<p>This thesis consists of the structure-preserving numerical methods for PNP-NS equation and dynamic liquid crystal systems in Oseen-Frank energy. </p> <p>In Chapter 1, we give a brief introduction of the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system, and the dynamical liquid system in Oseen-Frank energy in one-constant approximation case and a special non-one-constant case. Each of those systems has a special structure and properties we want to keep at the discrete level when designing numerical methods.</p> <p>In Chapter 2, we introduce a first-order numerical scheme for the PNP-NS system that is decoupled, positivity preserving, mass conserving, and unconditionally energy stable. The numerical scheme is designed in the context of Wasserstein gradient flow based on the form ∇ · (c∇ ln c). The mobility terms are treated explicitly, and the chemical potential terms are treated implicitly so that the solution of the numerical scheme is the minimizer of a convex functional, which is the key to the unique solvability and positivity preserving of the numer-<br> ical scheme. Proper boundary conditions for chemical potentials are chosen to guarantee the mass-conservation property. The convection term in Poisson-Nernst-Planck(PNP) equation part is treated explicitly with an O(∆t) term introduced so that the numerical scheme is decoupled and unconditionally energy stable. Pressure correction methods are used for the Navier-Stokes(NS) equation part. And we proved the optimal convergence rate with an irregular high-order asymptotic expansion technique.</p> <p>In Chapter 3, we propose a first-order implicit numerical method for a dynamic liquid crystal system in a one-constant-approximation case(which is also known as heat flow of harmonic maps to S2). The solution is the minimizer of a convex functional under the unit length constraint, and from this point, the weak convergence of the numerical scheme could be proved. The numerical scheme is solved in an iterative procedure. This procedure could be proved to be energy decreasing and this implies the convergence of the algorithm.</p> <p>In Chapter 4, we study the dynamic liquid crystal system in a more generalized Oseen- Frank energy compared to Chapter 3. We are assuming K2 = K3 = −K4, the domain Ω is a rectangular region in R3, and d satisfies the periodic boundary condition on ∂Ω. And we propose a class of numerical schemes for this system that preserve the unit length constraint. The convergence of the numerical scheme has been proved under necessary assumptions. And numerical experiments are presented to validate the accuracy and demonstrate the performance of the proposed numerical scheme.</p>

The focus of this thesis lies on the thermoelectric transport properties of rare-earth compounds containing Ce, Eu, and Yb. These systems have been investigated either to study fundamental problems or to evaluate their potential for thermoelectric applications.

Popis magnetodynamických vlastností nanomagnetů a nanostrukturovaných magnetických materiálů vyžaduje metody vhodné pro zkoumání typické časové odezvy těchto systémů, tj. v řádu nanosekund a méně. Nedostatek technik, vhodných právě pro charakterizaci v časové doméně, je spojen s možnostmi současné elektroniky. Další možný přístup, jak popsat vlastnosti nanomagnetů, je charakterizace ve frekvenční doméně v pásmu GHz. Nejrozšířenější technikou charakterizace ve frekvenční doméně je měření feromagnetické rezonance (FMR). Ze spekter FMR lze získat cenné informace o systému: parametr tlumení, saturační magnetizace atd. Metoda, kterou využíváme k detekci excitací spinových vln, má za cíl zjednodušení charakterizace. Využíváme termoelektrickou detekci spinových vln v magnetických drátech prostřednictvím anomálního Nernstova jevu. Metoda je založena na disipaci tepla uvnitř magnetické vrstvy v důsledku útlumu spinových vln, a proto dochází k vytvoření teplotního gradientu směrem k substrátu (kolmo k povrchu). To vede k vytvoření elektrického pole kolmého jak na teplotní gradient, tak na směr magnetizace. Napětí je obvykle v řádu V, proto může být měřeno obvyklým laboratorním vybavením. Navzdory své jednoduchosti poskytuje tato metoda velmi zajímavé výsledky a může být použita pro charakterizaci magnonických vlnovodů, magnonických metamateriálů, emitorů spinových vln a dalších zařízení, pracujících se spinovými vlnami.

The focus of this thesis lies on the thermoelectric transport properties of rare-earth compounds containing Ce, Eu, and Yb. These systems have been investigated either to study fundamental problems or to evaluate their potential for thermoelectric applications.

