This report will look at optimization under parameters of uncertainties. It will describe the subject in its wider form, then two model examples will be studied, followed by an application to an ABB product. The Monte Carlo method will be described and scrutinised, with the quasi-Monte Carlo method being favoured for large problems. An example will illustrate how the choice of Monte Carlo method will affect the efficiency of the simulation when evaluating  functions of different dimensions. Then an overview of mathematical optimization is given, from its simplest form to nonlinear, nonconvex  optimization problems containing uncertainties.A Monte Carlo simulation is applied to the design process and cost function for a custom made ABB transformer, where the production process is assumed to contain some uncertainties.The result from optimizing an ABB cost formula, where the in-parameters contains some uncertainties, shows how the price can vary and is not fixed as often assumed, and how this could influence an accept/reject decision.

>Magister Scientiae - MSc / Measurements of nuclear level lifetimes are an important aspect of experimental nuclear physics. Such measurements determine transition matrix elements for nuclear structure research and also provide the widths of relevant excited states in nuclei that are of astrophysical interest. In the latter, the measured widths are used to obtain reaction rates in main sequence stars such as the Sun and in binary-star systems where the accretion of material from one star to another provides an opportunity to study extreme stellar environments such as novae and x-ray bursts. This thesis work describes the design and simulation of a new experimental set up at iThemba LABS that will allow for highprecision femtosecond-level lifetime measurements of nuclear states using the Doppler Shift Attenuation Method (DSAM). We use the Solid Edge computer-aided design (CAD) software to design a new scattering chamber with a cooled target ladder specifically for such measurements using inverse-kinematic transfer reactions with ion implanted targets. The light charged ejectiles from the reaction will be detected with a ΔE - E silicon telescope, while Doppler shifted rays will be registered using a high-purity and 100% efficient germanium (HPGe) detector. We also describe preliminary Monte Carlo simulation codes that are being developed in a relativistically invariant framework to optimize the experimental set up and to obtain predicted lineshapes of γ rays from several astrophysically relevant states in nuclei using this experimental set up. / National Research Foundation (NRF)

Abstract Optical coherence tomography (OCT) is a modern rapidly developing technique for non-invasive imaging of the internal structure of optically non-uniform objects based on the principles of low-coherent interferometry. However, multiple scattering of light in the objects under study brings distortions to the images obtained by OCT. The analysis of formation of the OCT signals is required for understanding the role of multiple scattering in this formation and providing recommendations for optimal configuration of a measuring setup. In the present thesis formation of the OCT signals and images is analyzed implementing Monte Carlo simulations of light propagation in scattering media. Blood, intralipid solution, human skin and paper samples are chosen as the objects under study due to the interest in the diagnostics of these objects in biomedicine and paper industry. Multilayer models of skin phantoms, skin and paper were developed in the frames of the present study for simulation of OCT signals and two-dimensional OCT images of these objects. The contribution of different scattering orders as well as different fractions of photons (least and multiply scattered, diffusive and non-diffusive) to these images was found allowing to evaluate the maximal depth of non-distorted imaging in each particular case. The simulated OCT images were compared to the experimental ones demonstrating qualitative similarity. This fact allowed the author to analyze qualitatively the influence of parameters of the OCT setup on the images which have also been acquired in this work. The formation of the OCT images of paper samples with various refractive index matching liquids was also studied.

>Magister Scientiae - MSc / The study of ²²Na beta decay offers an opportunity to test the Standard Model of Particle Physics via measurements of the β−γ angular correlation. A previous measurement of this correlation yielded a non-zero value, indicating the need for a higher-order matrix element to the decay, beyond the allowed V − A approximation. On assuming the Conserved Vector Current (CVC) hypothesis for weak interactions and using the magnetic dipole M1 width of the analog 2+ state in ²²Na, one obtains an unexpectedly large 'second-class' form factor for 22Na β decay that is in disagreement with the Standard Model prediction. This thesis describes an analysis of data obtained from a previous ²¹Ne(p, γ) experiment to obtain the M1 width of the 2+ state of interest in ²²Na. This work aims to use the M1 width and the independently measured of the β − γ angular correlation to obtain a higher-order Standard-Model-allowed weak magnetism form factor for the decay, in an attempt to explain the observed anomaly mentioned above. / National Research Foundation (NRF)

Pricing of more complex derivatives is very often based on Monte Carlo simulations. Estimates given by these simulations are derived from thousands of scenarions for the underlying asset price developement. These estimates can be more precise in case of higher number of scenarions or in case of modifications of a simulation mentioned in this master thesis. First part of the thesis includes theoretic description of variance reduction techniques, second part consists of implementation of all techniques in pricing a barrier option and of their comparison. We conclude the thesis by two statements. The former one says that usage of each technique is subject to simulation specifics, the latter one recommends to use MC simulations even in the case a closed-form formula was derived.

