Diese Arbeit befaßt sich mit der Koppelung von Vertex-Modellen an die planaren $\phi^4$-Zufallsgraphen des Zugangs zur Quantengravitation über dynamische Polygonifizierungen. Das betrachtete System hat eine doppelte Bedeutung, einerseits als die Koppelung einer konformen Feldtheorie mit zentraler Ladung $C=1$ an zweidimensionale Euklidische Quantengravitation, andererseits als Anwendung von geometrischer, "annealed" Unordnung auf ein prototypisches Modell der statistischen Mechanik. Da das Modell mit Hilfe einer großangelegten Reihe von Monte Carlo Simulationen untersucht wird, müssen entsprechende Techniken für die Simulation von dynamischen Quadrangulierungen bzw. die dualen $\phi^4$-Graphen entwickelt werden. Hierzu werden verschiedene Algorithmen und die dazugehörigen Züge vorgeschlagen und hinsichtlich ihrer Ergodizität und Effizienz untersucht. Zum Vergleich mit exakten Ergebnissen werden die Verteilung der Koordinationszahlen bzw. bestimmte Analoga davon konstruiert. Für Simulationen des $F$-Modells auf $\phi^4$-Zufallsgraphen wird ein Ordnungsparameter für den antiferroelektrischen Phasenübergang mit Hilfe einer Plakettenspindarstellung formuliert. Ausführliche "finite-size scaling"-Analysen des Kosterlitz-Thouless-Phasenübergangs des $F$-Modells auf dem Quadratgitter und auf Zufallsgraphen werden vorgestellt und die Positionen der jeweiligen kritischen Punkte sowie die dazugehörigen kritischen Exponenten werden bestimmt. Die Rückreaktion des Vertex-Modells auf die Zufallsgraphen wird in Form der Koordinationszahlverteilung, der Verteilung der "Baby-Universen" und dem daraus resultierenden String-Suszeptibilitäts-Exponenten sowie durch die geometrische Zweipunktfunktion analysiert, die eine Schätzung der intrinsischen Hausdorff-Dimension des gekoppelten Systems liefert. / In this thesis, the coupling of ice-type vertex models to the planar $\phi^4$ random graphs of the dynamical polygonifications approach to quantum gravity is considered. The investigated system has a double significance as a conformal field theory with central charge $C=1$ coupled to two-dimensional Euclidean quantum gravity and as the application of a special type of annealed connectivity disorder to a prototypic model of statistical mechanics. Since the model is analyzed by means of large-scale Monte Carlo simulations, suitable simulation techniques for the case of dynamical quadrangulations and the dual $\phi^4$ random graphs have to be developed. Different algorithms and the associated update moves are proposed and investigated with respect to their ergodicity and performance. For comparison to exact results, the co-ordination number distribution of the dynamical polygonifications model, or certain analogues of it, are constructed. For simulations of the 6-vertex $F$ model on $\phi^4$ random graphs, an order parameter for its anti-ferroelectric phase transitions is constructed in terms of a "plaquette spin" representation. Extensive finite-size scaling analyses of the Kosterlitz-Thouless point of the square-lattice and random graph $F$ models are presented and the locations of the critical points as well as the corresponding critical exponents are determined. The back-reaction of the coupled vertex model on the random graphs is investigated by an analysis of the co-ordination number distribution, the distribution of "baby universes" and the string susceptibility exponent as well as the geometric two-point function, yielding an estimate for the internal Hausdorff dimension of the coupled system.

