Upper-tropospheric (200 hPa) velocity potential is useful in identifying areas of rising or sinking atmospheric motions on varying temporal scales (e.g., weekly, seasonal, interannual) especially in the global tropics. These areas are associated with enhancement (rising motion) or suppression (sinking motion) of tropical convection and subsequent weather phenomena dependent on these processes (e.g., tropical cyclones). This study employed three commonly used global weather reanalysis datasets (NCEP/NCAR Reanalysis 1, JMA JRA-55, ECMWF ERA5) to calculate and compare upper-tropospheric velocity potential fields on varying temporal scales and quantify any differences that existed between them from 1958 to 2020 over four key regions of variability (Equatorial Africa, Amazon Basin, Equatorial Central Pacific, and Equatorial Indonesia). To supplement this analysis, the highly correlated variables to velocity potential of outgoing longwave radiation (OLR) and daily precipitation rate were used and directly compared with independent OLR and precipitation datasets to determine the reanalysis' level of agreement with the independent data. The ECMWF ERA5 held the highest agreement to these data over all regions examined and was reasoned to have the highest confidence in capturing the variability of upper-tropospheric velocity potential fields for the study period. Confidence was decreased in the usefulness of the NCEP/NCAR Reanalysis 1 as it consistently performed poorly over much of the study domain. The results of this study also emphasized the usefulness in ensemble-based approaches to assessing climate variability and understanding potential biases and uncertainties that are inherent in the data sources. / Master of Science / Historical weather data across the globe is analyzed using global weather reanalysis datasets which provide the most complete picture of how the atmosphere has evolved over the course of the last several decades. This data is a vital component in today's research investigating climate change and variability over time. This study examined how the history of upper-tropospheric velocity potential was captured in three commonly used global weather reanalysis datasets (NCEP/NCAR Reanalysis 1, JMA JRA-55, ECMWF ERA5) from 1958 to 2020 over four key regions of variability (Equatorial Africa, Amazon Basin, Equatorial Central Pacific, and Equatorial Indonesia). The variable of velocity potential is useful in identifying areas of rising or sinking atmospheric motions on varying time scales (e.g., weekly, seasonal, interannual) especially in the global tropics. These areas are associated with enhancement (rising motion) or suppression (sinking motion) of tropical convection (i.e., thunderstorms) and subsequent weather phenomena dependent on these processes (e.g., tropical cyclones). The analysis conducted found that the newest of the reanalysis datasets, the ECMWF ERA5, held the highest agreement to independent weather observations over all regions examined was reasoned to have the highest confidence in capturing the variability of upper-tropospheric velocity potential fields for the study period. Confidence was decreased in the usefulness of the NCEP/NCAR Reanalysis 1, the oldest of the reanalysis datasets, as it consistently performed poorly over much of the study domain. The results of this study also emphasized the usefulness in ensemble-based approaches to assessing climate variability and understanding potential biases and uncertainties that can be found in the data sources.

In this thesis, an approach for robot motion control with collision avoidance and human-following is investigated. Using velocity potential fields approach in a modified, quasi-harmonic, solution, the navigation controller is developed. A quasi-harmonic function based controller uses harmonic solutions for collision avoidance and smoothly changes toward a non-harmonic solution which tends toward a zero velocity command only when approaching the goal. After the motion controller was created, human-following strategy was designed to let a non-holonomic robot have the ability to follow a human in an unknown environment with obstacles. The approach is based on velocity potential fields that permit to generate velocity vector commands that drive the robot at a safe distance with regard to the human while avoiding obstacles. The quasi-harmonic approach is investigated analytically using symbolic math solutions of MAPLETM as well as in simulations using MATLABTM. Motion simulations of both holonomic and non-holonomic robot motion illustrate how the proposed approach operates. Experiments are also made with LEGO MINDSTROMS NXT robot to test the algorithm in environment with simple and complex obstacles.

