Amoss is an equation-orientated stochastic simulation platform, developed on open-source software. It is designed to facilitate the development and simulation of Sasol value chain models using the Moss methodology. The main difficulties with the original Moss methodology was that plant recycles were difficult to incorporate and that plant or model changes meant rebuilding the entire Moss model. The first version of automatic-Moss was developed by Edgar Whyte in an effort to address these problems. It was successful as a proof of concept, but generated simulations were numerically unstable and very slow. A second version of the tool was to be developed to address numerical stability and simulation speed. The stochastic simulations stemming from Amoss models are large-scale and contain mixed continuous/conditional algebraic equation sets, with first order stochastic differential equations. Additionally, optimal flow allocation as a disjunctive optimisation is often encountered. The complexity of these factors makes finite difference approximation the main solution. The equation ordering, simulation approach and code generation features of the Amoss tool were investigated and re-implemented. A custom equation ordering method, which uses interval arithmetic and weighted maximal matching for numerically stable matching, followed by Dulmage-Mendelsohn decomposition and Cellier’s tearing, was implemented. For implicitly ordered systems, a fixed-point iterative Newton method, where conditional variables are separated from continuous variables for solving stability, was implemented. The optimal allocation problem with heuristic allocation was generalised to plants with recycles. Fast simulation code utilising parallel processing, efficient solving and function evaluation, efficient intermediate data storage and fast file writing, was implemented. Amoss simulations are now substantially faster than the industry equivalent and can reliably model Moss methodology problems. / Dissertation (MEng (Control Engineering))--University of Pretoria, 2021. / Sasol / Chemical Engineering / MEng (Control Engineering) / Unrestricted

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Die Arbeit befaßt sich mit der Beschreibung der linearen optischen Eigenschaften von heterogenen absorbierenden Materialien, insbesondere von Clustermaterialien. Das Ziel der Arbeit besteht in der Ausarbeitung einer analytischen Methode zur Berechnung des optischen Verlustes (Extinktion) des heterogenen Materials. Die präsentierte Methode basiert auf der klassischen Beschreibung der Licht-Materie-Wechselwirkung mit Hilfe dielektrischer Funktionen. Das Modell berücksichtigt eine mögliche Absorption in der Einbettmatrix, Mehrfachstreungseffekte in Systemen mit dichtgepackten Clustern und die Clusterstatistik. Um die Absorption in der Einbettmatrix beschreiben zu können, wird die Mie-Theorie der Lichtstreuung an einem sphärischen Teilchen in einer nichtabsorbierenden Umgebung erweitert. Die Clusterstatistik wird dadurch berücksichtigt, daß die optischen Eigenschaften eines makroskopischen Clustersystems als eine Mittelung der Eigenschaften kleinerer Clusteraggregate berechnet werden. Die zur Berechnung verwendeten Clusteraggregate, deren statistische Eigenschaften der Probenherstellungsmethode entsprechen, werden mit Hilfe von Monte-Carlo-Simulation des Clusterwachstums auf Oberflächen generiert. Nach einer Beschreibung des theoretischen Apparats werden numerische Beispiele dargestellt, die die Anwendung der Methode demonstrieren. Die Extinktion von Eisenclustern in Fulleritmatrix wird in der Einzelteilchennäherung berechnet und mit experimentellen Daten verglichen. Die Extinktionskoeffizienten von Silberclustern in zwei molekularen Matrizen werden mit der Berücksichtigung der Clusterstatistik und Mehrfachstreungseffekten berechnet. Der Vergleich mit den experimentellen Werten läßt auf den Einfluß der betrachteten Effekte auf charakteristische Merkmale in den Spektren von makroskopischen Clustersystemen schlißen.

Die Beschaffenheit metallischer Legierungsschmelzen hat einen entscheidenden Einfluss auf die Qualität der festen Legierung. Im Rahmen dieser Diplomarbeit wurde sich gezielt mit der Nahordnung in ternären Ag-Cu-Ge Legierungsschmelzen sowie der binären Randlegierungen beschäftigt. Dazu wurden die Legierungen mithilfe der Röntgendiffraktion untersucht. Zusätzlich wurden die erhaltenen experimentellen Ergebnisse durch Computersimulationen ergänzt und mit Modellrechnungen verglichen.

The purpose of this paper is solving the European option pricing problem under the Black–Scholes model. Our approach is to use the so-called stochastic Runge–Kutta (SRK) numericalscheme to find the corresponding expectation of the functional to the stochastic differentialequation under the Black–Scholes model. Several numerical solutions were made to study howquickly the result converges to the theoretical value. Then, we study the order of convergenceof the SRK method with the help of MATLAB.

The formation of Ge nanowires in V-grooves has been studied experimentally as well as theoretically. As substrate oxide covered Si V-grooves were used formed by anisotropic etching of (001)Si wafers and subsequent oxidation of their surface. Implantation of 1E17 Ge+ cm^-2 at 70 keV was carried out into the oxide layer covering the V-grooves. Ion irradiation induces shape changes of the V-grooves, which are captured in a novel continuum model of surface evolution. It describes theoretically the effects of sputtering, redeposition of sputtered atoms, and swelling. Thereby, the time evolution of the target surface is determined by a nonlinear integro-differential equation, which was solved numerically for the V-groove geometry. A very good agreement is achieved for the predicted surface shape and the shape observed in XTEM images. Surprisingly, the model predicts material (Si, O, Ge) transport into the V-groove bottom which also suggests an Ge accumulation there proven by STEM-EDX investigations. In this Ge rich bottom region, subsequent annealing in N2 atmosphere results in the formation of a nanowire by coalescence of Ge precipitates shown by XTEM images. The process of phase separation during the nanowire growth was studied by means of kinetic 3D lattice Monte-Carlo simulations. These simulations also indicate the disintegration of continuous wires into droplets mediated by thermal fluctuations. Energy considerations have identified a fragmentation threshold and a lower boundary for the droplet radii which were confirmed by the Monte Carlo simulation. The here given results indicate the possibility of achieving nanowires being several nanometers wide by further growth optimizations as well as chains of equally spaced clusters with nearly uniform diameter.

