Dissertations / Theses on the topic 'Dynamic phasor model'

The objective of this dissertation is to carry out dynamic modeling, analysis and control of power systems with Renewable Energy Sources (RES) such as: Photovoltaic (PV) power sources and wind farms. The dissertation work is mainly focused on microgrid since it plays a major role in modern power systems and tend to have higher renewable power penetration. Two main theoretical concepts, dynamic phasor and impedance modeling have been adopted to model and analyze the power systems/mocrogrids with RES. The initial state calculation which is essential for small signal analysis of a system is carried out as the first step of the dissertation work. Dynamic phasor and impedance modeling techniques have been utilized to model and analyze power systems/micogrids as the second phase of the work. This part consists of two main studies. First case investigates the impedance modeling of Thyristor Controller Series Capacitor (TCSC) for sub-synchronous resonance (SSR) analysis where a wind farm is connected to a power system through series compensated line. Second case utilizes the dynamic phasor concept to model a microgrid in unbalanced condition. Here the unbalance is caused by a single phase PV connected to the microgrid. Third Phase of the dissertation work includes upper level control of the microgrid. Here prediction and optimization control for a microgrid with a wind farm, a PV system, an energy storage system and loads is evaluated. The last part of the dissertation work focuses on real time modeling and hardware in loop simulation test bed for microgrid applications. This dissertation has led to four journal papers (three accepted, one submitted) and five conference papers.

This thesis aims at modeling the separated liquid-liquid flows with application for flushing. In the beginning, there will be a short review of the governing equations and the fundamental concepts used in this thesis. Two models are introduced and developed based on two previous PhD dissertations from NTNU(Trygve Wangensteen and Tor Kindsbekken Kjeldby). The properties of the fluids in these models are based on Oil, Exxsol D80, mu_o=1.79 [cP] and tapped water, mu_w=1.11 [cP]. These models will be numerically developed for both dynamic and stationary flows. The numerical scheme used for these models is explicit. A complete explanation about discretization is given in chapter 4.After developing the dynamic and stationary solutions for both models, there will be two major case studies. The first one is to understand when the dynamic and stationary solutions depart from one another as the mixture velocity varies between low velocities to high velocities. It turns out that The solutions look quite similar until the mixture velocity reaches the value of around U_M=1 [m/s]. Then the solutions become more and more different especially at the oil front. The second case study is about keeping the mixture velocity constant and varying the pipe angle. The pipe angle variation range lies between -2.5 and +5 degrees. For negative inclinations, the dynamic and stationary solutions agree quite well. However when the positive slope is put to the test and gravity is acting against the flow, the dynamic and stationary solutions differ more.\\Finally there will be a discussion on where this different behavior stems from. The two fluid model introduced at the beginning of this report is studied closely, term by term. These terms represent the frictional forces that balance the pressure gradient in the pipe. These forces are plotted for four different cases with mixture velocities varying from U_M=0.25 [m/s] to U_M=5 [m/s]. These figures reveal which forces dominate the solution for relatively low and high mixture velocities. The dominating forces are the ones that balance the pressure gradient. It turns out that the level gradient is quite significant and a dominant term in almost all cases. However as the mixture velocity increases, the acceleration terms grow to the same order of magnitude as the level gradient. But for the most part, the spatial and the temporal acceleration act symmetrically, and in effect cancel each other out. There will be a thorough discussion about this in the final chapter.

The technique of Brownian Dynamics simulation has been used to follow the evolution of model colloidal systems during phase separation in the liquid-vapour and solid-vapour regions of the phase diagram. Systems of monodisperse spherical particles interacting via LJ m:n type potentials were quenched in temperature from the one-phase region into the two phase region. Various structural and rheological properties were followed as the systems evolved, including the radial distribution functions, the small angle scattering peak of the structure factor, the interaction energy and the linear response rheology. The scaling behaviour of these quantities was found to be similar to that observed in light scattering experiments following the phase separation of colloidal systems. The aggregate structure could not be represented well by a single fractal dimension. Some evidence of fractal structure was found early in the phase separation, however the reversibility of the interactions allowed for a high degree of restructuring which led to a collapse of the initially tenuous structure into dense aggregates. The local structure was sensitive to the range of the interaction potential - as the potential became more short-ranged, increasing evidence of crystallisation of the denser phase was apparent from the form of g(f). Particles with 12:6 interactions formed structures displaying the rheological strength associated with an elastic gel. However restructuring was continual, resulting in a dense compact structure. The short-range 36:18 potential retained a tenuous gel-like structure and displayed an arrest of phase separation on long lengthscales. However, the particles did not have the interaction strength necessary to give significant rigidity to the system. This suggests that to form an arrested state with elastic gel-like rheology it would be necessary to have a more permanent form of interaction, in addition to the short-range reversible interactions used in this work.

Interior permanent magnet synchronous motor (IPMSM) has been widely used in hybrid electric vehicles (HEVs) since the high power density and efficiency. However, the primary drawback of IPMSM is the demagnetization phenomenon caused by the permanent magnets. Modeling of the demagnetization fault are important in developing and designing a protection system for the traction on HEVs, thus, an efficient and accurate IPMSM model for demagnetization fault simulation is necessary. By using the conventional dq0 IPMSM model, the current indicators of demagnetization fault are affected by noise which will cause inaccuracy of the simulation. For this reason, a dynamic phasors model of IPMSM is presented in this thesis. In this thesis, firstly, the dynamic phasors model of IPMSM is verified by using small-signal transient analysis for its stability. Secondly, the time-domain transient simulations of positive sequence currents are shown and compared to the conventional dq0 model with demagnetization fault.

Harmonic domain models have been developed for Thyristor Controller Reactors (TCR) and other power electronic devices. Recently, these models have been extended to describe not just the steady-state harmonic interactions but harmonic transients as well. However, these dynamic models consistently do not incorporate models for controls. On the other hand, for the TCR as a FACTS Controller, dynamic models are available in which only the fundamental frequency component of the Controller is included; excluding harmonic interactions presumes that these do not affect the dynamics of the Controller. This thesis describes the development of a Harmonic State Space (HSS) model of a three phase TCR. As an extended state space description, this model describes the dynamics of the Controller while capturing harmonic interactions. It also includes the effect of switching instant variation which significantly improves the effectiveness of the model and allows the controller feedback characteristics to be included. The result of this model was validated with a purely time-domain simulation in PSCAD/EMTDC. Using the HSS to model a power system with TCR, it is illustrated that harmonic interactions play a significant role in the dynamics of the system. It is observed that for the specific system analysed, the least-damped pole-pair which dominates the dynamics of the system is associated with the 5th harmonic. Failure to include interactions with this specific harmonic produces an inaccurate dynamic description. Preliminary to the development of HSS model, a linearised harmonic domain model of a TCR which establishes the harmonic interactions across the device is also developed. Results of this model are validated with a time-domain simulation. This characterisation paves the way for a reduced harmonic state space model that is used in the HSS model. The principles and procedures established in this thesis can be applied to the development of models for other FACTS Controllers or HVDC links.

This PhD thesis is concerned with applications of nonlinear systems of conservation laws to gas dynamics and traffic flow modeling. The first part is devoted to the analytical description of a fluid flowing in a tube with varying cross section. We study the 2x2 model of the p-system and than, we extend the properties to the full 3x3 Euler system. We also consider a general nxn strictly hyperbolic system of balance laws; we study the Cauchy problem for this system and we apply this result to the fluid flow in a pipe wiyh varying section. Concerning traffic flow, we introduce a new macroscopic model, based on a non-smooth 2x2 system of conservation laws. We study the Riemann problem for this system and the qualitative properties of its solutions that are relevant from the point of view of traffic.

Anisotropy in the spatial arrangement of species and also geometric anisotropy in the components of liquid and soft matter systems gives rise to complex phase and non-trivial dynamic behaviors. Many systems are encompassed by this description including polymers, guest molecules in porous gels or nano-structured materials and also orientable fluids. In order to understand these systems, computational studies provide valuable insight. The study of such systems computationally is difficult if not prohibitive thus it is necessary to reduce these systems to simple models that capture the essential physical processes that govern the dynamics and phase behavior. Two simple models fit into this category: systems where the surrounding solvent is held stationary, a Lorentz model and also systems where a liquid crystal is formed from hard spherocylinders and is driven by an electric field. The Lorentz models studied provide a description of the dynamical regimes accessible when the probe and/or scatterers are given geometric anisotropy. The resulting dynamics are studied when order is present in the stationary solvent, i.e. structured versus isotropic solvent structure. Effective channels depending upon the competition of length scales as well as the structure of the stationary solvent leads to transitions in the dynamics of the traversing probe. Geometric anisotropy in nematogens in liquid crystals leads to the formation of mesophases indicative of a liquid crystal. When coupled to a rotating electric field, the dynamics and phase of the nematogens can be controlled.

