Thesis (M.Sc.Eng.) / To determine satellite trajectories in low earth orbit, engineers need to adequately estimate aerodynamic forces. But to this day, such a task su↵ers from inexact values of drag forces acting on complicated shapes that form modern spacecraft. While some of the complications arise from the uncertainty in the upper atmosphere, this work focuses on the problems in modeling the flow interaction with the satellite geometry. The only numerical approach that accurately captures e↵ects in this flow regime—like self-shadowing and multiple molecular reflections—is known as Test Particle Monte Carlo. This method executes a ray-tracing algorithm to follow particles that pass through a control volume containing the spacecraft and accumulates the momentum transfer to the body surfaces. Statistical fluctuations inherent in the approach demand particle numbers on the order of millions, often making this scheme too costly to be practical. This work presents a parallel Test Particle Monte Carlo method that takes advantage of both graphics processing units and multi-core central processing units. The speed at which this model can run with millions of particles enabled the exploration of regimes where a flaw was revealed in the model’s initial particle seeding. A new model introduces an analytical fix to this flaw—consisting of initial position distributions at the boundary of a spherical control volume and an integral for the correct number flux—which is used to seed the calculation. This thesis includes validation of the proposed model using analytical solutions for several simple geometries and demonstrates uses of the method for the aero-stabilization of the Phobos-Grunt Martian probe and pose-estimation for the ICESat mission. / 2031-01-01

<p>During operation of heavy ion accelerators a significant pressure rise has been observed when the intensity of the high energy beam was increased. The cause for this pressure rise is ion induced desorption, which is the result when beam ions collide with residual gas molecules in the accelerator, whereby they undergo charge exchange. Since the change in charge state will affect the bending radius of the particles after they have passed a bending magnet, they will not follow the required trajectory but instead collide with the vacuum chamber wall and gas are released. For the Future GSI project FAIR (Facility for Antiproton and Ion Research) there is a need to upgrade the SIS18 synchrotron in order to meet the requirements of the increased intensity. The aim of this work was to measure the desorption yields, η, (released molecules per incident ion) from materials commonly used in accelerators: 316LN stainless steel, Cu, Etched Cu, gold coated Cu, Ta and TiZrV coated stainless steel with argon and uranium beams at the energies 5-100 MeV/u. The measurements were performed at GSI and at The Svedberg Laboratory where a new dedicated teststand was built. It was found that the desorption yield scales with the electronic energy loss to the second power, decreasing for increasing impact energy above the Bragg Maximum. A feasibility study on the possibility to use laser refractometry to improve the accuracy of a specific throughput system was performed. The result was an improvement by up to 3 orders of magnitude, depending on pressure range.</p>

During operation of heavy ion accelerators a significant pressure rise has been observed when the intensity of the high energy beam was increased. The cause for this pressure rise is ion induced desorption, which is the result when beam ions collide with residual gas molecules in the accelerator, whereby they undergo charge exchange. Since the change in charge state will affect the bending radius of the particles after they have passed a bending magnet, they will not follow the required trajectory but instead collide with the vacuum chamber wall and gas are released. For the Future GSI project FAIR (Facility for Antiproton and Ion Research) there is a need to upgrade the SIS18 synchrotron in order to meet the requirements of the increased intensity. The aim of this work was to measure the desorption yields, η, (released molecules per incident ion) from materials commonly used in accelerators: 316LN stainless steel, Cu, Etched Cu, gold coated Cu, Ta and TiZrV coated stainless steel with argon and uranium beams at the energies 5-100 MeV/u. The measurements were performed at GSI and at The Svedberg Laboratory where a new dedicated teststand was built. It was found that the desorption yield scales with the electronic energy loss to the second power, decreasing for increasing impact energy above the Bragg Maximum. A feasibility study on the possibility to use laser refractometry to improve the accuracy of a specific throughput system was performed. The result was an improvement by up to 3 orders of magnitude, depending on pressure range.

Cette thèse contient deux sujets différents la simulation d'événements rares et un transport d'homotopie pour l'estimation du modèle de volatilité stochastique, dont chacun est couvert dans une partie distincte de cette thèse. Les méthodes de particules, qui généralisent les modèles de Markov cachés, sont largement utilisées dans différents domaines tels que le traitement du signal, la biologie, l'estimation d'événements rares, la finance, etc. Il existe un certain nombre d'approches basées sur les méthodes de Monte Carlo, tels que Markov Chain Monte Carlo (MCMC), Monte Carlo séquentiel (SMC). Nous appliquons des algorithmes SMC pour estimer les probabilités de défaut dans un processus d'intensité basé sur un processus stable afin de calculer un ajustement de valeur de crédit (CV A) avec le wrong way risk (WWR). Nous proposons une nouvelle approche pour estimer les événements rares, basée sur la génération de chaînes de Markov en simulant le système hamiltonien. Nous démontrons les propriétés, ce qui nous permet d'avoir une chaîne de Markov ergodique et nous montrons la performance de notre approche sur l'exemple que nous rencontrons dans la valorisation des options. Dans la deuxième partie, nous visons à estimer numériquement un modèle de volatilité stochastique, et à le considérer dans le contexte d'un problème de transport, lorsque nous aimerions trouver «un plan de transport optimal» qui représente la mesure d'image. Dans un contexte de filtrage, nous le comprenons comme le transport de particules d'une distribution antérieure à une distribution postérieure dans le pseudo-temps. Nous avons également proposé de repondérer les particules transportées, de manière à ce que nous puissions nous diriger vers la zone où se concentrent les particules de poids élevé. Nous avons montré sur l'exemple du modèle de la volatilité stochastique de Stein-Stein l'application de notre méthode et illustré le biais et la variance. / The thesis introduces simulation techniques that are based on particle methods and it consists of two parts, namely rare event simulation and a homotopy transport for stochastic volatility model estimation. Particle methods, that generalize hidden Markov models, are widely used in different fields such as signal processing, biology, rare events estimation, finance, etc. There are a number of approaches that are based on Monte Carlo methods that allow to approximate a target density such as Markov Chain Monte Carlo (MCMC), sequential Monte Carlo (SMC). We apply SMC algorithms to estimate default probabilities in a stable process based intensity process to compute a credit value adjustment (CV A) with a wrong way risk (WWR). We propose a novel approach to estimate rare events, which is based on the generation of Markov Chains by simulating the Hamiltonian system. We demonstrate the properties, that allows us to have ergodic Markov Chain and show the performance of our approach on the example that we encounter in option pricing.In the second part, we aim at numerically estimating a stochastic volatility model, and consider it in the context of a transportation problem, when we would like to find "an optimal transport map" that pushes forward the measure. In a filtering context, we understand it as the transportation of particles from a prior to a posterior distribution in pseudotime. We also proposed to reweight transported particles, so as we can direct to the area, where particles with high weights are concentrated. We showed the application of our method on the example of option pricing with Stein­Stein stochastic volatility model and illustrated the bias and variance.