In this thesis, robot navigation using the Particle Filter based FastSLAM approach for obstacle avoidance derived from a modified Velocity Potential Field method was investigated. A switching controller was developed to deal with robot’s efficient turning direction when close to obstacles. The determination of the efficient turning direction is based on the local map robot derived from its on board local sensing. The estimation of local map and robot path was implemented using the FastSLAM approach. A particle filter was utilized to obtain estimated robot path and obstacles (local map). When robot sensed only obstacles, the estimated robot positions was regarding to obstacles based the measurement of the distance between the robot and obstacles. When the robot detected the goal, estimation of robot path will switch to estimation with regard to the goal in order to obtain better estimated robot positions. Both simulation and experimental results illustrated that estimation with regard to the goal performs better than estimation regarding only to obstacles, because when robot travelled close to the goal, the residual error between estimated robot path and the ideal robot path becomes monotonously decreasing. When robot reached the goal, the estimated robot position and the ideal robot position converge. We investigated our proposed approach in two typical robot navigation scenarios. Simulations were accomplished using MATLAB, and experiments were conducted with the help of both MATLAB and LabVIEW. In simulations and experiments, the robot successfully chose efficiently turning direction to avoid obstacles and finally reached the goal.

In this thesis basic principles of sound system design are presented. A software simulation in Matlab is written for prediction of sound field with sources of real directivity in both freefield and in a closed room using velocity potential. Reflections are simulated using mirror sources of first and second order. Frequency dependent sound absorption coefficients are implemented in the simulation. There is a GUI designed to operate on most common horizontal configurations. Those are then evaluated and advantages and dissadvantages are demonstrated using the simulation software.

This report presents the work done within the framework of my master thesis in the program Infrastructure Engineering at KTH Royal Institute of Technology, Stockholm. This project has been proposed and sponsored by the French company Setec TPI, part of the Setec group, located in Paris. The overall goal of this study is to investigate fluid-structure interaction and particularly sloshing in liquid-containing structures subjected to seismic or other dynamic action. After a brief introduction, the report is composed of three main chapters. The first one presents and explains fluid-structure interaction equations. Fluid-structure interaction problems obey a general flow equation and several boundary conditions, given some basic assumptions. The purpose of the two following chapters is to solve the corresponding system of equations. The first approach proposes an analytical solution: the problem is solved for 2D rectangular tanks. Different models are considered and compared in order to analyze and describe sloshing phenomenon. Liquid can be decomposed in two parts: the lower part that moves in unison with the structure is modeled as an impulsive added mass; the upper part that sloshes is modeled as a convective added mass. Each of these two added mass creates hydrodynamic pressures and simple formulas are given in order to compute them. The second approach proposes a numerical solution: the goal is to be able to solve the problem for any kind of geometry. The differential problem is resolved using a singularity method and Gauss functions. It is stated as a boundary integral equation and solved by means of the Boundary Element Method. The linear system obtained is then implemented on Matlab. Scripts and results are presented. Matlab programs are run to solve fluid-structure interaction problems in the case of rectangular tanks: the results concur with the analytical solution which justifies the numerical solution. This report gives a good introduction to sloshing phenomenon and gathers several analytical solutions found in the literature. Besides, it provides a Matlab program able to model effects of sloshing in any liquid-containing structures.

Multi-vehicle systems offer many advantages in engineering applications such as increased efficiency and robustness. However, the disadvantage of multi-vehicle systems is that they require a high level of organization and coordination in order to successfully complete a task. Formation control is a field of engineering that addresses this issue, and provides coordination schemes to successfully implement multi-vehicle systems. Two approaches to group coordination were proposed in this work: geometric and self-organizing formations. A geometric reconfiguring formation was developed using the leader-follower method, and the self-organizing formation was developed using the velocity potential equations from fluid flow theory. Both formation controllers were first tested in simulation in MATLAB, and then implemented on the X80 mobile robot units. Various experiments were conducted to test the formations under difficult obstacle scenarios. The robots successfully navigated through the obstacles as a coordinated as a team using the self-organizing and geometric formation control approaches.

Multi-vehicle systems offer many advantages in engineering applications such as increased efficiency and robustness. However, the disadvantage of multi-vehicle systems is that they require a high level of organization and coordination in order to successfully complete a task. Formation control is a field of engineering that addresses this issue, and provides coordination schemes to successfully implement multi-vehicle systems. Two approaches to group coordination were proposed in this work: geometric and self-organizing formations. A geometric reconfiguring formation was developed using the leader-follower method, and the self-organizing formation was developed using the velocity potential equations from fluid flow theory. Both formation controllers were first tested in simulation in MATLAB, and then implemented on the X80 mobile robot units. Various experiments were conducted to test the formations under difficult obstacle scenarios. The robots successfully navigated through the obstacles as a coordinated as a team using the self-organizing and geometric formation control approaches.