In questa tesi viene presentata un'analisi numerica dell'evoluzione dinamica del modello di Heisenberg XXZ, la cui simulazione è stata effettuata utilizzando l'algoritmo che va sotto il nome di DMRG. La transizione di fase presa in esame è quella dalla fase paramagnetica alla ferromagnetica: essa viene simulata in una catena di 12 siti per vari tempi di quench. In questo modo si sono potuti esplorare diversi regimi di transizione, da quello istantaneo al quasi-adiabatico. Come osservabili sono stati scelti l'entropia di entanglement, la magnetizzazione di mezza catena e lo spettro dell'entanglement, particolarmente adatti per caratterizzare la fisica non all'equilibrio di questo tipo di sistemi. Lo scopo dell'analisi è tentare una descrizione della dinamica fuori dall'equilibrio del modello per mezzo del meccanismo di Kibble-Zurek, che mette in relazione la sviluppo di una fase ordinata nel sistema che effettua la transizione quantistica alla densità di difetti topologici, la cui legge di scala è predicibile e legata agli esponenti critici universali caratterizzanti la transizione.

The present thesis is concerned with the stochastic phase dynamics of neuron models and spike time reliability. It is well known that noise exists in all natural systems, and some beneficial effects of noise, such as coherence resonance and noise-induced synchrony, have been observed. However, it is usually difficult to separate the effect of the nonlinear system itself from the effect of noise on the system's phase dynamics. In this thesis, we present a stochastic theory to investigate the stochastic phase dynamics of a nonlinear system. The method we use here, called ``the stochastic multi-scale method'', allows a stochastic phase description of a system, in which the contributions from the deterministic system itself and from the noise are clearly seen. Firstly, we use this method to study the noise-induced coherence resonance of a single quiescent ``neuron" (i.e. an oscillator) near a Hopf bifurcation. By calculating the expected values of the neuron's stochastic amplitude and phase, we derive analytically the dependence of the frequency of coherent oscillations on the noise level for different types of models. These analytical results are in good agreement with numerical results we obtained. The analysis provides an explanation for the occurrence of a peak in coherence measured at an intermediate noise level, which is a defining feature of the coherence resonance. Secondly, this work is extended to study the interaction and competition of the coupling and noise on the synchrony in two weakly coupled neurons. Through numerical simulations, we demonstrate that noise-induced mixed-mode oscillations occur due to the existence of multistability states for the deterministic oscillators with weak coupling. We also use the standard multi-scale method to approximate the multistability states of a normal form of such a weakly coupled system. Finally we focus on the spike time reliability that refers to the phenomenon: the repetitive application of a stochastic stimulus to a neuron generates spikes with remarkably reliable timing whereas repetitive injection of a constant current fails to do so. In contrast to many numerical and experimental studies in which parameter ranges corresponding to repetitive spiking, we show that the intrinsic frequency of extrinsic noise has no direct relationship with spike time reliability for parameters corresponding to quiescent states in the underlying system. We also present an ``energy" concept to explain the mechanism of spike time reliability. ``Energy" is defined as the integration of the waveform of the input preceding a spike. The comparison of ``energy" of reliable and unreliable spikes suggests that the fluctuation stimuli with higher ''energy" generate reliable spikes. The investigation of individual spike-evoking epochs demonstrates that they have a more favorable time profile capable of triggering reliably timed spike with relatively lower energy levels.

Epidemics are a constant threat, able to bring the entire world to a halt in the case of extreme outbreaks. Computational epidemiology seeks to understand the spread of disease at a population rather than individual level. In this understanding, the field hopes to predict the spread of disease by either simulating microscopic interactions giving rise to infection, or by using mean-field models to emulate the average resultant epidemic spread. This knowledge can be used to predict the future spread of disease and create specific intervention strategies which exploit our understanding of disease spread. The epidemic threshold, the level of infectiousness below which epidemics will not persist, but above which, large levels of infections are maintained, is key to this epidemic analysis. In this pursuit, understanding criticality in the form of the epidemic threshold is frequently studied, however many questions remain unanswered. Another significant challenge to epidemic modeling is the accurate representation of population mobility, as it forms the basis of long range transmission events, and its accuracy directly impacts the relevance of a model to real scenarios. In particular, moving beyond a static treatment of mobility factors into dynamic treatments presents a significant additional step in both modeling and criticality analysis. Specifically, some open challenges addressed in this thesis are: i) Understanding critical thresholds of epidemics in the language of statistical mechanics where phase transitions are rigorously defined. ii) Improving frameworks for the treatment of mobility in epidemic models and criticality analysis of models with dynamic mobility. iii) Extending analysis of critical phenomena for epidemic models with dynamic mobility . iv) Understanding the specific implications of Australian demographics, mobility and geography on the critical dynamics of epidemic spread.

In this thesis, atomic force microscopy studies in Tapping Mode have been performed on a system composed of hematite nanoparticles deposed on either a MoS2 (molybdenite) or SiO2 (silice) substrate. The nature of nanoparticles facets was determined combining both atomic force microscopy and transmission electron microscopy. Later on, this nanoparticles and substrates were used as a model system to deduce material properties of a SiO2 surface using force spectroscopy. From the determination of interactions between the AFM tip and the SiO2 surface, the Hamaker constant was deduced. Contact interactions as a function of humidity were evidenced which confirmed the hydrophobic character of hematite nanoparticles<br>Dans cette thèse, des études de microscopie à force atomique en mode tapping ont été effectuées sur un système de nano-particules d'hématites sur substrat de MoS2 (molybdénite) ou de SiO2 (silice). La nature des facettes des nano-particules a été déterminée en combinant à la microscopie à force atomique la microscopie électronique en transmission. Ensuite ces nano-particules et leurs substrats ont été utilisées comme système modèle pour sonder comment interroger les propriétés de surface par spectroscopie et microscopie à force atomique, au-delà de la simple information de topographie, à partir de la détermination des interactions entre la pointe d'AFM et la surface des échantillons. Les interactions de Van der Waals à longue distance et la constante de Hamaker ont été déterminées. Les interactions de contact en présence et en absence d'humidité ont été mises en évidence, menant, entre autres, à la détermination du caractère hydrophobe des nano-particules

