Im Mittelpunkt dieser Arbeit steht die Untersuchung der kollektiven Dynamik des binaeren Systems Rb-Sb im fluessigen Zustand. Die dynamische Struktur wurde fuer zwei Zusammensetzungen durch inelastische Neutronenstreuung bestimmt. Die daraus ermittelten Dispersionsrelationen geben Aufschluss ueber die kollektiven Anregungen im System. Um kuenftig noch bessere Experimente durchfuehren zu koennen, wurden die Parameter eines neues Neutronen Brillouin Spektrometers mittels Monte-Carlo Simulation optimiert. / In the first part of this report the collective atomic dynamics of liquid Rb-Sb is discussed. The dynamic structure factors were measured by inelastic neutron scattering. The resulting dispersion relations show how the dynamics of this system alters with the change in the interatomic potential. To improve the experimental part the setup of a new neutron Brillouin spectrometer was optimized by a Monte-Carlo simulation. These results are presented in the second part.

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.

The atomic dynamics in liquids is still a challenging subject. The objective of this thesis was to study how the dynamics depends on the TYPE of the atomic interaction. Dynamic properties extracted from inelastic neutron scattering experiments on three binary systems clearly show a discontinous behaviour in the transition from a pure metallic to an ionic and partly covalent bonding regime. Further, results of Monte-Carlo simulations of a new type of spectrometer, a Neutron-Brillouin-Spectrometer, that is currently under construction, are presented. / In dieser Arbeit wurde der Einfluss der Art der zwischenatomaren Wechselwirkung auf die atomare Dynamik in Fluessigkeiten untersucht. Dafuer wurden geeignete binaere Systeme ausgewaehlt und deren Dichtefluktuationen mittels unelastischer Neutronenstreuung gemessen. Neben den teilweise bekannten strukturellen Veraenderungen, die beim Uebergang von rein metallischen zu ionischen und teilweise kovalenten Bindungen auftreten, konnten vor allem die Auswirkungen wechselnder Bindungsverhaeltnisse auf eine Reihe dynamischer Eigenschaften nachgewiesen werden. Besonders hervorzuheben sind dabei der Nachweis eines Hochfrequenzbandes im Frequenzspektrum des fluessigen RbSb sowie in den fluessigen Na-Sn Legierungen die Aufspaltung der aus der longitudinalen Stromkorrelationsfunktion abgeleiteten Dispersion in zwei Baender, die die verschiedenartige Dynamik der unterschiedlich schweren Komponenten widerspiegeln. Desweiteren werden in dieser Arbeit Ergebnisse umfangreicher Monte-Carlo Simulationen fuer ein im Bau befindliches neuartiges Neutronen-Brillouin-Spektrometer vorgestellt.

The paper considers approximations of time-continuous epsilon-correlated random processes by interpolation of time-discrete Moving-Average processes. These approximations are helpful for Monte-Carlo simulations of the response of systems containing random parameters described by epsilon-correlated processes. The paper focuses on the approximation of stationary epsilon-correlated processes with a prescribed correlation function. Numerical results are presented.

In the paper we study sequences of random functions which are defined by some interpolation procedures for a given random function. We investigate the problem in what sense and under which conditions the sequences converge to the prescribed random function. Sufficient conditions for convergence of moment characteristics, of finite dimensional distributions and for weak convergence of distributions in spaces of continuous functions are given. The treatment of such questions is stimulated by an investigation of Monte Carlo simulation procedures for certain classes of random functions. In an appendix basic facts concerning weak convergence of probability measures in metric spaces are summarized.

A simple methodology for determining the input referred offset voltage of comparators is presented. This in general is difficult as the output of a comparator is discrete valued. The method relies on a Monte-Carlo-Simulation with certain comparator input values and some postprocessing of the comparator output data. The comparator is always operated in its intended environment, there is no modification of the comparator itself nor some unusual stimuli required. There is also no known restriction for the type of comparators to be analyzed.

Thesis (doctoral)--Universität, Passau, 2000.