Adverse changes in the Earth's climate are thought to be due to the output of carbon dioxide from power stations. This has led to the development of many new materials to remove CO2 from these gas streams. Polymers of intrinsic microporosity (PIMs) are a novel class of polymers that are rigid with sites of contortion. These properties result in inefficient packing and so lead to large pore volumes and high surface areas. The inclusion of Tröger’s base, a contortion site made up of two nitrogen atoms, is thought to lead to increased uptake of CO2. The combination of electrostatic interactions with strong van der Waals forces should interact favourable with the quadrupole moment of CO2.Here a molecular simulation study of a selection of these polymers is presented. The study begins by developing a quick screening method on single polymer chains. This shows that the high surface area and adsorption affinity are a result of the contorted nature of PIMs along with the inclusion of groups such as Tröger’s base.The creation of atomistic models that reproduce the space packing ability of these polymers is also explored. Methods developed for PIMs in literature are investigated along with a new method developed during this study. GCMC simulations are then used to investigate the adsorption of CO2. In this study it is seen that that these polymers possess a well percolated network of both ultramicropores and supermicropores with a significant fraction of these pores being close to the kinetic diameter of CO 2. It is posited that these pores may be the result of the inclusion of Tröger’s base. It is also shown that this produces a particularly favourable site for adsorption. The phenomenon of swelling as a result of CO2 adsorption is also investigated using a variety of methods that make use of the output from the GCMC simulations. It was found that swelling is negligible for pressures of up to 1 bar. This result is important as swelling in the polymer can lead to a reduction in selectivity and an increase in permeability, which can affect the overall material’s performance.

This Thesis investigates computationally the behaviour of two novel microporous materials,organic molecules of intrinsic microporosity (OMIMs) and polymers of intrinsic microporosity(PIMs). OMIMs and PIMs are organic amorphous materials, which achieve microporosityby packing inefficiently. The design of amorphous materials is challenging because their self-assembly process is not known. Predictive molecular simulations can help in recognising thefeatures that affect the properties of these materials, and guiding in the design of new structures with desired performances. OMIMs are highly concave shaped molecules, consisting of a core and a series of termini, which provide the geometry and the general chemical environment of these structures, respectively. PIMs are polymers consisting of fundamental units such as stiff segments and contortionsites, which form either linear or network like porous structures. While chronologically olderthan OMIMs, they share with them a common design philosophy. This Thesis is presented in alternative format, and the results, consisting of five journal articles,can be divided into three main parts. The first part focuses on recognising a reliable method to generate representative models ofOMIMs. Different computational protocols and molecular mechanics descriptions were investigated; the development of the utilised simulation protocol was based on comparison of several simulation methods and force fields to experimental wide angle X-ray scattering (WAXS) patterns. Our work suggests that OMIMs can be described successfully by both PCFF and UFF; the final packed material can be generated using a 21-step compression-decompression molecular dynamics protocol, previously developed to generate virtual model of PIMs. The examination of the simulated structures has provided a deeper understanding of the features that affect the packing behaviour of this class of materials, suggesting that OMIMs have a greater microporosity when the molecules are the most shape-persistent, which required rigid structures and bulky end groups. The adsorption behaviour described by different generic force fields (Dreiding, OPLS and UFF) was also investigated to guide on the selection of the solid-fluid interactions when modelling OMIMs, for future comparison with experimental data. Our results suggest that very strong interactions between argon adsorbate and OMIM-based framework are described by UFF, while the weakest adsorbent is obtained using OPLS force field. The second part of the research focuses on assessing the effect that different termini’s chemistry and bulkiness have over the packing behaviour, adsorption properties and solubility of the OMIMs. The microporous frameworks generated by two selected families of cruciform OMIMs (benzene and naphthalene- based) were investigated with respect to their packing behaviour, porosity and adsorption properties. Our analysis suggests that the final density of the material, as well as the surface area and pore volume, depend on the ending group’s bulkiness. Bulkier molecules lead to materials with lower densities, but it was found that the adsorption behaviour is not just related to the material’s density, but also to the pore size and shape, which are determined by the way the molecules pack. The relationship between adsorption capacity and physical properties was analysed and the role of surface area, free volume and enthalpic interaction was used to identify different adsorption regimes. It was found that the uptake of argon at low pressure is proportional to the strength of the adsorbent-adsorbate interaction while at moderate pressure it is dependent on the free volume and surface area. The dissolution of three cruciform OMIMs was investigated in dichloromethane, ethyl acetateand toluene. Direct interface molecular dynamics simulations showed that the solubility process consists of two steps; the diffusion of the solvent in the OMIM-rich phase, and the departure of the OMIMs in the solvent bulk. We proposed a simple model to represent this mechanism. Furthermore, results from infinite dilution simulations show that the solvent-OMIMs interactions can be related to the chemistry of the OMIMs and to the solvent’s properties. We found that, in general, increasing the length of the OMIM’s arm affects negatively the solubility of the material, while adding bulky alkyl groups favours the interaction with the solvent molecules. The third part concentrates on the characterisation of PIMs and their application as CO2 adsorbent. Properties of four polymers of intrinsic microporosity containing Tröger’s base units were assessed for CO2 capture experimentally and computationally. Structural properties included average pore size, pore size distribution, surface area, and accessible pore volume, whereas thermodynamic properties focused on density, CO2 sorption isotherms, and enthalpies of adsorption. It was found that the shape of the contortion site plays a more important role than the polymer density when assessing the capacity of the material, and that the presence of a Tröger base unit only slightly affects the amount adsorbed at low pressures, but it does not have any significant influence on the enthalpy of adsorption fingerprint. A comparison of the materials studied with those reported in the literature allowed us to propose a set of guidelines for the design of polymers for CO2 capture applications.