Las biomembranas constituyen la estructura de separación fundamental en las celulas animales, y son importantes en el diseño de sistemas bioinspirados. Su simulación presenta desafíos, especialmente cuando ésta implica dinámica y grandes cambios de forma o se estudian sistemas micrométricos, impidiendo el uso de modelos atomísticos y de grano grueso. El objetivo principal de esta tesis es el desarrollo de un marco computacional para entender la dinámica de biomembranas inmersas en fluido viscoso usando modelos de campo de fase. Los modelos de campo de fase introducen un campo escalar contínuo que define una interfase difusa, cuya física está codificada en las ecuaciones en derivadas parciales que la gobiernan. Estos modelos son capaces de soportar cambios dramáticos de forma y topología, y facilitan el acoplamiento de distintos fenómenos físicos. No obstante, presentan desafíos numéricos significativos, como el alto orden de las ecuaciones, la resolución de frentes móviles y abruptos, o una eficiente integración en el tiempo. En esta disertación abordamos estos puntos mediante la combinación de una discretización espacial con métodos sin malla usando las funciones base locales de máxima entropía, y una formulación variacional Lagrangiana para acoplamiento elástico-hidrodinámico. La suavidad del método sin malla genera una aproximación precisa del campo de fase y puede lidiar fácilmente con adaptatividad local, la aproximación Lagrangiana extiende de manera natural esta adaptividad a la dinámica, y la formulación variacional permite una integración variacional temporal no linealmente estable y robusta. La implementación numérica de estos métodos en un entorno de computación de alto rendimiento ha motivado el desarrollo de un nuevo código computacional. Este código integra el estado del arte de las librerías en paralelo e incorpora importantes contribuciones técnicas para solventar cuellos de botella que aparecen con el uso de métodos sin malla en computación a gran escala. El código resultante es flexible y ha sido aplicado a otros problemas científicos en varias colaboraciones que incluyen flexoelectricidad, conformado metálico, fluidos viscosos o fractura en materiales con energía de superficie altamente anisotrópica.<br>Biomembranes are the fundamental separation structure in animal cells, and are also used in engineered bioinspired systems. Their simulation is challenging, particularly when large shape changes and dynamics are involved, or micrometer systems are considered, ruling out atomistic or coarse-grained molecular modeling. The main goal of this thesis is to develop a computational framework to understand the dynamics of biomembranes embedded in a viscous fluid using phase-field models. Phase-field models introduce a scalar continuous field to define a diffuse moving interface, whose physics is encoded in partial differential equations governing it. These models can deal with dramatic shape and topological transformations and are amenable to multiphysics coupling. However, they present significant numerical challenges, such as the high-order character of the equations, the resolution of sharp and moving fronts, or the efficient time-integration. We address all these issues through a combination of meshfree spacial discretization using local maximum-entropy basis functions, and a Lagrangian variational formulation of the coupled elasticity-hydrodynamics. The smooth meshfree approach provides accurate approximations of the phase-field and can easily deal with local adaptivity, the Lagrangian approach naturally extend adaptivity to dynamics, and the variational formulation enables nonlinearly-stable robust variational time integration. The numerical implementation of these methods in a high-performance computing framework has motivated the development of a new computer code, which integrates state-of-the-art parallel libraries and incorporates important technical contributions to overcome bottlenecks that arise in meshfree methods for large-scale problems. The resulting code is flexible and has been applied to other scientific problems in a number of collaborations dealing with flexoelectricity, metal forming, creeping flows, or fracture in materials with strongly anisotropic surface energy.

This master thesis is focused on the synchronous generator mathematical model analysis. Based on the analysis are compiled mathematical models of main generator and exciter cooperating in brushless synchronous generator excitation system. Mathematical models of both machines are based on system of differential equations and their validity is verified in Matlab-Simulink. The master thesis is devided into three main parts. First part is focused on the derivation of differential equations to describe the behavior of electrical quantities of machines. In the second part are compiled and simulated mathematical models of both synchronous machines in Matlab-Simulink. The correctness of models are verified by approximate analytical calculations of selected steady and dynamic states. The last part is focused on design and simulation of concept for main generator rapid field winding deexcitation in brushless synchronous genereator excitation system.

The work presented in this PhD Thesis aims to investigate, with the methods of soft matter physics, systems of biological interest. Inspired by the observation of algae, migrating cells and and protein complexes inside the single cell, simple mathematical models have been implemented to obtain computer simulations of complex systems of biological interest and to deepen our understanding on their physical properties. The first part of the work deals with active matter systems, in which each particle is able to self-propel. Active self-rotations are rarely studied in this context, although present in biological systems such as Chlamydomonas reinhardtii algae. We built a simple model for active particles in 2D based on ABPs (Active Brownian Particles) model, accounting for inter-particle interactions and adding an active torque to each particle to simulate the ability of self-rotating. Employing MD simulations, we studied this model system of active rotators in different conditions, to shed light on the role of self- rotation in active matter systems at the jammed-unjammed transition. We then applied our model based on ABPs to the study of interacting active matter invading narrow channels, to investigate the role of single particles properties in determining invasion behavior. The second part of the work deals with nuclear pores, protein complexes inserted in the nuclear envelope of eukaryotic cells, acting as communication gates between nucleus and cytoplasm. Nuclear pores spatial organization and geometric arrangement on the nuclear surface are still poorly understood. Hence we propose the use of tools commonly employed to study the atomic structural and topological features of soft matter, to study nuclear pores spatial organization. Furthermore, to interpret the experimental results, we hypothesize an effective interaction among nuclear pores and implemented it in extensive numerical simulations of octagonal clusters, mimicking typical pore shapes.

The two-phase MD technique employed in this work determines the liquid and vapor phase densities from a histogram of molecular densities within phase clusters in the simulation cell using a new Monte Carlo (MC) sampling method. These equilibrium densities are then fitted in conjunction with known critical-point scaling laws to obtain the critical temperature, and the critical density. This MC post-processing method was found to be more easily implemented in code, and it is efficient and easily applied to complex, structured molecules. This method has been successfully applied and benchmarked for a simple Lennard-Jones (LJ) fluid and a structured molecule, propane. Various degrees of internal flexibility in the propane models showed little effect on the coexisting densities far from critical point, but internal flexibility (angle bending and bond vibrations) seemed to affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point. The developed MD+MC method was then used to test the efficacy of two all-atom, site-site pair potential models (with and without point charges) developed solely from the energy landscape obtained from high-level ab initio pair interactions for the first time. Both models produced equivalent phase domes and critical loci. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here. Lastly, the transferability of the ab initio potential model was evaluated by applying it to 1-pentanol. An attempt has been made to separate the errors due to transferability of the potential model from errors due to the use of a true-pair potential. The results suggested a good level of transferability for the site-site model. The lack of multi-body effects appears to be dominant weakness in using the generalized ab initio potential model for determination of the phase dome and critical properties of larger alcohols.

The Diploma thesis is focused on rheological properties of bituminous binders and mixtures. Above all, it describes the changes of these properties of samples of bituminous binders and mixtures. Those were brought by the process of laboratory aging, since it simulates the changes occurring in the in the real-life conditions. The theoretical part depicts the field of rheology and methods utilized for simulating the ageing of binders and mixtures. The practical part describes the process of preparation of samples and its testing. Firstly, the ageing of bituminous mixture by the means of BSA method (Braunschweiger Alterung) took place, which was followed by preparing the solids for testing the modulus of stiffness and main testing. The rest of the mixture was used for extracting the binder. Tests with the binder were focused on the usage of dynamic shear rheometer (complex shear modulus, dynamic viscosity). The last part of the work is dedicated to the comparison of the outcomes of testing.

The theory of thermodynamic phase transitions has played a central role both in theoretical physics and in dynamical systems for several decades. One of its fundamental results is the classification of various physical models into equivalence classes with respect to the scaling behavior of solutions near the critical manifold. From that point of view, systems characterized by the same set of critical exponents are equivalent, regardless of how different the original physical models might be. For non-equilibrium phase transitions, the current theoretical framework is much less developed. In particular, an equivalent classification criterion is not available, thus requiring a specific analysis of each model individually. In this thesis, we propose a potential classification method for time-dependent dynamical systems, namely comparing the possible deformations of the original problem, and identifying dynamical systems which share the same deformation space. The specific model on which this procedure is developed is the Kuramoto model for interacting, disordered oscillators. Studied in the mean-field limit by a variety of methods, its associated synchronization phase transition appears as an appropriate model for cooperative phenomena ranging from coupled Josephson junctions to self-ordering patterns in biological and social systems. We investigate the geometric deformation of the dynamical system into the space of univalent maps of the unit disk, related to the Douady-Earle extension and the Denjoy-Wolff theory, and separately the algebraic deformation into the space of nonlinear sigma models for unitary operators. The results indicate that the Kuramoto model is representative for a large class of non-equilibrium synchronization models, with a rich phase-space diagram.