Polymer nanocomposite foams have attracted tremendous interests due to their multifunctional properties in addition to the inherited lightweight benefit of being foamed materials. Polymer nanocomposite foams using high performance polymer and bio-degradable polymer with carbon nanotubes were fabricated, and the effects of foam density and pore size on properties were characterized. Electrical conductivity modeling of polymer nanocomposite foams was conducted to investigate the effects of density and pore size. High performance polymer Polyetherimide (PEI) and multi-walled carbon nanotube (MWCNT) nanocomposites and their foams were fabricated using solvent-casting and solid-state foaming under different foaming conditions. Addition of MWCNTs has little effect on the storage modulus of the nanocomposites. High glass transition temperature of PEI matrix was maintained in the PEI/MWCNT nanocomposites and foams. Volume electrical conductivities of the nanocomposite foams beyond the percolation threshold were within the range of electro-dissipative materials according to the ANSI/ESD standard, which indicates that these lightweight materials could be suitable for electro-static dissipation applications with high temperature requirements. Biodegradable Polylactic acid (PLA) and MWCNT nanocomposites and their foams were fabricated using melt-blending and solid-state foaming under different foaming conditions. Addition of MWCNTs increased the storage modulus of PLA/MWCNT composites. By foaming, the glass transition temperature increased. Volume electrical conductivities of foams with MWCNT contents beyond the percolation threshold were again within the range of electro-dissipative materials according to the ANSI/ESD standard. The foams with a saturation pressure of 2 MPa and foaming temperature of 100 °C showed a weight reduction of 90% without the sacrifice of electrical conductivity. This result is promising in terms of multi-functionality and material saving. At a given CNT loading expressed as volume percent, the electrical conductivity increased significantly as porosity increased. A Monte-Carlo simulation model was developed to understand and predict the electrical conductivity of polymer/MWCNT nanocomposite foams. Two different foam morphologies were considered, designated as Case 1: volume expansion without nanotube rearrangement, and Case 2: nanotube aggregation in cell walls. Simulation results from unfoamed nanocomposites and the Case 1 model were validated with experimental data. The results were in good agreement with those from PEI/MWCNT nanocomposites and their foams, which had a similar microstructure as modeled in Case 1. Porosity effects on electrical conductivity were investigated for both Case 1 and Case 2 models. There was no porosity effect on electrical conductivity at a given volume percent CNT loading for Case 1. However, for Case 2 the electrical conductivity increased as porosity increased. Pore size effect was investigated using the Case 2 model. As pore size increased, the electrical conductivity also increased. Electrical conductivity prediction of foamed polymer nanocomposites using FEM was performed. The results obtained from FEM were compared with those from the Monte-Carlo simulation method. Feasibility of using FEM to predict the electrical conductivity of foamed polymer nanocomposites was discussed. FEM was able to predict the electrical conductivity of polymer nanocomposite foams represented by the Case 2 model with various porosities. However, it could not capture the pore size effect in the electrical conductivity prediction. The FEM simulation can be utilized to predict the electrical conductivity of Case 2 foams when the percolation threshold is determined by Monte-Carlo simulation to save the computational time. This has only been verified when the pore size is small in the range of a few micrometers. / text

Poly (Ethylene Oxide) (PEO, with a general formula (CH₂-CH₂-O)[subscript pi] ) is completely soluble in water at room temperature over an extremely wide molecular weight range and has been widely studied by experiment and theory. The objective of our work is to study the solubility behavior by the method of Monte Carlo simulation. The insertion factor lnB, which is equivalent to the infinite dilute Henry's Law Constant, is used to represent the solubility of various molecules in water. Our research started with simple fluid and aqueous solutions of small molecules including hard spheres, inert gases, hydrocarbons and dimethyl ether (DME, as a precursor for PEO). Solubility consists of a favorable energy term and an unfavorable entropy term. Against the common belief of entropy-dominating-hydrophobicity effect, it is actually the ability of the solute to interact with solvent (or the energetic factor) that dominates solubility. The solubility minimum appearing for both hydrophobic and hydrophilic solutes along the water coexistence curve is the result of competition between the favorable energy contribution and the unfavorable entropy contribution. Normal alkanes with carbon number from 1 to 20 have been modeled by LJ chains to study the solubility of non-polar polymer chains in water. Various constraints have been put on the LJ model to evaluate their effect on solubility. No significant difference was observed for LJ chain with or without fixed bond angles, but torsional interaction changed the chain solubility dramatically. The temperature and chain-length effect on chain solubility has been examined and it can be explained by the balancing between the intra-chain interaction and entropy penalty. By choosing the right torsional interaction parameters we may be able to reproduce by simulations the solubility minimum of normal alkanes at C₁₁. PEO was modeled by united atom chains with length up to 30. The most probable distance between two nearest ether oxygens in both vacuum and aqueous solutions matches the hydrogen bond length in bulk water. Hydrogen bonding plays an important role in the unique water solubility behavior of PEO since the water-PEO interaction effectively increases the total number of hydrogen bonds and results in a favorable change in energy. A trans-gauche-trans conformation along the O-C-C-O bonds does enable hydrogen bond formation between one water molecule and two nearest or next nearest ether oxygens. A helix structure is not required for the PEO to have favorable interactions with water. Two polymers with similar structure as PEO but are insoluble in water: Poly (methylene oxide) (PMO) and Poly (propylene oxide) (PPO) have been studied to compare with PEO. Their difference in structure from PEO, though slight, reduces the chance of hydrogen bond forming between water and chains so as to decrease the solubility. / text