L'effet Nernst a connu, ces quinze dernières années, un regain d'attention, en particulier en raison de son comportement dans les cuprates supraconducteurs à haute température critique dopés aux trous. En effet, on observe dans ces composés la persistance tant en température qu'en champ magnétique d'un signal Nernst fini en dehors de la phase supraconductrice, alors que ce dernier n'est censé être non nul, dans le cas de métaux simples, que dans la phase vortex. Ce résultat a revêtu une certaine importance en ce sens qu'il appuyait expérimentalement, parmi d'autres résultats, un scénario de type paires préformées et excitations de type vortex dans la phase normale des cuprates dopés aux trous. Cependant, l'interprétation de l'effet Nernst souffre d'un manque de données expérimentales dans d'autres systèmes à électrons fortement corrélés. C'est initialement ce qui a motivé le travail de cette thèse, qui rassemble des résultats obtenus de 2001 à 2004 au Laboratoire de Physique Quantique - ESPCI à Paris, et qui est majoritairement constitué de mesures d'effet Nernst dans une autre classe de composés à électrons fortement corrélés : les fermions lourds. Plus particulièrement, nous avons mesuré l'effet Nernst à pression nulle dans une fenêtre de température comprise entre 1,5K et 50K et pour des champs magnétiques de 0 à 12T, dans trois composés : CeCoIn5, URu2Si2 et CeRu2Si2. Ces mesures constituent, à l'heure actuelle, les seules mesures d'effet Nernst effectuées sur des fermions lourds. Dans les trois cas, nous avons découvert dans la phase métallique l'émergence d'un effet Nernst géant dont l'amplitude dépasse de plusieurs ordres de grandeur la taille du signal attendu dans un métal simple, et qui atteint celle caractéristique des vortex dans la phase mixte des cuprates, à savoir quelques µV/KT. Plus particulièrement, CeCoIn5 héberge un effet Nernst négatof très important dans la partie non liquide de Fermi de son diagramme de phase, associée à la présence d'un point critique à Bc=5T. Cependant, l'effet Nernst que nous avons mesuré ne présente aucune anomalie à Bc, mais plutôt dans la limite B=0T, où le coefficient Nernst atteint 1µV/KT. L'émergence d'un effet Nernst positif important dans URu2Si2 coïncide avec l'entrée dans la phase ordre caché, et encore ici c'est à bas champ que le coefficient Nernst atteint son maximum de 4µV/KT, qui constitue le plus grand effet Nernst jamais mesuré dans une phase métallique. Enfin, c'est le métamagnétisme de CeRu2Si2 qui semble particulièrement affecter l'effet Nernst, puisque celui-ci présente, à Hm, un changement de signe particulièrement prononcé et coïncidant avec le maximum de chaleur spécifique. Par ailleurs, une des caractéristiques générales frappantes de cette émergence est qu'elle coïncide, dans les trois composés, avec la présence d'un angle de Hall également très élevé, et dont, en particulier dans CeCoIn5 et CeRu2Si2, la structure est assez proche de celle de l'effet Nernst. La présence de ce signal reste encore aujourd'hui particulièrement intrigante, en particulier en l'absence de mesures systématiques sur d'autres composés aux fermions lourds. Cependant, mais de façon très schématique, nous avons montré que la renormalisation de la masse pouvait être un ingrédient à l'origine de cet effet Nernst géant. De plus, pour chacun des composés des pistes peuvent être avancées pour déterminer l'origine de cet émergence : proximité d'un point critique quantique, fluctuations antiferromagnétiques, ondes de densité... Nous discutons en fin de cette thèse les divers scénarios et proposons des mesures futures afin de confirmer ou d'infirmer ces diverses propositions.

The intrusion of chlorides and carbon dioxide into a reinforced concrete (RC) structure can initiate corrosion of the reinforcing steel, which, due to its expansive nature, can damage the structure and adversely affects its serviceability and safety. Corrosion will initiate if at the steel surface the concrete free chloride concentration exceeds a defined limit, or its pH falls below a critical level. Hence, determination of the time to reaching these critical limits is key to the assessment of RC structures durability and service life. Due to the ionic nature of the chlorides and the bicarbonate anion (HCO3-) formed by the CO2 in the multi-ionic pore solution, the transport of both species is driven by Fickian diffusion combined with electromigration and ionic activity, which can be mathematically expressed by the Nernst-Planck-Poisson (NPP) equations. For a complete representation of the phenomenon, however, the NPP equations must be supplemented by the relevant chemical equilibrium equations to ensure chemical balance among the various species within the concrete pore solution. The combination of NPP with the chemical equilibrium equations is often termed the NPP reactive transport model. In this study, such a model is developed, coded into the MATLAB platform, validated by available experimental data, and applied to analyze the time-dependent concrete carbonation and the movement of chlorides in carbonated and non-carbonated concrete. The results of these analyses can be used to predict the time to corrosion initiation. The transient one-dimensional governing equations of NPP are numerically solved using the Galerkin’s finite element formulation in space and the backward (implicit) Euler scheme in the time domain. The associated system of chemical equilibrium equations accounts for the key homogeneous and heterogeneous chemical reactions that take place in the concrete during carbonation and chlorides transport. At each stage of the analysis, the effects of these reactions on the changes in the pore solution chemical composition, pH, cement chloride binding capacity, concrete porosity, and the hydrated cement solids volumetric ratio are determined. The study demonstrates that given accurate input data, the presently developed NPP reactive transport model can accurately simulate the complex transport processes of chlorides and CO2 in concrete as a reactive porous medium, and the ensuing physical and chemical changes that occur due to the reaction of these species with the pore solution and the other cement hydration products. This conclusion is supported by the good agreement between results of the current analyses with the corresponding available experimental data from physical tests involving carbonation, and chloride diffusion in non-carbonated and carbonated concrete. / Thesis / Doctor of Philosophy (PhD)