Este trabalho apresenta uma dedução das equações para a dinâmica de vórtices em superfícies utilizando argumentos físicos e balanço de momento, obtendo o resultado já conhecido devido a Boatto/Koiller e Hally. Na primeira parte, elaboramos uma releitura da contribuição de diversos pesquisadores incluindo, além dos já citados, o trabalho de Marchioro e Pulvirenti sobre a propriedade de localização para a equação de Euler e também a importante contribuição de Flucher e Gustafsson no que diz respeito à determinação da função de Green e função de Robin hidrodinâmicas em domínios do plano. Na segunda parte revisamos o problema da dinâmica de um traçador passivo induzida por um vórtice no disco unitário e estendemos para o caso com vorticidade de fundo constante. Por fim, analisamos a dinâmica de dois vórtices no toro plano, a qual reduz-se ao estudo da dinâmica do centro de vorticidade com hamiltoniana dada pela função de Green. É feita uma descrição das bifurcações das curvas de níveis desta hamiltoniana com respeito a variações do parâmetro modular. Mostramos que o campo hamiltoniano em questão é preservado por biholomorfismos e, portanto, o espaço dos parâmetros pode ser reduzido ao espaço de Moduli do toro plano. Mudanças dentro de uma mesma classe de equivalência por biholomorfismos podem alterar apenas a classe de homotopia das curvas de nível. / In this thesis the equations for the motion of vortices on Riemannian surfaces is studied. Using conservation of momentum and physical arguments, the classical equations of Hally and Boatto/Koiller are recovered. Then the localization result for the Euler\'s equation with flat metric (Marchioro and Pulvirenti) and the determination of the Green\'s and Robin\'s functions on plane domains are revisited in the context of Riemannian surfaces. On a second part of the thesis two examples are analyzed. At first the dynamics of a passive tracer in the unit disk on the flat plane with constant background vorticity. At second the dynamics of two vortices on flat tori. This last system is integrable. The dynamics is determined by the level sets of the Green\'s function which depends on the modular parameter of the torus. The full bifurcation diagram of the system as a function of the module parameter is determined.

Este trabalho apresenta uma dedução das equações para a dinâmica de vórtices em superfícies utilizando argumentos físicos e balanço de momento, obtendo o resultado já conhecido devido a Boatto/Koiller e Hally. Na primeira parte, elaboramos uma releitura da contribuição de diversos pesquisadores incluindo, além dos já citados, o trabalho de Marchioro e Pulvirenti sobre a propriedade de localização para a equação de Euler e também a importante contribuição de Flucher e Gustafsson no que diz respeito à determinação da função de Green e função de Robin hidrodinâmicas em domínios do plano. Na segunda parte revisamos o problema da dinâmica de um traçador passivo induzida por um vórtice no disco unitário e estendemos para o caso com vorticidade de fundo constante. Por fim, analisamos a dinâmica de dois vórtices no toro plano, a qual reduz-se ao estudo da dinâmica do centro de vorticidade com hamiltoniana dada pela função de Green. É feita uma descrição das bifurcações das curvas de níveis desta hamiltoniana com respeito a variações do parâmetro modular. Mostramos que o campo hamiltoniano em questão é preservado por biholomorfismos e, portanto, o espaço dos parâmetros pode ser reduzido ao espaço de Moduli do toro plano. Mudanças dentro de uma mesma classe de equivalência por biholomorfismos podem alterar apenas a classe de homotopia das curvas de nível. / In this thesis the equations for the motion of vortices on Riemannian surfaces is studied. Using conservation of momentum and physical arguments, the classical equations of Hally and Boatto/Koiller are recovered. Then the localization result for the Euler\'s equation with flat metric (Marchioro and Pulvirenti) and the determination of the Green\'s and Robin\'s functions on plane domains are revisited in the context of Riemannian surfaces. On a second part of the thesis two examples are analyzed. At first the dynamics of a passive tracer in the unit disk on the flat plane with constant background vorticity. At second the dynamics of two vortices on flat tori. This last system is integrable. The dynamics is determined by the level sets of the Green\'s function which depends on the modular parameter of the torus. The full bifurcation diagram of the system as a function of the module parameter is determined.