As Europe’s power production becomes increasingly reliant on intermittent renewable energy sources, uncertainties are likely to arise in power generation plans. Similarly, with the growing prevalence of electric vehicles, electric demand is also becoming more uncertain. These uncertainties in both production and demand can lead to challenges for European power systems. This thesis proposes the use of Monte-Carlo simulations to translate uncertainties in power generation and demand into uncertainties in the power grid. To integrate stochasticity in the forecasts, this thesis separates the multivariate probabilistic forecasting problem by first forecasting the marginal loads individually and probabilistically. Copula theory is then used to integrate spatial correlations and create realistic scenarios. These scenarios serve as inputs for Monte-Carlo simulations to estimate uncertainties in the power system. The methodology is tested using power injection data and the power system model of Switzerland. The results demonstrate that integrating stochasticity in forecasts improves the reliability of the power system. The proposed approach effectively models the uncertainty in both production and demand and provides valuable information for decision-making. / I takt med att Europas elproduktion blir alltmer beroende av intermittenta förnybara energikällor kommer det sannolikt att uppstå osäkerheter i planerna för elproduktion. På samma sätt blir efterfrågan på elektricitet mer osäker i takt med att elfordon blir allt vanligare. Dessa osäkerheter i både produktion och efterfrågan kan leda till utmaningar för de europeiska kraftsystemen. I denna avhandling föreslås att Monte-Carlo-simuleringar används för att omvandla osäkerheter i elproduktion och efterfrågan till osäkerheter i elnätet. För att integrera stokasticitet i prognoserna separerar denna avhandling det multivariata probabilistiska prognosproblemet genom att först individuellt och probabilistiskt prognostisera belastningar. Kopulateori används sedan för att integrera rumsliga korrelationer och skapa realistiska scenarier. Dessa scenarier tjänar som indata för Monte-Carlo-simuleringar för att uppskatta osäkerheterna i kraftsystemet. Metodiken testas med hjälp av data om inmatning av el och med hjälp av Schweiz kraftsystem. Resultaten visar att integrering av stokasticitet i prognoser förbättrar kraftsystemets tillförlitlighet. Den föreslagna metoden modellerar effektivt osäkerheten i både produktion och efterfrågan och ger värdefull information för beslutsfattandet.

growing concern on achieving environmental sustainability and at the same time making economical savings has become a necessity in our society. The prices of different battery energy storage technologies together with PV cells are declining all around the globe which has led to the fact that there is an increased interest in investing and using these technologies to be able to reach environmental sustainability. The combined system however, must be accurately calculated both when it comes to the sizing and the different costs related to the combined system to be able to make an economical saving. This thesis addresses both of those aspects in Sweden where a residential building with roof-top installed PV system is assessed with a battery energy storage system. An investigation is necessary to be able to assess the different battery storage technologies available in the market today with their specific technical and economical specifications. The electricity market in Sweden, the role of the Distribution System Operator on the electricity pricing with different time tariffs and fuse size subscription, PV generation and battery specifications are investigated and modeled in this study. Sizing of the different battery technologies for the given system is accomplished through a methodology that is developed in this project for the Swedish system. The calculated size of the battery is then used in the Life Cycle Cost analysis, using Monte Carlo simulations for a chosen period of 25 years.Calculations shows that the most appropriate size for the battery system with the given parameters is 6 kWh for all the battery types investigated in this study. The size of the batteries is also shown to be mainly dependent on the charging/discharging time together with the set fuse size margin. Profitability of the Battery Energy Storage system is proven to be mainly dependent on the fuse size downgrade. Sulphur-Sodium battery result in the greatest savings while Vanadium Redox batteries in the least when sizing the batteries. Lithium-Ion battery technology however is most likely to result in the lowest Levelized Cost of Electricity, total- and cycle costs while the highest Net Present Value with 90 % probability in the Monte Carlo simulations. Lithium-Ion battery technology is also found to have the highest probability of having a positive NPV compared to the lowest probability for Sulphur-Sodium battery technology. Lead-Acid battery technology is however shown to have the least uncertainties compared to other Battery Energy Storage technologies due to its maturity. It is additionally shown that government subsidy plays a crucial role when investing in the battery storage system. However, even with the case of removed government subsidy, Lithium-Ion battery technology still results in the largest probability of having a positive NPV while Sulphur-Sodium battery technology results in the lowest probability of having a positive NPV. / Den växande oron för att uppnå miljömässig hållbarhet och samtidigt göra ekonomiska besparingar har blivit en nödvändighet i vårt samhälle. Priserna på olika energilagrings teknologier så som batterier tillsammans med PV-celler minskar runt om i världen vilket har lett till att det finns ett ökat intresse när det gäller att investera och använda dessa teknologier för att kunna nå miljömässig hållbarhet. Det kombinerade systemet måste dock noggrant beräknas både när det gäller storleken och de olika kostnaderna för det kombinerade systemet för att kunna göra en ekonomisk besparing. Denna avhandling behandlar båda dessa aspekter i Sverige där en bostadsbyggnad med takmonterat PV system utvärderas med ett batteri system. En undersökning är nödvändig för att kunna bedöma de olika batteri teknologier som finns tillgängliga på marknaden idag med sina specifika tekniska och ekonomiska specifikationer. Elmarknaden i Sverige, Distribution System Operatörs roll för elprissättning med olika tidstariffer och säkringsabonnemang, PV-generation och batterispecifikationer undersöks och modelleras i denna studie. Dimensionering av olika batteri teknologier för det givna systemet uppnås genom en metod som utvecklats i detta projekt för det svenska systemet. Den beräknade storleken på batteriet används sedan i livscykelkostnadsanalysen, med Monte Carlo-simuleringar under en vald period på 25 år. Beräkningar visar att den optimala storleken för batterisystemet med de angivna parametrarna är 6 kWh för alla batterityper som undersöktes i denna studie. Batteriets storlek visar sig också vara huvudsakligen beroende av laddning / urladdningstiden tillsammans med den inställda säkrings storleken. Lönsamheten hos batterilagringssystemet visar sig vara huvudsakligen beroende av säkringens nedgradering. Svavel-Natriumbatteriet resulterar i de största besparingarna medan Vanadium Redox batteriet i de minsta när dimensionering av batteriet äger rum. Litium-Ion batteriet är emellertid sannolikt att leda till den lägsta nivån av elkostnader, total- och cykelkostnader, medan det högsta nettoförsäljningsvärdet med 90% sannolikhet i Monte Carlo-simuleringarna. Litium-Ion batteriet befanns också ha den högsta sannolikheten att ha en positiv NPV jämfört med Svavel-Natriumbatteriet som resulterar i den lägsta sannolikheten. Lead-Acid batteriet visar sig ha den minsta osäkerheten i jämförelse med andra batterilagrings teknologier på grund av dess mognad. Det framgår dessutom att statlig subvention spelar en avgörande roll när man investerar i ett batteri lagrings system. Dock även med borttagna statliga subventioner, resulterar Litium-Ion batteriet fortfarande största sannolikheten för att ha en positiv NPV, medan Svavel-Natriumbatteriet resulterar den lägsta sannolikheten för att ha en positiv NPV.

