Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites.

Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

A 2D BEM-FEM approach for time harmonic fluid-structure interaction analysis of thin elastic bodies.

[EN]This paper deals with two-dimensional time harmonic fluid-structure interaction problems when the fluid is at rest, and the elastic bodies have small thicknesses. A BEM-FEM numerical approach is used, where the BEM is applied to the fluid, and the structural FEM is applied to the thin elastic bodies.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Hochgenaue Berechnungen von Energien und molekularen Eigenschaften mit Hilfe der Coupled-Cluster-Theorie

Coupled-Cluster-Theorie (CC) ist in der heutigen Quantenchemie eine der erfolgreichsten Methoden zur genauen Beschreibung von Molekülen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, daß neben den Berechnungen von Energien eine Reihe von Eigenschaften wie Strukturparameter, Schwingungsfrequenzen und Rotations-Schwingungs-Parameter kleiner und mittelgrofler Moleküle zuverlässig und präzise vorhergesagt werden können. Im ersten Teil der Arbeit wird mit dem Spin-adaptierten Coupled-Cluster-Ansatz (SA-CC) ein neuer Weg zur Verbesserung der Beschreibung von offenschaligen Systemen vorgestellt. Dabei werden zur Bestimmung der unbekannten Wellenfunktionsparameter zusätzlich die CC-Spingleichungen gelöst. Durch dieses Vorgehen wird gewährleistet, daß die erhaltene Wellenfunktion eine Spineigenfunktion ist. Die durchgeführte Implementierung des Spin-adaptierten CC-Ansatzes unter Berücksichtigung von Einfach- und Zweifachanregungen (CCSD) für high-spin Triplett-Systeme wird ausführlich erläutert. Im zweiten Teil werden CC-Additionsschemata vorgestellt, die auf der Annahme der Additivität von Elektronenkorrelations- und Basissatzeffekten basieren. Die etablierte Vorgehensweise, verschiedene Beiträge zur Energie mit an den Rechenaufwand angepassten Basissätzen separat zu berechnen und aufzusummieren, wird hier auf Gradienten und Kraftkonstanten übertragen. Für eine Beschreibung von Bindungslängen und harmonischen Schwingungsfrequenzen mit experimenteller Genauigkeit ist die Berücksichtigung von Innerschalenkorrelationseffekten sowie Dreifach- und Vierfachanregungen im Clusteroperator der Wellenfunktion nötig. Die Basissatzkonvergenz wird dabei zusätzlich mit Extrapolationsmethoden beschleunigt. Die quantitative Vorhersage der Bindungslängen von 17 kleinen Molekülen, aufgebaut aus Atomen der ersten Langperiode, ist so mit einer Genauigkeit von wenigen Hundertstel Pikometern möglich. Für die Schwingungsfrequenzen dieser Moleküle weist das CC-Additionsschema basierend auf den berechneten Kraftkonstanten im Vergleich zu experimentellen Ergebnissen einen mittleren absoluten Fehler von 3.5 cm-1 und eine Standardabweichung von 2.2 cm-1 auf. Darüber hinaus werden zur Unterstützung von experimentellen Untersuchungen berechnete spektroskopische Daten einiger größerer Moleküle vorgelegt. Die in dieser Arbeit vorgestellten Untersuchungen zur Isomerisierung von Dihalogensulfanen XSSX (X= F, Cl) oder die Berechnung von Struktur- und Rotations-Schwingungs-Parametern für die Moleküle CHCl2F und CHClF2 zeigen, daß bereits störungstheoretische CCSD(T)-Näherungsmethoden qualitativ gute Vorhersagen experimenteller Resultate liefern. Desweiteren werden Diskrepanzen von experimentellen und berechneten Bindungsabständen bei den Molekülen Borhydrid- und Carbenylium durch die Berücksichtigung des elektronischen Beitrages zum Trägheitsmoment beseitigt.

In defence of modeling simultaneity for a correct approximation of cultural aspects: implications for food consumers studies with latent variables

Dealing with latent constructs (loaded by reflective and congeneric measures) cross-culturally compared means studying how these unobserved variables vary, and/or covary each other, after controlling for possibly disturbing cultural forces. This yields to the so-called ‘measurement invariance’ matter that refers to the extent to which data collected by the same multi-item measurement instrument (i.e., self-reported questionnaire of items underlying common latent constructs) are comparable across different cultural environments. As a matter of fact, it would be unthinkable exploring latent variables heterogeneity (e.g., latent means; latent levels of deviations from the means (i.e., latent variances), latent levels of shared variation from the respective means (i.e., latent covariances), levels of magnitude of structural path coefficients with regard to causal relations among latent variables) across different populations without controlling for cultural bias in the underlying measures. Furthermore, it would be unrealistic to assess this latter correction without using a framework that is able to take into account all these potential cultural biases across populations simultaneously. Since the real world ‘acts’ in a simultaneous way as well. As a consequence, I, as researcher, may want to control for cultural forces hypothesizing they are all acting at the same time throughout groups of comparison and therefore examining if they are inflating or suppressing my new estimations with hierarchical nested constraints on the original estimated parameters. Multi Sample Structural Equation Modeling-based Confirmatory Factor Analysis (MS-SEM-based CFA) still represents a dominant and flexible statistical framework to work out this potential cultural bias in a simultaneous way. With this dissertation I wanted to make an attempt to introduce new viewpoints on measurement invariance handled under covariance-based SEM framework by means of a consumer behavior modeling application on functional food choices.

High precision swept volume approximation with conservative error bounds

In technical design processes in the automotive industry, digital prototypes rapidly gain importance, because they allow for a detection of design errors in early development stages. The technical design process includes the computation of swept volumes for maintainability analysis and clearance checks. The swept volume is very useful, for example, to identify problem areas where a safety distance might not be kept. With the explicit construction of the swept volume an engineer gets evidence on how the shape of components that come too close have to be modified.rnIn this thesis a concept for the approximation of the outer boundary of a swept volume is developed. For safety reasons, it is essential that the approximation is conservative, i.e., that the swept volume is completely enclosed by the approximation. On the other hand, one wishes to approximate the swept volume as precisely as possible. In this work, we will show, that the one-sided Hausdorff distance is the adequate measure for the error of the approximation, when the intended usage is clearance checks, continuous collision detection and maintainability analysis in CAD. We present two implementations that apply the concept and generate a manifold triangle mesh that approximates the outer boundary of a swept volume. Both algorithms are two-phased: a sweeping phase which generates a conservative voxelization of the swept volume, and the actual mesh generation which is based on restricted Delaunay refinement. This approach ensures a high precision of the approximation while respecting conservativeness.rnThe benchmarks for our test are amongst others real world scenarios that come from the automotive industry.rnFurther, we introduce a method to relate parts of an already computed swept volume boundary to those triangles of the generator, that come closest during the sweep. We use this to verify as well as to colorize meshes resulting from our implementations.