Die vorliegende Arbeit stellt Ergebnisse von Monte-Carlo-Simulationen zur Adsorption und Selbstorganisation amphiphiler Moleküle an Feststoffoberflächen vor. Ziel der Arbeit ist die Untersuchung des Zusammenhanges zwischen Moleküleigenschaften und thermodynamischen Bedingungen für die Bildung von adsorbierten Aggregaten. Im Rahmen eines coarse grainined-Gittermodells wird die Adsorption von Modelltensiden auf ebenen Oberflächen beschrieben. Es werden hydrophile, hydrophobe und chemisch heterogene Modelloberflächen berücksichtigt. Die Resultate der Simulationen stehen im Einklang mit experimentellen Untersuchungen und liefern Interpretationshilfen für die beobachteten Strukturen. Für den Einsatz von Tensidmischungen bei der Kalziumfluorit-Flotation konnte gezeigt werden, dass die Wirkung des Co-Sammler-Tensids auf einer Adsolubilisation im Adsorptionsfilm beruht.

Diese Dissertation befasst sich mit dem Verhalten eines generischen semiflexi- blen Polymermodells. Insbesondere untersucht es den Einfluss von Steifigkeit auf die unterschiedlichen thermodynamisch stabilen Konformationen. Es wird erläutert wie durch die Steifigkeit des Polymers verschiedene struk- turierte Phasen induziert werden. Insbesondere wird dabei auf die sta- bilen verknoteten Phasen eingegangen. Der zweite Teil der Dissertation beschäftigt sich dann mit dem Einfluss einer kugelförmigen Einsperrung auf das Phasendiagramm des selben Polymermodells. Es wird gezeigt wie in Abhängigkeit der Ordnung des Phasenüberganges die Einsperrung entweder zu einem stabilisierenden oder destabilisierenden Effekt führt. Im dritten Teil der Dissertation werden dann die komplexen Monte-Carlo Simulationen erläutert die für die Simulation der physikalischen Systeme genutzt wurde. Diese Algorithmen wurden in ein Framework integriert, so dass diese wieder verwendet werden können.

Air traffic has an increasing influence on climate; therefore identifying mitigation options to reduce the climate impact of aviation becomes more and more important. Aviation influences climate through several climate agents, which show different dependencies on the magnitude and location of emission and the spatial and temporal impacts. Even counteracting effects can occur. Therefore, it is important to analyse all effects with high accuracy to identify mitigation potentials. However, the uncertainties in calculating the climate impact of aviation are partly large (up to a factor of about 2). In this study, we present a methodology, based on a Monte Carlo simulation of an updated non-linear climate-chemistry response model AirClim, to integrate above mentioned uncertainties in the climate assessment of mitigation options. Since mitigation options often represent small changes in emissions, we concentrate on a more generalised approach and use exemplarily different normalised global air traffic inventories to test the methodology. These inventories are identical in total emissions but differ in the spatial emission distribution. We show that using the Monte Carlo simulation and analysing relative differences between scenarios lead to a reliable assessment of mitigation potentials. In a use case we show that the presented methodology can be used to analyse even small differences between scenarios with mean flight altitude variations.

The replica exchange method (REM) has been widely used in the computer simulation of complex systems, such as proteins, glasses, and atomic clusters, where conventional methods based on sampling the canonical ensemble struggle to attain ergodicity over a rugged energy landscape characterized by multiple minima separated by high energy barriers. While the standard temperature REM (tREM) has proven to be highly effective in the equilibrium sampling of stable single phase states, tREM is seriously challenged in the vicinity of a first-order phase transition. The generalized Replica Exchange Method (gREM) was developed to address these outstanding computational problems and provide a method for simulating strong phase transitions in condensed matter systems. The central idea behind gREM is to incorporate the merit of generalized ensemble sampling into the replica exchange paradigm. The key ingredients of gREM are parameterized effective sampling weights, which smoothly join ordered and disordered phases with a succession of unimodal energy distributions that transform unstable or metastable energy states of the canonical ensemble into stable states that can be fully characterized. The inverse mapping between the sampling weights and the effective temperature provides a sure way to design the effective sampling weights and achieve ergodic sampling. Various applications of gREM are presented, including studies of the solid-liquid phase change of an adapted Dzugutov model of glass formation, the mechanism of spinodal decomposition in the vapor-liquid transition of a simple fluid, and the apparent crossover from a first-order to continuous transition with increasing density in the freezing of a nanofilm of water confined between featureless and atomistic surfaces. Extensive gREM simulations combined with the Statistical Temperature Weighted Histogram Analysis Method (ST-WHAM) demonstrate the effectiveness of the approach and provide comprehensive characterization of thermodynamic and structural properties intrinsic to phase transitions in these diverse systems.