The ferromagnetic shape memory alloy, Fe7Pd3, not only offers promising applications, but also reveals a number of unresolved scientific questions, including coupling between a series of martensite and order–disorder transitions, which are in the focus of the present study. To address and understand these aspects, which are of particular importance for controlling phase stability in Fe7Pd3, an ab initio based Monte Carlo simulation code is developed, whose results demonstrate that equilibrated ordered or disordered phases show distinct dependencies coupled to temperature and lattice structure. Moreover, in equiatomic domains emerging from initially randomized disorder, an intermediate, entropy stabilized phase is identified with significantly higher magnetic anisotropy energy, being advantageous for miniaturized applications. This phase, among other observed configurations, is comprehensively characterized by free energy landscapes and magneto-structural coupling derived from vibrational analysis of molecular dynamics trajectories and full relativistic spin polarized density functional theory ground state calculations, respectively.

No description available.

In reregulated and restructured electricity markets the production and retail of electricity is conducted on competitive markets, the transmission and distribution on the other hand can be considered as natural monopolies. The financial regulation of Distribution System Operators (DSOs) has in many countries, partly as a consequence of the restructuring in ownership, gone through a major switch in regulatory policy. From applying regulatory regimes were the DSOs were allowed to charge their customers according to their actual cost plus some profit, i.e. cost-based regulation, to regulatory models in which the DSOs performance are valued in order to set the allowable revenue, i.e. Performance-Based Regulation (PBR). In regulatory regimes that value performance, the direct link between cost and income is weakened or sometimes removed. This give the regulated DSOs strong cost cutting incentives and there is consequently a risk of system reliability deterioration due to postponed maintenance and investments in order to save costs. To balance this risk the PBR-framework is normally complemented with some kind of quality regulation (QR). How both the PBR and QR frameworks are constructed determines the incentive that the DSO will act on and will therefore influence the system reliability development. This thesis links the areas of distribution system reliability and performancebased regulation. First, the key incentive features within PBR, that includes the quality of supply, are identified using qualitative measures that involve analyses of applied regulatory regimes, and general regulatory policies. This results in a qualitative comparison of applied PBR models. Further, the qualitative results are quantified and analysed further using time sequential Monte Carlo simulations (MCS). The MCS enables detailed analysis of regulatory features, parameter settings and financial risk assessments. In addition, the applied PBRframeworks can be quantitatively compared. Finally, some focus have been put on the Swedish regulation and the tool developed for DSO regulation, the Network Performance Assessment Model (NPAM), what obstacles there might be and what consequences it might bring when in affect. / QC 20101221

