A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

A computational fluid dynamics model has been developed to study an oil-coated particle immersed in a uniform aqueous flow, to determine the conditions that favour oil separation. The governing flow equations are discretized using a finite volume approach, and the oil/water interface is captured using the Volume-of-Fluid (VOF) method in a 2D spherical coordinate system. The model predicts different mechanisms for oil separation. At a Reynolds number, Re, equal to 1, and at a low capillary number, Ca << 1, the high interfacial tension can induce rapid contact line motion, to the extent that the oil film can advance past its equilibrium position and separate from the particle. This mechanism requires that the contact angle measured through the oil phase is large. On the other hand, as Ca approaches 1, the shear exerted by the external flow stretches the oil into a thread that will eventually rupture and separate.

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The basic problem with angle-only or bearings-only tracking is to estimate the trajectory of a target (i.e., position and velocity) by using noise corrupted sensor angle data. In this thesis, the tracking platform is an Aerial Vehicle and the target is simulated as another Aerial Vehicle. Therefore, the problem can be defined as a single-sensor bearings only tracking. The state consists of relative position and velocity between the target and the platform. In the case where both the target and the platform travel at constant velocity, the angle measurements do not provide any information about the range between the target and the platform. The platform has to maneuver to be able to estimate the range of the target. Two problems are investigated and tested on simulated data. The first problem is tracking non-maneuvering targets. Extended Kalman Filter (EKF), Range Parameterized Kalman Filter and particle filter are implemented in order to track non-maneuvering targets. As the second problem, tracking maneuvering targets are investigated. An interacting multiple model (IMM) filter and different particle filter solutions are designed for this purpose. Kalman filter covariance matrix initialization and regularization step of the regularized particle filter are discussed in detail.

This work serves to present the background, approach, and selected results for the initial master thesis and prototyping phase of Open Space, a joint visualization software development project by National Aeronautics and Space Administration (NASA), Linköping University (LiU) and the American Museum of Natural History (AMNH). The thesis report provides a theoretical introduction to heliophysics, modeling of space weather events, volumetric rendering, and an understanding of how these relate in the bigger scope of Open Space. A set of visualization tools that are currently used at NASA and AMNH are presented and discussed. These tools are used to visualize global heliosphere models, both for scientific studies and for public presentations, and are mainly making use of geometric rendering techniques. The paper will, in detail, describe a new approach to visualize the science models with volumetric rendering to better represent the volumetric structure of the data. Custom processors have been developed for the open source volumetric rendering engine Voreen, to load and visualize science models provided by the Community Coordinated Modeling Center (CCMC) at NASA Goddard Space Flight Center (GSFC). Selected parts of the code are presented by C++ code examples. To best represent models that are defined in non-Cartesian space, a new approach to volumetric rendering is presented and discussed. Compared to the traditional approach of transforming such models to Cartesian space, this new approach performs no such model transformations, and thus minimizes the amount of empty voxels and introduces less interpolation artifacts. Final results are presented as rendered images and are discussed from a scientific visualization perspective, taking into account the physics representation, potential rendering artifacts, and the rendering performance.

This thesis contains solutions to chosen problems of applied mathematics. It comprises examples related to geometrical applications of the double and triple integrals´ theory, ie calculation methods of areas, volumes, mass and coordinates of gravity centres. Each problem´s solution is described in detail and supplemented with a picture. The problems are arranged according to complexity.