Ziel dieser Arbeit ist es eine Beziehung zwischen den biophysikalischen Eigenschaften der Nervenmembran, und den ausgeführten Berechnungen und Filtereigenschaften eines tonisch feuernden Neurons, unter Einbeziehen intrinsischer Fluktuationen, herzustellen. Zu diesem Zweck werden zu erst die mikroskopischen Fluktuationen, die durch das stochastische Öffnen und Schließen der Ionenkanäle verursacht werden, zu makroskopischer Varibilität in den Zeitpunkten des Auftretens der Aktionspotentiale übersetzt, denn es sind diese Spikezeiten die in vielen sensorischen Systemen informationstragenden sind. Die Methode erlaubt es das stochastischer Verhalten komplizierter Ionenkanalstrukturen mit einer großen Zahl an Untereinheiten, in Spikezeitenvariabilität zu übersetzen. Als weiteres werden die Filtereigenschaften der Nervenzellen in der überschwelligen Dynamik, also bei Existenz eines stabilen Grenzzyklus, aus ihren Phasenantwortkurven (PAK), einer Eigenschaft des linearisierten adjungierten Flusses auf dem Grenzzyklus, in einem stöhrungstheoretischen Ansatz berechnet. Es ergibt sich, dass Charakteristika des Filter, wie beispielsweise die DC Komponente und die Eigenschaften des Filters um die Fundamentalfrequenz und ihrer Harmonien, von den Fourierkomponenten der PAK abhängen. Unter Verwendung der hergeleiteten Filter und weiterer Annahmen ist es möglich das frequenzabhängige Signal-zu-Rauschen Verhältnis zu berechnen, und damit eine untere Schranke für die Informationstransferrate eines Leitfähigkeitsmodells zu berechnen. Unter Zuhilfenahme der numerischen Kontinuierungsmethode ist es möglich die Veränderungen in der Spikevariabilität und den Filtern für jeden biophysikalischen Parameter des System zu verfolgen. Weiterhin wurde die verwendete Phasenreduktion durch eine Korrektur ergänzt, die die Radialdynamik einbezieht. Es zeigt sich, dass die Krümmung der Isochronen einen Einfluss darauf hat ob das Rauschen einen positiven oder negativen Frequenzschift hervorruft.<br>The goal of the thesis is to establish quantitative, analytical relations between the biophysical properties of nerve membranes and the performed neuronal computations for neurons in a tonically spiking regime and in the presence of intrinsic noise. For this purpose, two major lines of investigation are followed. Firstly, microscopic noise caused by the stochastic opening and closing of ion channels is mapped to the macroscopic spike jitter that affects neural coding. The method is generic enough to allow one to treat Markov channel models with complicated, high-dimensional state spaces and calculate from them the noise in the coding variable, i.e., the spike time. Secondly, the suprathreshold filtering properties of neurons are derived, based on the phase response curves (PRCs) by perturbing the associated Fokker-Planck equations. It turns out that key characteristics of the filter, such as the DC component of the gain and the behaviour near the fundamental frequency and its harmonics are related to the particular Fourier components of the PRC and hence the bifurcation type of the neuron. With the help of the derived filter and further approximations one is able to calculate the frequency resolved signal-to-noise ration and finally the total information transmission rate of a conductance based model. Using the method of numerical continuation it is possible to calculate the change in spike time noise level as well as the filtering properties for arbitrary changes in biophysical parameter such as varying channel densities or mean input to the cell. We extend the phase reduction to include correction terms from the amplitude dynamics that are related to the curvature of the isochrons and provide a method to identify the required amplitude sensitivities numerically. It can be shown that the curvature of the isochron has a direct consequence for the noise induced frequency shift.

The ubiquity of free boundary problems in biology, with which we are mainly concerned, led us to adopt a mathematical technique to render them tractable and relatively easy to solve. The phase field method, used when dealing with dynamical systems with moving boundary condition, addresses arising difficulties involved with tracking those boundaries. In this work we model the motion of neutrophils, cells of the immune system, in response to chemical driving. Their morphology changes dynamically as they move to neutralize their target, a mechanism called chemotaxis. Additionally, we propose a model for neural cell growth, which is insti- gated by mediators, a process termed chemotropism. When coupled to an internal mechanism of actin polymerization, this induces the advancement of the axonal tip. Lastly, we used the method to build a generalized model from which both chemo- tactic and chemotropic models can be derived. These three problems were solved by the construction of free energy functionals F that captured the main features of the dynamics, in relation to the order parameters φ that distinguished the phases of the system as well as their interfaces. We considered the membrane of the cells, their inside and outside, as well as their leading edges. The governing partial dif- ferential equations were obtained by a variational differentiation of F with respect to the fields. Following this method, we were able to model cell morphodynamics in two and three dimensions. The major contribution of our work lies in the reduction of the complexity of those problems: we solve partial differential equations of fields coupled to the underlying dynamics at the molecular level, which are derived from a closed form generalized functional describing both the cell motion, deformation and growth.<br>L'abondance des problèmes à interface libre dans la biologie auxquels nous sommes principallement interéssés, nous a conduits à adopter une technique qui les rend relativement faciles à resoudre. Phase Field Method, utilisée pour examiner des systèmes dynamiques possédants des conditions aux limites en mouvement, resoud la diffuculté provenant de suivre leur évolution. Dans ce travail, on modèle le mouvement des neutrophiles qui sonts des cellules du système immunitaire en réponse aux signaux chimiques. Leur morphologie change dynamiquement quand ils se deplancent pour neutraliser leur cible: ce mécanisme est appelé chimiotaxie. Egalement, on propose un modèle pour le développement des cellules nerveuses induit par des médiateurs. Ce processus est nommé chémotropisme. Ce dernier, quand il est lié au mécanisme interne responsable de la polymérisation de l'actine, induit l'avancement du bout de l'axone. Finalement, on a employé la méthode pour construire un modèle généralisé qui permet de dériver les deux modèles chimiotactique et chémotropique. Ces problèmes ont été resouds en construisant des fonctionelles d'énergie libre F , capturant les caractéristiques principaux de la dynamique en fonction d'un paramètre d'order φ qui permet de dinstinguer les différentes phases du système aussi bien que les interfaces qui les séparent. Les éequations aux dérivées partielles décrivant leur evolution sont déterminées en effectuant une différenciation variationelle de F par rapport au champs φ. En suivant cette méthode, on était capable de reproduire la dynamique des morphologies en deux et trois dimensions. La contribution majeure de notre travail réside dans la réduction de la complexité de ces problèmes en suivant les équations aux dérivées partielles. Ces dernières sont liées aux mécanismes internes au niveau moléculaire dérivés dune fonctionelle généralisée F qui décrit le mouvement de la cellule ainsi que sa déformation et sa croissance.

This dissertation presents useful nonlinear models for fluid forcing on a moving body in two distinct contexts, and methods for analyzing the geometric structure within those and other mathematical models. This manuscript style dissertation presents three works within the theme of understanding fluid forcing and geometric structure. When a bluff body is free to move in the presence of an incoming bluff body wake, the average forcing on the body is dependent on its position relative to the upstream bluff body. This position-dependent forcing can be conceptualized as a stiffness, much like a spring. This work presents an updated model for the quasi-steady fluid forcing of a wake and extends the notion of wake stiffness to consider a nonlinear spring. These results are compared with kinematic experimental results to provide an example of the application of this framework. Fluid force models also play a role in understanding the behavior of passive aerodynamic gliders, such as gliding animals or plant material. The forces a glider experiences depend on the angle that its body makes with respect to its direction of motion. Modeling the glider as capable of pitch control, this work considers a glider with a fixed angle with respect to the ground. Within this model, all trajectories in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, in the search for manifolds such as the terminal velocity manifold, this dissertation introduces a new diagnostic for identifying the low dimensional geometric structure of models. The trajectory divergence rate uses instantaneous vector field information to identify regions of large normal stretching and strong normal convergence between nearby invariant manifolds. This work lays out the mathematical basis of the trajectory divergence rate and shows its application to approximate a variety of structures including slow manifolds and Lagrangian coherent structures. This dissertation applies nonlinear theoretical and numerical techniques to analyze models of fluid forcing and their geometric structure. The tools developed in this dissertation lay the groundwork for future research in the fields of flow-induced vibration, plant and animal biomechanics, and dynamical systems.<br>Ph. D.

In the present study, a finite volume method is employed to modelthe advection-diffusion phenomenon during a pure substance meltingprocess. The exercise is limited to a benchmark problem consisting ofthe 2D melting from a vertical wall of a PCM driven by natural convectionin the melt. Numerical results, mainly the temporal evolutionof average Nusselt number at the hot wall and the average liquid fraction,are validated by available literature data and the effect of thermalinertia in the heat transfer is considered as well. Finally, motivatedby recent publications and the model presented here, possible new researchtopics are proposed.