Counterparty risk calculations have gained importance after the latest financial crisis. The bankruptcy of Lehman Brothers showed that even large financial institutiones face a risk of default. Hence, it is important to measure the risk of default for all the contracts written between financial institutions. Credit Value Adjustment, CVA, is an industry standard method for such calculations. Nevertheless, the implementation of this method is contract dependent and the necessary computer simulations can be very intensive. Monte Carlo simulations have for a long time been known as a precise but slow technique to evaluate the cash flows for contracts of all kinds. Measuring the exposure of a contract written on structured products might require half a day of calculations if the implementation is written without significant optimization. Several ideas have been presented by researchers and applied in the industry, the idea explored and implemented in this thesis was based on using Artificial Neural Networks in Python. This procedure require a decomposition of the Expected Exposure calculation within the CVA and generating a large data set using a standard Monte Carlo simulation. Three network architectures have been tested and the final performance was compared with using standard techniques for the very same calculation. The performance gain was significant, a portfolio of 100 counterparties with 10 contracts each would take 20 minutes of calculations in total when using the best performing architecture whereas a parallel C++ implementation of the standard method would require 2.6 days.

Dans le contexte de la modélisation aléatoire des événements récurrents, un modèle statistique particulier est exploré. Ce modèle est fondé sur la théorie des processus de comptage et est construit dans le cadre d'analyse de défaillances dans les réseaux d'eau. Dans ce domaine nous disposons de données sur de nombreux systèmes observés durant une certaine période de temps. Les systèmes étant posés à des instants différents, leur âge est utilisé en tant qu'échelle temporelle dans la modélisation. Le modèle tient compte de l'historique incomplet d'événements, du vieillissement des systèmes, de l'impact négatif des défaillances précédentes sur l'état des systèmes et des covariables. Le modèle est positionné parmi d'autres approches visant à l'analyse d'événements récurrents utilisées en biostatistique et en fiabilité. Les paramètres du modèle sont estimés par la méthode du Maximum de Vraisemblance (MV). Une covariable dépendante du temps est intégrée au modèle. Il est supposé qu'elle est extérieure au processus de défaillance et constante par morceaux. Des méthodes heuristiques sont proposées afin de tenir compte de cette covariable lorsqu'elle n'est pas observée. Des méthodes de simulation de données artificielles et des estimations en présence de la covariable temporelle sont proposées. Les propriétés de l'estimateur (la normalité, le biais, la variance) sont étudiées empiriquement par la méthode de Monte Carlo. L'accent est mis sur la présence de deux directions asymptotiques : asymptotique en nombre de systèmes n et asymptotique en durée d'observation T. Le comportement asymptotique de l'estimateur MV constaté empiriquement est conforme aux résultats théoriques classiques. Il s'agit de l'asymptotique en n. Le comportement T-asymptotique constaté empiriquement n'est pas classique. L'analyse montre également que les deux directions asymptotiques n et T peuvent être combinées en une unique direction : le nombre d'événements observés. Cela concerne les paramètres classiques du modèle (les coefficients associés aux covariables fixes et le paramètre caractérisant le vieillissement des systèmes). Ce n'est en revanche pas le cas pour le coefficient associé à la covariable temporelle et pour le paramètre caractérisant l'impact négatif des défaillances précédentes sur le comportement futur du système. La méthodologie développée est appliquée à l'analyse des défaillances des réseaux d'eau. L'influence des variations climatiques sur l'intensité de défaillance est prise en compte par une covariable dépendante du temps. Les résultats montrent globalement une amélioration des prédictions du comportement futur du processus lorsque la covariable temporelle est incluse dans le modèle. / In the context of stochastic modeling of recurrent events, a particular model is explored. This model is based on the counting process theory and is built to analyze failures in water distribution networks. In this domain the data on a large number of systems observed during a certain time period are available. Since the systems are installed at different dates, their age is used as a time scale in modeling. The model accounts for incomplete event history, aging of systems, negative impact of previous failures on the state of systems and for covariates.The model is situated among other approaches to analyze the recurrent events, used in biostatistics and in reliability. The model parameters are estimated by the Maximum Likelihood method (ML). A method to integrate a time-dependent covariate into the model is developed. The time-dependent covariate is assumed to be external to the failure process and to be piecewise constant. Heuristic methods are proposed to account for influence of this covariate when it is not observed. Methods for data simulation and for estimations in presence of the time-dependent covariate are proposed. A Monte Carlo study is carried out to empirically assess the ML estimator's properties (normality, bias, variance). The study is focused on the doubly-asymptotic nature of data: asymptotic in terms of the number of systems n and in terms of the duration of observation T. The asymptotic behavior of the ML estimator, assessed empirically agrees with the classical theoretical results for n-asymptotic behavior. The T-asymptotics appears to be less typical. It is also revealed that the two asymptotic directions, n and T can be combined into one unique direction: the number of observed events. This concerns the classical model parameters (the coefficients associated to fixed covariates, the parameter characterizing aging of systems). The presence of one unique asymptotic direction is not obvious for the time-dependent covariate coefficient and for a parameter characterizing the negative impact of previous events on the future behavior of a system.The developed methodology is applied to the analysis of failures of water networks. The influence of climatic variations on failure intensity is assessed by a time-dependent covariate. The results show a global improvement in predictions of future behavior of the process when the time-dependent covariate is included into the model.