Les études observationnelles en pharmacoépidémiologie sont souvent mises en place pour évaluer un médicament mis sur le marché récemment ou concurrencé par de nombreuses alternatives thérapeutiques. Cette situation conduit à devoir évaluer l'effet d'un médicament dans une cohorte comprenant peu de sujets traités, c'est à dire une population où l'exposition d'intérêt est rare. Afin de prendre en compte les facteurs de confusion dans cette situation, certains auteurs déconseillent l'utilisation du score de propension au profit du score pronostique, mais cette recommandation ne s'appuie sur aucune étude évaluant spécifiquement les faibles prévalences de l'exposition, et ignore le type d'estimation, conditionnelle ou marginale, fournie par chaque méthode d'utilisation du score pronostique.La première partie de ce travail évalue les méthodes basées sur le score de propension pour l'estimation d'un effet marginal en situation d'exposition rare. La deuxième partie évalue les performances des méthodes basées sur le score pronostique rapportées dans la littérature, introduit de nouvelles méthodes basées sur le score pronostique adaptées à l'estimation d'effets conditionnels ou marginaux, et les compare aux performances des méthodes basées sur le score de propension. La dernière partie traite des estimateurs de la variance des effets du traitement. Nous présentons les conséquences liées à la non prise en compte de l'étape d'estimation du score de propension et du score pronostique dans le calcul de la variance. Nous proposons et évaluons de nouveaux estimateurs tenant compte de cette étape. / Pharmacoepidemiologic observational studies are often conducted to evaluate newly marketed drugs or drugs in competition with many alternatives. In such cohort studies, the exposure of interest is rare. To take into account confounding factors in such settings, some authors advise against the use of the propensity score in favor of the prognostic score, but this recommendation is not supported by any study especially focused on infrequent exposures and ignores the type of estimation provided by each prognostic score-based method.The first part of this work evaluates the use of propensity score-based methods to estimate the marginal effect of a rare exposure. The second part evaluates the performance of the prognostic score based methods already reported in the literature, compares them with the propensity score based methods, and introduces some new prognostic score-based methods intended to estimate conditional or marginal effects. The last part deals with variance estimators of the treatment effect. We present the opposite consequences of ignoring the estimation step of the propensity score and the prognostic score. We show some new variance estimators accounting for this step.

We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the o ccupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find an evidence for a dynamical phase transition well below the transition temperature of the pure system.

Title: Prototype of detector for detection of reactor's antineutrinos Author: Lukáš Fajt Department: Institute of Particle and Nuclear Physics Supervisor: Doc. Ing. Ivan Štekl, CSc., IEAP, CTU in Prague Abstract: This master thesis is related to the development of the complex detector of reac- tor's antineutrinos, so called S3 , which is based on the polystyrene scintillation detectors. The detector S3 (dimensions 40 x 40 x 40 cm3 ) will be located in the close vicinity of a nuclear reactor (5-12 m) and its purpose will be to measure reactor's power, isotopic composition of the nuclear fuel and moreover verification of the sterile neutrino hypothesis by detecting reactor's antineutrinos via the Inverse Beta Decay (IBD) interaction. Within the thesis, the first prototype of the antineutrino detector was constructed. It is composed of 18 scintillation plates (40 x 20 x 1 cm3 ) and corresponding electronics. With this prototype the first test with cosmic muons were performed. Within the thesis, the energy reso- lution of the scintillation plates was significantly improved by the optimization of their chemical composition and selection of the optimal refractive material. The proper energy resolution is very important for the detector functionality. In addition, a new methods for the production of coating layer...