A existência de opiniões distintas em uma sociedade na qual indivíduos interagem constantemente atraiu o interesse de cientistas sociais e físicos estatísticos. Em 1997, Robert Axelrod propôs um modelo vetorial para o estudo da formação de domínios culturais diferentes em uma rede de agentes interagentes. Nesse modelo, os agentes são representados por um vetor de F componentes em que cada componente assume um dentre Q estados inteiros. O modelo apresenta uma transição de um estado monocultural (ordenado) para um estado multicultural (desordenado) que tem sido estudada na literatura através de parâmetros de ordem tais como o tamanho relativo do maior domínio cultural (S) e a fração de domínios culturais diferentes (g). Desde então, propriedades como robustez à introdução de ruídos, à variação de topologia e à introdução de campos local, global e externo foram investigadas. Nosso trabalho está organizado em três partes principais. Na primeira, apresentamos a proposta de novas medidas baseadas no conceito de atividade por agente para o estudo do modelo de Axelrod na rede quadrada. Mostramos que a variância da atividade do sistema (A) pode ser usada para indicar os pontos de transição e que sua distribuição de frequência pode indicar a ordem da transição. Na segunda, estimamos o diagrama de fases no plano (F,Q) e comparamos resultados obtidos em redes com condição de contorno aberta e fechada. Para isso, utilizamos as susceptibilidades dos parâmetros de ordem S e A para determinar os valores críticos Qc(F) para alguns valores de F. Na terceira, analisamos a formação de domínios culturais com a introdução de agentes persistentes para modelar efeitos de mídia interna. Nossos resultados revelam uma dependência de Qc com a probabilidade de ocupação p de agentes persistentes que nos permite obter o diagrama de fases no plano (p,Q). Interpretamos a linha crítica como resultado da competição de duas forças opostas (denominadas efeito de barreira e efeito de ligação) causadas por agentes não-persistentes que aderem aos persistentes.<br>The existence of different opinions in a society where individuals constantly interact has attracted the interest of social scientists and statistical physicists. In 1997, Robert Axelrod proposed a vectorial model to study the formation of cultural domains in a network of interacting agents. In this model, the agents are represented by a F components vector in which one from Q integer states is assigned to each component. The model presents a transition from a monocultural state (ordered) to a multicultural one (disordered) that has been studied by using order parameters such as the relative size of the biggest cultural domain (S) and the fraction of different domains (g). Since then, some properties as the robustness to the introduction of noise, to the variation of topology and to the introduction of local, global and external fields were studied. Our work is organized in three main parts. In the first part we present the proposal of new measurements based on the concept of activity per agent to study the Axelrod\'s model in a square lattice. We show the variance of system\'s activity (A) can be used to indicate the transition points and that the system\'s activity frequency distribution can be used to indicate the order of the transition. In the second part we estimate the phase diagram in the (F,Q) plane and compare the results obtained from simulations performed in lattices with open and closed boundary conditions. For this purpose, we use the susceptibility of order parameters S and A to determine the critical values Qc(F) for some values of F. In the third part we analyze the formation of cultural domains by introducing persistent agents to model effects of internal media. Our results reveal a dependence of Qc on the occupation probability p of persistent agents that allows us to obtain the phase diagram in the (p,Q) plane. We interpret the critical locus as a result of two opposite forces (called barrier effect and bonding effect) caused by non-persistent agents which adhere the persistent ones.

Gas chromatography (GC) is an analytical chemistry tool used to determine the chemical composition of a gas sample by separating sample analytes as they travel through a GC column. Recent efforts have been made to understand and control gas chromatography separations with a negative thermal gradient on the column. The present work presents results from thermal gradient GC separations on two GC columns in different configurations (serpentine and radial) in a stainless-steel plate. Methods to fabricate the GC systems capable of isothermal, temperature programmed and thermal gradient separations are presented. Isothermal experimental data from the serpentine column were used to fit retention and dispersion parameters in a transport model that simulates GC separation for hydrocarbons C12-C14. Transport model simulated retention times and peak widths matched experimental values well for isothermal, temperature programmed and thermal gradient separations. The validated transport model was used to study the effect of static (not varying temporally) thermal gradients on GC separations with varying injection widths, injection band shapes and stationary phase thickness. Resolution results from different heating conditions were considered comparable if retention times for each analyte were within 5%. An optimal, static thermal gradient is shown to reduce analyte band spreading from axially-varying velocity gradients with resolution improvements over isothermal separations of up to 8% for analytes with similar retention factors. Static thermal gradients have a larger effect on fronting peak shape than tailing peak shape. Stationary phase distribution acts similar to a velocity gradient and can be corrected by a thermal gradient. Another transport model was created from isothermal experimental data on a commercial column for hydrocarbons C12-C20. An optimal, static thermal gradient does not improve resolution for all analyte pairs. An optimal, dynamic (varying tempo-rally) thermal gradient is created by uniformly increasing the temperature on an optimal, static thermal gradient. Improvements in resolution of up to 20% are achievable over temperature programmed GC separation. A dynamic thermal gradient can also correct for a poor sample injection by creating a temperature trap at the beginning of the column.

La réactivité à la phase gazeuse, ou réactivité intrinsèque, a une grande importance puisque l’absence d’interactions avec un solvant peut donner lieu à une réactivité très diffèrent donc, nous permettant d’avoir une meilleure connaissance des propriétés moléculaires. Avec l’émergence en 1900 de nouvelles techniques expérimentales, plus précisément des techniques pour ioniser plus doucement, la chimie des ions en phase gazeuse s’est développée significativement et a supposé en changement dans l’idée de la réactivité chimique. Cet manuscrit est divisé en deux parties chacune d’elles concernant un aspect diffèrent de la réactivité en phase gazeuse.La premier partie, Part I, étude l’acidité intrinsèque d’une série de bases de Lewis du groupe 15 du tableau périodique, l’accent étant mis sur le changements d’acidité ayant lieue après la formation du complexe de Lewis. Divers acides de Lewis appartenant ou groupe 13 on été tenus en compte. Afin d’expliquer l’origine de l’augment d’acidité observé plusieurs méthodes théoriques on été employés. Pour le calcul de l’acidité intrinsèque ont a employé la théorie de la fonctionnelle de la densité (DFT, sigle pour Density Functional Theory) et des méthodes qui sont basées à la fonction d’onde. Pour décrire les variations dans la configuration électronique ayant lieu à la formation du complexe (et qui sont les responsables du changement d’acidité susmentionné) nous avons utilisé des méthodes complémentaires pour l’analyse de la population électronique (AIM, ELF et NBO). Il est important de souligner qu’une partie des résultats présentés dans cet manuscrit on été déjà corroborés par les résultats expérimentaux.La deuxième partie, Part II, est centrée sur l’étude de la réactivité unimoléculaire des ions formamide-M2+ (M = Ca, Sr). Dans ce cas particulier, les ions choisis avaient été déjà étudiés expérimentalement avec la technique de dissociation induite par collision (CID, sigle pour Collision Induced Dissociation). Tout au long de cette deuxième partie, nous avons étudié et caractérisé les différents mécanismes de fragmentation des deux ions, en utilisant diffèrent méthodes théoriques qui sont complémentaires entre eux. Premièrement, ont a évalué divers fonctionnelles afin de trouver le plus approprié pour maintenir le coût computationnelle bas au même temps que d’obtenir des résultats fiables. Ensuite, on a modélisé par moyen de simulations de dynamique la réactivité aux temps courts (&lt; 2.5 femto seconds). En outre, en se servant des données obtenues antérieurement, on a étudié la cinétique de fragmentation avec la théorie statistique RRKM, pour les réactions «lents » (t &gt; 2.5 fs). L’utilisation de cette procédure multi-échelle nous permet de rationaliser l’origine de tous les produits observés expérimentalement ainsi que de donner une explication aux différences entre les deux ions considérés. Pour finir, dans le quatrième chapitre sont énumérés et décrits brièvement les différents méthodes employés au cours de cet travail, tant théorétiques que expérimentaux<br>The so-called intrinsic reactivity (gas-phase reactivity) is of great importance since the absence of interaction with a solvent can result in very different reactivity patterns, allowing for a better understanding of molecular properties. With the advent in the 1900s of new experimental techniques, notably soft ionization methods such as electrospray ionization, the gas-phase ion chemistry has significantly developed in the last decades of the 1900s with a concomitant change in our view of chemical reactivity. The present manuscript is divided in two different parts, each one dealing with different aspects of gas-phase reactivity.Part I is concerned with the study of the intrinsic acidity of a series of group 15 Lewis bases. The changes on the aforementioned intrinsic acidity as the Lewis bases form adducts with group 13 Lewis acids is the main subject of this part. Thus, the origin for the acidity enhancement observed upon adduct formation is rationalized by means of different theoretical methods. High-level DFT and ab initio calculation were performed in order to compute theoretical acidities of the molecules under survey. Complementary to this, population analysis techniques such as AIM, ELF, and NBO were used to analyze the changes on the electronic configurations of those molecules and therefore provide with an explanation to the observed acidities. It is worth to stress the fact that part of the results were as well confirmed by means of experimental measurements. Part II focuses in unimolecular reactivity of molecular ions, namely, formamide-M2+ (M = Ca, Sr). In this case, experiments studying the Collision Induced Reactivity (CID) of these ions were already performed and through the second part of this manuscript the fragmentation mechanism of both ions are studied and characterized using different, but complementary, theoretical techniques. It is worth to mention that in a very first-step, an assessment of different methods to perform reliable electronic structure calculations while maintaining the lower possible computational cost. In the one hand, a kinetic study of the fragmentation process using the statistical theory RRKM, to describe the long-time reactivity (&gt; fs). On the other hand, direct dynamics simulations are performed in order to describe the short-time (&lt; 2.5 fs) non-statistical reactivity. This multi-scale approach allowed us to account for all the products observed in the CID experimental spectra of formamide-M2+ ( M = Ca, Sr), as well as the differences between them. In the fourth chapter a summary of the experimental and theoretical procedures used to perform the work presented in this manuscript is provided