The company’s pricing is often highly impacted by the estimation of competitors’ project costs, which also is the main scope in this degree project. The purpose is to develop a pricing model dealing with uncertainties, since this is a main issue in the current pricing process. A pre-study has been performed, followed by a model implementation. An analysis of the model was then made, before conclusions were drawn. Project cost estimation foremost, but also probability distribution functions and pricing as a general concept, were investigated in the mainly literary pre-study. Two suitable methods for project cost estimation were identified; Monte Carlo simulation and Hierarchy Probability Cost Analysis. These lead to a theoretical project cost estimation model. A model was implemented in Matlab. It treats project cost estimation, but no other pricing aspects. The model was developed based on the theoretical one to the extent possible. Project costs were broken down in sub costs which were included in a Monte Carlo simulation. Competitors’ project costs were estimated using this technique. To analyse the model’s accuracy was difficult. It differs from the theoretical one in terms of how probability distribution functions and correlations are estimated. These problems depend on projects with shifting characteristics and limited data and time. A solid framework has been created though. Improvement possibilities exist, e.g. more accurate estimates and a model handling other pricing aspects. The major threat is that nobody maintains the model. Anyway, estimates are not more than just estimates. The model should therefore be viewed as a helpful tool, not an answer. / Företagets prissättning påverkas ofta till stor del av estimeringen av konkurrenters projektkostnader, vilket också är huvudområdet i detta examensarbete. Syftet är att utveckla en prissättningsmodell som hanterar osäkerheter, då detta är ett stort problem i rådande prissättningsprocess. En förstudie har utförts, följt av en modellimplementation. En analys av modellen gjordes sedan, innan slutsatser drogs. Projektkostnadsestimering främst, men även sannolikhetsfunktioner och prissättning som ett allmänt koncept, undersöktes i den i huvudsak litterära förstudien. Två lämpliga metoder för projektkostnadsestimering identifierades; Monte Carlo-simulering och Hierarchy Probability Cost Analysis. Dessa ledde till en teoretisk modell för projektkostnadsestimering. En modell implementerades i Matlab. Den behandlar projektkostnadsestimering, men inga andra prissättningsaspekter. Modellen utvecklades baserat på den teoretiska i möjlig utsträckning. Projektkostnader bröts ner i delkostnader som estimerades för konkurrenterna. Dessa ingick i en Monte Carlo-simulering. Konkurrenters projektkostnader estimerades med hjälp av denna teknik. Att analysera modellens noggrannhet var svårt. Den skiljer sig från den teoretiska beträffande hur sannolikhetsfunktioner och korrelationer estimeras. Dessa problem beror på projekt med skiftande karaktärsdrag samt begränsad data och tid. Ett solitt ramverk har dock skapats. Förbättringsmöjligheter finns, t.ex. noggrannare estimat och en modell som behandlar andra prissättningsaspekter. Det huvudsakliga hotet är att ingen underhåller modellen. Hur som helst är estimat inte mer än estimat. Modellen ska därför ses som ett hjälpverktyg, inte ett facit.