Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

Numerical simulation of rotor-stator interaction and tip clearance flow in centrifugal compressors

The effect of the tip clearance and vaneless diffuser width on the stage performance and flow fields of a centrifugal compressor were studied numerically and results were compared to the experimental measurements. The diffuser width was changed by moving the shroud side of the diffuser axially and six tip clearances size from 0.5 to 3 mm were studied. Moreover, the effects of rotor-stator interaction on the diffuser and impeller flow fields and performance were studied. Also transient simulations were carried out in order to investigate the influence of the interaction on the impeller and diffuser performance parameters. It was seen that pinch could improve the performance and it help to get more uniform flow at exit and less back flow from diffuser to the impeller.

Numerical Studies of Dark Energy Models and Observations

The cosmological standard view is based on the assumptions of homogeneity, isotropy and general relativistic gravitational interaction. These alone are not sufficient for describing the current cosmological observations of accelerated expansion of space. Although general relativity is extremely accurately tested to describe the local gravitational phenomena, there is a strong demand for modifying either the energy content of the universe or the gravitational interaction itself to account for the accelerated expansion. By adding a non-luminous matter component and a constant energy component with negative pressure, the observations can be explained with general relativity. Gravitation, cosmological models and their observational phenomenology are discussed in this thesis. Several classes of dark energy models that are motivated by theories outside the standard formulation of physics were studied with emphasis on the observational interpretation. All the cosmological models that seek to explain the cosmological observations, must also conform to the local phenomena. This poses stringent conditions for the physically viable cosmological models. Predictions from a supergravity quintessence model was compared to Supernova 1a data and several metric gravity models were studied with local experimental results. Polytropic stellar configurations of solar, white dwarf and neutron stars were numerically studied with modified gravity models. The main interest was to study the spacetime around the stars. The results shed light on the viability of the studied cosmological models.

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.

Lyophilized allografts without pre-treatment with glutaraldehyde are more suitable than cryopreserved allografts for pulmonary artery reconstruction

Various methods are available for preservation of vascular grafts for pulmonary artery (PA) replacement. Lyophilization and cryopreservation reduce antigenicity and prevent thrombosis and calcification in vascular grafts, so both methods can be used to obtain vascular bioprostheses. We evaluated the hemodynamic, gasometric, imaging, and macroscopic and microscopic findings produced by PA reconstruction with lyophilized (LyoPA) grafts and cryopreserved (CryoPA) grafts in dogs. Eighteen healthy crossbred adult dogs of both sexes weighing between 18 and 20 kg were used and divided into three groups of six: group I, PA section and reanastomosis; group II, PA resection and reconstruction with LyoPA allograft; group III, PA resection and reconstruction with CryoPA allograft. Dogs were evaluated 4 weeks after surgery, and the status of the graft and vascular anastomosis were examined macroscopically and microscopically. No clinical, radiologic, or blood-gas abnormalities were observed during the study. The mean pulmonary artery pressure (MPAP) in group III increased significantly at the end of the study compared with baseline (P=0.02) and final [P=0.007, two-way repeat-measures analysis of variance (RM ANOVA)] values. Pulmonary vascular resistance of groups II and III increased immediately after reperfusion and also at the end of the study compared to baseline. The increase shown by group III vs group I was significant only if compared with after surgery and study end (P=0.016 and P=0.005, respectively, two-way RM ANOVA). Microscopically, permeability was reduced by ≤75% in group III. In conclusion, substitution of PAs with LyoPA grafts is technically feasible and clinically promising.

Reconstruction of cranial bone defects with fiber-reinforced composite–bioactive glass implants

A cranial bone defect may result after an operative treatment of trauma, infection, vascular insult, or tumor. New biomaterials for cranial bone defect reconstructions are needed for example to mimic the biomechanical properties and structure of cranial bone. A novel glass fiber-reinforced composite implant with bioactive glass particulates (FRC–BG, fiber-reinforced composite–bioactive glass) has osteointegrative potential in a preclinical setting. The aim of the first and second study was to investigate the functionality of a FRC–BG implant in the reconstruction of cranial bone defects. During the years 2007–2014, a prospective clinical trial was conducted in two tertiary level academic institutions (Turku University Hospital and Oulu University Hospital) to evaluate the treatment outcome in 35 patients that underwent a FRC–BG cranioplasty. The treatment outcome was good both in adult and pediatric patients. A number of conventional complications related to cranioplasty were observed. In the third study, a retrospective outcome evaluation of 100 cranioplasty procedures performed in Turku University Hospital between years 2002–2012 was conducted. The experimental fourth study was conducted to test the load-bearing capacity and fracture behavior of FRC–BG implants under static loading. The interconnective bars in the implant structure markedly increased the load-bearing capacity of the implant. A loading test did not demonstrate any protrusions of glass fibers or fiber cut. The fracture type was buckling and delamination. In this study, a postoperative complication requiring a reoperation or removal of the cranioplasty material was observed in one out of five cranioplasty patients. The treatment outcomes of cranioplasty performed with different synthetic materials did not show significant difference when compared with autograft. The FRC–BG implant was demonstrated to be safe and biocompatible biomaterial for large cranial bone defect reconstructions in adult and pediatric patients.

Spectral Retinal Images Reconstruction

While red-green-blue (RGB) image of retina has quite limited information, retinal multispectral images provide both spatial and spectral information which could enhance the capability of exploring the eye-related problems in their early stages. In this thesis, two learning-based algorithms for reconstructing of spectral retinal images from the RGB images are developed by a two-step manner. First, related previous techniques are reviewed and studied. Then, the most suitable methods are enhanced and combined to have new algorithms for the reconstruction of spectral retinal images. The proposed approaches are based on radial basis function network to learn a mapping from tristimulus colour space to multi-spectral space. The resemblance level of reproduced spectral images and original images is estimated using spectral distance metrics spectral angle mapper, spectral correlation mapper, and spectral information divergence, which show a promising result from the suggested algorithms.

Construction. Primes et prêts spéciaux. [1954.] Aide complémentaire, logements économiques. 2e édition. [Textes mis à jour à la date du 15 mars 1954 par les soins du Ministère de la Reconstruction et du logement.]

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