Master of Science<br>Department of Electrical and Computer Engineering<br>Behrooz Mirafzal<br>Increasing energy demand, rising oil prices, and environmental concerns have forced attention to alternative energy sources that are environmentally friendly and independent of fossil fuels. Renewable energy sources (RES) have become an attractive alternative to the traditional energy sources for electric power generation. However, one of the main challenges of RES adaption arises when connecting RES to the electric grid. Voltage source inverters (VSIs), typically, connect RES to the electric grid. Similar to any engineering system, detailed dynamic models of the VSIs are needed for design and analysis purposes. However, due to the non-linearity of VSIs, development of dynamic models that can accurately describe their behavior is a complex task. In this thesis, a detailed averaged-state-space model of the two-level three-phase space vector pulse width modulation VSI and its companion LCL filter is derived. Because VSIs can operate under stand-alone and grid-tied modes, two models were derived for each case. In the derived models, the VSI modulation index m and phase angle ϕ are initially considered constant. In practice, however, these parameters are considered the main control parameters. To model these parameters as control inputs, small-signal models of the VSI under stand-alone and grid-tied modes were derived. To verify the accuracy of the developed large-signal and small-signal models, Matlab/Simulink simulations were carried out. The simulation results were compared against the models results. Moreover, the models were verified through lab experiments. The developed models can be used as design and analysis tools. In addition, the developed models can be used as fast and efficient simulation tools for system studies, when the modeling of switching transients is not needed. Nowadays, the number of VSIs connected to the electric grid is growing exponentially. The amount of time and computation needed to simulate VSIs using simulation software packages can be significantly decreased by the use of the developed models.

Master of Science<br>Department of Mechanical and Nuclear Engineering<br>Steven Eckels<br>Both cavitating and flashing flows are important phenomena in fluid flow. Cavitating flow, a common consideration in valves, orifices, and metering devices, is also a concern in loss of coolant accidents for liquid water in power plants when saturation pressures are below atmospheric pressure. Flashing flow is a common consideration for devices such as relief and expansion valves and fluid injectors as well as for loss of coolant accidents in which the coolant’s saturation pressure is above atmospheric. Of the two phenomena, flashing flow has received greater interest due to its applicability to safety concerns, though cavitating flow is perhaps of greater interest in terms of energy efficiency. It is possible for cavitating and flashing flow to actually become sonic. That is, the local velocity of a fluid can exceed the local speed of sound due to the unique properties of two-phase mixtures. When a flow becomes sonic, it is possible for the flow to accelerate and impose additional energy losses that would not otherwise occur. Models of this aspect of two-phase flow are not well developed, typically only being presented for the case of constant area ducts. In this paper two models for cavitating sonic flow are developed and described by applying the integral forms of the mass, momentum, and energy equations to a control volume of variable cross-sectional area. These models, based on the homogeneous equilibrium model (HEM) and separated flow model, are then applied to experimental data taken by the author with R-134a as the fluid of interest. Experimental data were taken with four instrumented converging-diverging nozzles of various geometries using a custom testing rig that allowed for precise control and measurement of flow parameters such as mass flow, temperature, and pressure. The resultant data from the models are then examined, focusing on the resultant velocities, Mach numbers, quality, and shear stresses.

The investigation of failure in brittle materials, subjected to dynamic transient loading conditions, represents one of the ongoing challenges in the mechanics community. Progresses on this front are required to support the design of engineering components which are employed in applications involving extreme operational regimes. To this purpose, this thesis is devoted to the development of a framework which provides the capabilities to model how crack patterns form and evolve in brittle materials and how they affect the quantitative description of failure. The proposed model is developed within the context of diffusive interfaces which are at the basis of a new class of theories named phase field models. In this work, a set of additional features is proposed to expand their domain of applicability to the modelling of (i) rate and (ii) pressure dependent effects. The path towards the achievement of the first goal has been traced on the desire to account for micro-inertia effects associated with high rates of loading. Pressure dependency has been addressed by postulating a mode-of-failure transition law whose scaling depends upon the local material triaxiality. The governing equations have been derived within a thermodynamically-consistent framework supplemented by the employment of a micro-forces balance approach. The numerical implementation has been carried out within an updated lagrangian finite element scheme with explicit time integration. A series of benchmarks will be provided to appraise the model capabilities in predicting rate-pressure-dependent crack initiation and propagation. Results will be compared against experimental evidences which closely resemble the boundary value problems examined in this work. Concurrently, the design and optimization of a complimentary, improved, experimental characterization platform, based on the split Hopkinson pressure bar, will be presented as a mean for further validation and calibration.

The theoretical part of this thesis describes the rheology of bituminous binders, aging of asphalt binders and laboratory methods simulating short and long term aging. The following describes an empirical tests (needle penetration, softening point ring ball method) and functional tests (complex shear modulus and phase angle, dynamic viscosity), which are performed in the dynamic shear rheometer. At the end of this section, laboratory aging of bituminous binders using method RTFOT and method RTFOT + PAV is described in more detail. In the practical part of this thesis, the results of all tests performed on the binders aged using RTFOT + PAV are introduced and compared with results of properties of non-aged binders and binders aged by 3xRTFOT.

This thesis is concerned with the development of numerical techniques to simulate compressible multi-phase flows, in particular a high-accuracy numerical approach with mesh adaptivity. The Discontinuous Galerkin (DG) method was chosen as the framework for this work for being characterized for its high-order of accuracy -thus low numerical diffusion- and being compatible with mesh adaptivity due to its locality. A DG solver named DiGGIT (Discontinuous Galerkin at the Georgia Institute of Technology) has been developed and several aspects of the method have been studied. The Local Discontinuous Galerkin (LDG) method -an extension of DG for equations with high-order derivatives- was extended to solve multiphase flows using Diffused Interface Methods (DIM). This multi-phase model includes the convection of the volume fraction, which is treated as a Hamilton-Jacobi equation. This is the first study, to the author's knowledge, in which the volume fraction of a DIM is solved using the DG and the LDG methods. The formulation is independent of the Equation of State (EOS) and it can differ for each phase. This allows for a more accurate representation of the different fluids by using cubic EOSs, like the Peng-Robinson and the van der Waals models. Surface tension is modeled with a new numerical technique appropriate for LDG. Spurious oscillations due to surface tension are common to all the capturing schemes, and this new approach presents oscillations comparable in magnitude to the most common schemes. The moment limiter (ML) was generalized for non-uniform grids with hanging nodes that result from adaptive mesh refinement (AMR). The effect of characteristic, primitive, or conservative decomposition in the limiting stage was studied. The characteristic option cannot be used with the ML in multi-dimensions. In general, primitive variable decomposition is a better option than with conservative variables, particularly for multiphase flows, since the former type of decomposition reduces the numerical oscillations at material discontinuities. An additional limiting technique was introduced for DIM to preserve positivity while minimizing the numerical diffusion, which is especially important at the interface. The accuracy-preserving total variation diminishing (AP-TVD) marker for ``troubled-cell' detection, which uses an averaged-derivative basis, was modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique. Furthermore, a new error estimator was proposed to determine where to refine or coarsen the grid. This estimator was compared against other estimator used in the literature and it showed an improved performance. In order to provide equal order of accuracy in time as in space, the commonly used 3rd-order TVD Runge-Kutta (RK) scheme in the DG method was replaced in some cases by the Spectral Deferred Correction (SDC) technique. High orders in time were shown to only be required when the error in time is significant. For instance, convection-dominated compressible flows require for stability a time step much smaller than is required for accuracy, so in such cases 3rd-order TVD RK resulted to be more efficient than SDC with higher orders. All these new capabilities were included in DiGGIT and have provided a generalized approach capable of solving sub- and super-critical flows at sub- and super-sonic speeds, using a high-order scheme in space and time, and with AMR. Canonical test cases are presented to verify and validate the formulation in one, two, and three dimensions. Finally, the solver is applied to practical applications. Shock-bubble interaction is studied and the effect of the different thermodynamic closures is assessed. Interaction between single-drops and a wall is simulated. Sticking and the onset of splashing are observed. In addition, the solver is used to simulate turbulent flows, where the high-order of accuracy clearly shows its benefits. Finally, the methodology is challenged with the simulation of a liquid jet in cross flow.