Les techniques d'imagerie optique, dans la gamme de longueurs d'onde visible et proche infrarouge, permettent d'examiner très facilement les tissus biologiques de manière non invasive. Toutefois la forte diffusion des tissus biologiques limite fortement leur examen en profondeur. Examinés en rétrodiffusion (examen de la peau ou du col de l'uterus par exemple), non seulement les mesures sont polluées par la réflexion spéculaire, mais l'information sur la source volumique du signal est également perdue du fait de la forte diffusion. La prise en compte de la diffusion dans le modèle de propagation de la lumière permet d'évaluer cette distribution volumique du signal lumineux en fonction des propriétés optiques du milieu. Pour sophistiquer l'approche, nous introduisons un filtrage polarimétrique, basé sur l'utilisation de la lumière polarisée elliptiquement, particulièrement approprié à la géométrie de rétrodiffusion, permettant avant tout un sondage sélectif en profondeur tout en s'affranchissant de la réflexion spéculaire. Cette technique permet ainsi d'examiner les tissus à l'échelle mésoscopique (jusqu'à l'échelle du millimètre). / Optical imaging techniques using the visible and near-infrared wavelengths allow an easy and non-invasive way of analysing biological tissues. However, the high scattering of biological tissues significantly limits the depth of examination. Backscattering examination (of skin or of the cervix for example) shows not only that the measurements are polluted by mirror reflection, but also that information about the source of the signal is lost as a result of the high scattering. Including scattering in the light propagation model allows the evaluation of the volume distribution of the light signal as a function of the optical properties of the medium. In order to make the approach more sophisticated, we introduced a polarimetric filtering that uses elliptically polarised light. This is not only particularly appropriate for backscattering geometry, but also allows firstly to probe at selected depths and secondly to eliminate mirror reflection. Thus, this technique allows the examination of tissues at a mesoscopic scale (up to the milimeter scale).

Cette thèse s’intéresse à la gestion du risque climatique par l’utilisation des produits dérivés climatiques. Les travaux réalisés dans le cadre de cette thèse sont une contribution aux aspects statistiques, économétriques et financiers de la modélisation et de l'évaluation des produits dérivés climatiques. Un intérêt particulier a été accordé au contexte marocain aussi bien au niveau du volet qualitatif que quantitatif. En plus des développements théoriques que nous avons apportés (tests statistiques pour vérifier l’impact du climat sur l’économie, amélioration d’un modèle de prévision de la température moyenne quotidienne, confirmation du choix de la température moyenne, au lieu des températures extrêmes, comme sous-jacent pour les contrats basés sur la température, etc.), nous avons proposé des cas de gestion entre opérateurs économiques marocains exerçant des activités sensibles à l’aléa climatique avec des profils de risque différents en leur apportant des solutions de couverture basées sur l’utilisation de produits dérivés climatiques. / This thesis focuses on the weather risk management by using weather derivatives. The work done in this thesis is a contribution to statistics, econometric and financial aspects of the modeling and the evaluation of weather derivatives. Particular attention was paid to the Moroccan context both in a qualitative point of view. In additionto theoretical developments that we have made (statistical tests to verify the impact of weather conditions on the economy, improvement of a model to forecast daily average temperatures, confirming the choice of the average temperature instead of extreme temperatures as the preferred under lying for contracts based on temperature, etc.), we also proposed case studies with Moroccan economic actors carrying out their weather sensitive activities and having different risk profiles and we provide them hedging solutions based on the use of weather derivatives.