-D electron temperature equation was employed with the collision frequencies obtained from the local field approximation. It was observed that the shape of the decay profiles matched with the experimental data. The number densities; however, are less almost an order of magnitude.<br><br>As a final step, the two-moment model, one-moment model plus thermal electron energy equation, was solved to involve non-local effects. The two-moment model allows capturing of non-local effects and improves agreement with the experimental data. Overall, it was observed that non-local regions dominate low-pressure pulsed discharges. The local field approximation is not adequate to solve these types of discharges.

No description available.

La bonne precision du champ magnetique est souvent necessaire pour l'imagerie a resonance magnetique. Une des possibilites pour creer ce champ est d'utiliser l'expansion de Legendre de la fonction de Green. Nous proposons une methode qui corrige les defauts de champ magnetique sur un volume d'interet par l'utilisation de petits aimants permanents (appeles "shims"). Leur position sera determinee logiciellement. Cette methode de calcul peut aussi etre utilisee pour creer quasi n'importe quel champ avec des valeurs negligeables des harmoniques d'ordre eleve.

Title: Computational study of probe diagnostics in high-temperature plasma Author: Jan Lachnitt Department: Department of Surface and Plasma Science Supervisor: prof. RNDr. Rudolf Hrach, DrSc., Department of Surface and Plasma Science Abstract: This work is concerned to the particle computer modelling of the interaction of plasma, especially edge plasma, with immersed solids, especially probes. First, the speed and accuracy of several algorithms of the electrostatic force calculation were compared. One of the algorithms has been newly proposed. Then, a two-dimensional model of the interaction of collision-less plasma with a probe was created. This model has been applied to experimental data from CASTOR tokamak. The crucial point of this work is the creation of a fully three-dimensional particle model. This model has been tested for accuracy and speed and has been parallelized for higher efficiency. Keywords: plasma, probe diagnostics, computational physics, particle modelling

Estudar as propriedades físicas do solo envolve conhecer a umidade, o transporte de água e solutos, a densidade, a identificação da porosidade, o que é essencial para o crescimento de raízes das plantas. Para esses estudos, a tomografia de raios X tem se mostrado uma técnica útil. As imagens tomográficas são obtidas através de projeções (sinais) que são reconstruídos com algoritmos adequados. No processo de aquisição dessas projeções, podem surgir ruídos provenientes de diferentes fontes. O sinal tomográfico apresenta ruídos que possuem uma distribuição de Poisson gerada pela contagem de fótons, bem como o detector de fótons é influenciado por uma presença de ruído eletrônico com uma distribuição Gaussiana. Essas diferentes distribuições podem ser mapeadas com transformadas não lineares específicas que alteram uma distribuição Gaussiana para outros tipos de distribuições, como a de transformada de Anscombe (Poisson) ou transformada de Box-Muller (Uniforme), mas são aproximações que apresentam erros acumulativos. As transformadas podem ser então mapeadas por um sistema de redes neurais, o que garante um melhor resultado com o filtro de Kalman não linear em que os pesos da rede e as medidas das projeções são estimados em conjunto. Este trabalho apresenta uma nova solução com filtragem de Kalman descentralizada utilizando redes neurais artificiais embarcada em uma arquitetura reconfigurável com o intuito de obter se um valor ótimo de melhoria na relação Sinal/Ruído de projeções tomográficas e consequentemente nas imagens reconstruídas proporcionando melhorias para os métodos de análise dos físicos de solos agrícolas. / To study the physical properties of soil moisture involves knowing the transport of water and solutes, density, porosity identification, which is essential for the growth of plant roots. For these studies, X-ray tomography has been shown to be a useful technique. The tomographic images are obtained through projections (signals) that are reconstructed with appropriate algorithms. In the process of acquiring these projections, noise can arise from different sources. The tomographic signal is noisy which have a Poisson distribution generated by photon counting, and the photon detector is influenced by a presence of electronic noise with a Gaussian distribution. These different distributions can be mapped to specific nonlinear transformed altering a Gaussian distribution for other types of distributions, such as the Anscombe transform (Poisson) or Box-Muller transform (Uniform), but are approximations that have cumulative errors. Transforms can then be mapped by a neural network system, which ensures a better result with nonlinear Kalman filter in which the network weights and measures of the projections are estimated together. This work presents a new solution to the unscented Kalman filtering using artificial neural networks embedded in a reconfigurable architecture in order to obtain an optimum value of improvement in S/N ratio of tomographic projections and consequently the images reconstructed by providing improvements for the methods of physical parameters of the agricultural soils.