Thermosetting polymers can cure at a gradient of cure temperatures due to a variety of factors, including heat transfer in the thermoset during heating and the exotherm due to the chemical reaction occurring during the cure. A new method for assessing the effect of cure conditions on mechanical behavior of toughened thermosets has been developed. Modeling of the phase separation process of a model thermoset system provided detailed understanding of the mechanism of property variation with cure temperature for this material. Subsequent characterization of gradient temperature cured samples has shown important variations, illustrating not only the importance of cure conditions, but the possibility of producing materials with new and useful properties. A special mold was developed to cure samples in a controlled gradient of temperature. Example systems known to show pronounced variations in microstructure cured in this gradient mold showed large variations of microstructure as a function of position within the sample, corresponding to the cure temperature at that point. A model toughened thermoset system was developed to demonstrate gradients of properties following cure in the gradient temperature mold. Cyanate ester materials were modified with hydroxyl-terminated butadiene-acrylonitrile copolymers as well as low Tg amorphous polyesters. The polyesters showed very desirable properties for a toughener, including relatively good thermo-oxidative stability in comparison with the butadiene-acrylonitrile toughener. However, the variation of properties of the cured materials with temperature was small, and to better understand the property variation possible using a gradient cure temperature technique, the butadiene-acrylonitrile toughened cyanate ester system was chosen for further study. This system showed a significant variation of glass transition temperature of the cyanate-rich phase as a function of cure temperature. Modeling of the phase separation process of this material was varied out employing a modeling procedure developed for epoxy materials. Various characteristics of the system were determined in order to apply the model to the chosen toughened thermoset. These included viscosity, surface, and thermodynamic parameters in addition to a careful characterization of the morphological parameters developed during cure at the chosen temperatures. Results show excellent predictive capability of the model for microstructure. Prediction of phase composition as a function of cure temperature is also possible, again with good agreement with experiment results. Higher cure temperatures result in a non-equilibrium phase composition, depressing the glass transition temperature of the continuous cyanate ester rich phase. This provides a mechanism by which properties of the system change as a function of position within a gradient temperature cured sample. Dynamic mechanical analysis was employed to characterize the relaxation properties of gradient and isothermally cured samples. The Havriliak Negami equation was chosen to describe the relaxation behavior of these samples. Comparison of the fitting of isotherms over the small, experimentally accessible range of frequencies showed that the use of time-temperature superpositioning could more reliably discern relatively small differences. The breadth of the relaxation corresponding to the glass transition of the polycyanurate phase was increased with a gradient cure temperature relative to isothermally cured samples. This increased broadness was expressed in an alternative way through the use of an autocorrelation function, which allows direct comparison of the time-dependent transition from a fully unrelaxed condition to a fully relaxed one.<br>Ph. D.

Energy storage using Phase Change Materials (PCMs) offers the advantage of higher heat capacity at specific temperature ranges, compared to single phase storage. Incorporating PCMs in lightweight buildings can therefore improve the thermal mass, and reduce indoor temperature fluctuations and energy demand. Large atrium buildings, such as Airport terminal spaces, are typically thermally lightweight structures, with large open indoor spaces, large glazed envelopes, high ceilings and non-uniform internal heat gains. The Heating, Ventilation and Air-Conditioning (HVAC) systems constitute a major portion of the overall energy demand of such buildings. This study presented a case study of the energy saving potential of three different PCM systems (PCM floor tiles, PCM glazed envelope and a retrofitted PCM-HX system) in an airport terminal space. A quasi-dynamic coupled TRNSYS®-FLUENT® simulation approach was used to evaluate the energy performance of each PCM system in the space. FLUENT® simulated the indoor air-flow and PCM, whilst TRNSYS® simulated the HVAC system. Two novel PCM models were developed in FLUENT® as part of this study. The first model improved the phase change conduction model by accounting for hysteresis and non-linear enthalpy-temperature relationships, and was developed using data from Differential Scanning Calorimetry tests. This model was validated with data obtained in a custom-built test cell with different ambient and internal conditions. The second model analysed the impact of radiation on the phase change behaviour. It was developed using data from spectrophotometry tests, and was validated with data from a custom-built PCM-glazed unit. These developed phase change models were found to improve the prediction errors with respect to conventional models, and together with the enthalpy-porosity model, they were used to simulate the performance of the PCM systems in the airport terminal for different operating conditions. This study generally portrayed the benefits and flexibility of using the coupled simulation approach in evaluating the building performance with PCMs, and showed that employing PCMs in large, open and thermally lightweight spaces can be beneficial, depending on the configuration and mode of operation of the PCM system. The simulation results showed that the relative energy performance of the PCM systems relies mainly on the type and control of the system, the night recharge strategy, the latent heat capacity of the system, and the internal heat gain schedules. Semi-active systems provide more control flexibility and better energy performance than passive systems, and for the case of the airport terminal, the annual energy demands can be reduced when night ventilation of the PCM systems is not employed. The semi-active PCM-HX-8mm configuration without night ventilation, produced the highest annual energy and CO2 emissions savings of 38% and 23%, respectively, relative to a displacement conditioning (DC) system without PCM systems.

Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration<br>In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement

The SIR can be expressed either as a system of nonlinear ordinary differential equations or as a nonlinear Volterra integral equation. In general, neither of these can be solved in closed form. In this thesis, it is shown that if we assume S(t) is a finite multi-exponential, i.e. function of the form S(t) = a+ ∑nk=1 rke-σkt or a logistic function which is an infinite-multi-exponential, i.e. function of the form S(t) = c + a/b+ewt, then we can have closed form solution. Also we will formulate a method to determine R0 the basic reproductive rate of an infection.

This thesis, which contains fourteen chapters in two parts, presents theoretical and computer simulation studies of dynamics in supercooled liquids and thermotropic liquid crystals. These two apparently diverse physical systems are unified by a startling similarity in their complex slow dynamics. Part I consists of six chapters on supercooled liquids while Part II comprises seven chapters on thermotropic liquid crystals. The fourteenth chapter provides a concluding note. Part I starts with an introduction to supercooled liquids given in chapter 1. This chapter discusses basic features of supercooled liquids and the glass transition and portrays some of the theoretical frameworks and formalisms that are widely recognized to have contributed to our present understanding. Chapter 2 introduces a new model of binary mixture in order to study dynamics across the supercooled regime. The system consists of an equimolar mixture of the Lennard-Jones spheres and the Gay-Berne ellipsoids of revolution, and thus one of its components has orientational degrees of freedom (ODOF). A decoupling between trans-lational diffusion and rotational diffusion is found to occur below a temperature where the second rank orientational correlation time starts showing a steady deviation from the Arrhenius temperature behavior. At low temperatures, the optical Kerr effect (OKE) signal derived from the system shows a short-to-intermediate time power law decay with a very weak dependence on temperature, if at all, of the power law exponent as has been observed experimentally. At the lowest temperature investigated, jump motion is found to occur in both the translational and orientational degrees of freedom. Chapter 3 studies how the binary mixture, introduced in the previous chapter, explores its underlying potential energy landscape. The study reveals correlations between the decoupling phenomena, observed almost universally in supercooled molecular liquids, and the manner of exploration of the energy landscape of the system. A significant deviation from the Debye model of rotational diffusion in the dynamics of ODOF is found to begin at a temperature at which the average inherent structure energy of the system starts falling as the temperature decreases. Further, the coupling between rotational diffusion and translational diffusion breaks down at a still lower temperature, where a change occurs in the temperature dependence of the average inherent structure energy. Chapters 4-6 describe analytical and numerical approaches to solve kinetic models of glassy dynamics for various observables. The β process is modeled as a thermally activated event in a two-level system and the a process is described as a β relaxation mediated cooperative transition in a double-well. The model resembles a landscape picture, conceived by Stillinger [Science 267, 1935 (1995)], where the a process is assumed to involve a concerted series of the β processes, the latter being identified as elementary relaxations involving transitions between contiguous basins. For suitable choice of parameter values, the model could reproduce many of the experimentally observed features of anomalous heat capacity behavior during a temperature cycle through the glass transition as described in chapter 4. The overshoot of the heat capacity during the heating scan that marks the glass transition is found to be caused by a delayed energy relaxation. Chapter 5 shows that the model can also predict a frequency dependent heat capacity that reflects the two-step relaxation behavior. The high-frequency peak in the heat capacity spectra appears with considerably larger amplitude than the low-frequency peak, the latter being due to the a relaxation. The model, when simplified with a modified description of the a process that involves an irreversible escape from a metabasin, can be solved analytically for the relaxation time. This version of the model captures salient features of the structural relaxation in glassy systems as described in chapter 6. In Part II, thermotropic liquid crystals are studied in molecular dynamics simulations using primarily the family of the Gay-Berne model systems. To start with, chapter 7 provides a brief introduction to thermotropic liquid crystals, especially from the perspective of the issues discussed in the following chapters. This chapter ends up with a detail description of the family of the Gay-Berne models. Chapter 8 demonstrates that a model system for calamitic liquid crystal (comprising rod-like molecules) could capture the short-to-intermediate time power law decay in the OKE signal near the isotropic-nematic (I-N) phase transition as observed experimentally. The single-particle second rank orientational time correlation function (OTCF) for the model liquid crystalline system is also found to sustain a power law decay regime in the isotropic phase near the I-N transition. On transit across the I-N phase boundary, two power law decay regimes, separated by a plateau, emerge giving rise to a step-like feature in the single-particle second rank OTCF. When the time evolution of the rotational non-Gaussian parameter is monitored as a diagnostic of spatially heterogeneous dynamics, a dominant peak is found to appear following a shoulder at short times, signaling the growth of pseudonematic domains. These observations are compared with those relevant ones obtained for the supercooled binary mixture, as discussed in chapter 2, in the spirit of the analogy suggested recently by Fayer and coworkers [J. Chem. Phys. 118, 9303 (2003)]. In chapter 9, orientational dynamics across the I-N transition are investigated in a variety of model systems of thermotropic liquid crystals. A model discotic system that consists of disc-like molecules as well as a lattice system have been considered in the quest of a universal short-to-intermediate time power law decay in orientational relaxation, if any. A surprisingly general power law decay at short to intermediate times in orientational relaxation is observed in all these systems. While the power law decay of the OKE signal has been recently observed experimentally in calamitic systems near the I-N phase boundary and in the nematic phase by Fayer and coworkers [J. Chem. Phys. 116, 6339 (2002), J. Phys. Chem. B 109, 6514 (2005)], the prediction for the discotic system can be tested in experiments. Chapter 10 presents the energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals by determining the inherent structures of a family of one-component Gay-Berne model systems. This study throws light on the interplay between the orientational order and the translational order in the mesophases the systems exhibit. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures. The inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the I-N transition and this breakdown is found to occur at a temperature below which the system explores increasingly deeper potential energy minima. There exists a remarkable similarity in the manner of exploration of the potential energy landscape between the Gay-Berne systems studied here and the well known Kob-Andersen binary mixture reported previously [Nature, 393, 554 (1998)]. In search of a dynamical signature of the coupling between orientational order and translational order, anisotropic translational diffusion in the nematic phase has been investigated in the Gay-Berne model systems as described in chapter 11. The translational diffusion coefficient parallel to the director D// is found to first increase and then decrease as the temperature drops through the nematic phase. This reversal occurs where the smectic order parameter of the underlying inherent structures becomes significant for the first time. The non-monotonic temperature behavior of D// can thus be viewed from an energy landscape analysis as a dynamical signature of the coupling between orientational and translational order at the microscopic level. Such a view is likely to form the foundation of a theoretical framework to explain the anisotropic translation diffusion. Chapter 12 investigates the validity of the Debye model of rotational diffusion near the I-N phase boundary with a molecular dynamics simulation study of a Gay-Berne model system for calamitic liquid crystals. The Debye model is found to break down near the I-N phase transition. The breakdown, unlike the one observed in supercooled molecular liquids where a jump diffusion model is often invoked, is attributed to the growth of orientational pair correlation. A mode-coupling theory analysis is provided in support of the explanation. Chapter 13 presents a molecular dynamics study of a binary mixture of prolate ellipsoids of revolution with different aspect ratios interacting with each other through a generalized Gay-Berne potential. Such a study allows to investigate directly the aspect ratio dependence of the dynamical behavior. In the concluding note, chapter 14 starts with a brief summary of the outcome of the thesis and ends up with suggestion of a few relevant problems that may prove worthwhile to be addressed in future.

We consider a mean-field interacting particle system embedded in a site-dependent and i.i.d. random environment. We make it evolve as a continuous time Markov chain on its state space. The dynamics are given depending on few parameters and they are completely described by that of the order parameter of the model. We derive the dynamics of this last quantity, in the infinite volume limit, and then their long time behavior is studied. The limiting dynamics of the order parameter are deterministic and, depending on the values of the parameters, exhibit a phase transition. Our main interest is the study of the critical fluctuations, that are the fluctuations of the order parameter around its limiting dynamics when the parameters take the values for which the phase transition occurs. We aim at analyzing the effect of the disorder in the dynamics of them, as compared with the homogeneous case. We deal with spin-flip and interacting diffusion systems, but we do not treat the subject in total generality, we focus on specific models: the random Curie-Weiss model; a non-reversible spin-flip system motivated by Finance and the homogeneous and inhomogeneous Kuramoto models.<br>Consideriamo un sistema di particelle interagenti a campo-medio immerso in un ambiente aleatorio i.i.d. e sito-dipendente. Il sistema viene fatto evolvere come una catena di Markov a tempo continuo sullo spazio degli stati. La dinamica dipende da pochi parametri e puo` essere completamente descritta attraverso quella del parametro d'ordine del modello. Ricaviamo la dinamica di quest'ultimo nel limite di volume infinito e quindi ne studiamo il comportamento per tempi lunghi. Tale dinamica limite risulta essere deterministica e, al variare dei parametri, presenta una transizione di fase. Il nostro interesse principale e` lo studio delle fluttuazioni critiche, cioe` le fluttuazioni del parametro d'ordine attorno alla dinamica limite quando i parametri assumono i valori tali per cui si verifica la transizione di fase. Lo scopo e` l'analisi degli effetti causati dal disordine su di esse, confrontandole con le analoghe fluttuazioni per il caso omogeneo. Trattiamo sistemi di spin e di diffusioni, ma non in totale generalita`. Ci concentriamo su dei modelli specifici: il modello di Curie-Weiss con aggiunta di campo aleatorio; un sistema di spin non-reversibile motivato dalla Finanza e il modello di Kuramoto omogeneo e non.

This research involves applying mathematical modelling techniques coupled with data on work and safety practices to investigate workplace safety programs and improvement strategies. The thesis investigated the potential impact of different safety intervention programs prior to their implementation within the workplace. As there was a lack of mathematical modelling of the interactions between workers and workplace safety intervention programs and how these interactions and programs impacted the safety of the worker while at work, this research presents mathematical models that may be used as a basis for further investigation regarding Occupational Health and Safety.