Stromrichtertransformatoren der Hochspannungsgleichstromübertragung bilden das Bindeglied zwischen Gleichspannungs- und Drehstromsystem. Um den ausfallsicheren Betrieb über die gesamte Lebensdauer zu gewährleisten, muss deren Öl-Papier-Isoliersystem entsprechend dimensioniert werden. Eine optimale Dimensionierung setzt ein detailliertes Verständnis über die Beanspruchung des Isoliersystems sowie deren zuverlässige Modellierung sowohl unter Betriebsspannung als auch bei den überlagerten, transienten Überspannungen voraus. Im Rahmen dieser Arbeit wird daher das dielektrische Verhalten des Öl-Papier-Isoliersystems in Anlehnung an dielektrische Prüfungen sowohl unter Gleichspannungsbelastung als auch einer zusammengesetzten Spannungsbelastung aus einer Gleich- und einer Blitzstoßspannung (einer sog. Mischspannungsbelastung) untersucht. Der Vergleich von numerischen Berechnungen auf Grundlage eines ladungsträgerbasierten Ansatzes nach Poisson-Nernst-Planck (PNP) mit Durchschlagexperimenten gibt dabei Aufschluss über die Beanspruchung des Öl-Papier-Isoliersystems. Weiterhin wird gezeigt, dass der in den etablierten, resistiv-kapazitiven Berechnungsmodellen vernachlässigte Ladungsträgereinfluss in Bezug auf die Beanspruchung des Isoliersystems unzureichende Ergebnisse zur Folge hat und demnach zwingend zu berücksichtigen ist. Die an realitätsnahen, Öl-Papier-isolierten Anordnungen erzielten Ergebnisse zeigen nicht nur den Einfluss der an Grenzflächen oder im Papier akkumulierten Ladungsträger auf die Beanspruchung des Isoliersystems. Ebenso werden die Annahmen des ladungsträgerbasierten Ansatzes und die Berechnungsergebnisse des PNP-Modells qualitativ bestätigt. Infolge der Ladungsakkumulation im Papier tritt die höchste Beanspruchung im Ölspalt und nicht im Papier auf. Öl-Papier-isolierte Anordnungen werden somit geringer beansprucht, als eine Strömungsfeldberechnung vermuten lässt. Dies widerspricht den Annahmen der etablierten Berechnungsmodelle und wird im Weiteren durch Polaritätseffekte an homogenen, aber unsymmetrischen, papierisolierten Elektrodenanordnungen oder durch den nachweisbaren Einfluss des Ölvolumens im Prüfgefäß auf die Beanspruchung einer Anordnung verdeutlicht. Unter Mischspannungsbelastung wird weiterhin gezeigt, dass eine Überlagerung der Gleichspannung und damit auch der Polaritätswechsel keine höhere Beanspruchung des Isoliersystems im Vergleich zur reinen Gleichspannungsbelastung zur Folge hat. Die etablierten, resistiv-kapazitiven Modelle ließen jedoch den Polaritätswechsel als kritischste Beanspruchung vermuten. Somit wird nicht nur die Anwendbarkeit der ladungsträgerbasierten PNP-Modellierung an Öl-Papier-Isolieranordnungen qualitativ verifiziert. Ebenso wird demonstriert, dass die stark vereinfachten Annahmen der etablierten Berechnungsmodelle die Beanspruchungen unter Gleich- und der untersuchten Mischspannungsbelastung nicht abbilden können. Der Einsatz klassischer Strömungsfeldberechnungen zur Nachbildung der Beanspruchung des Öl-Papier-Isoliersystems unter Gleichspannungsbelastung entspricht damit nicht mehr dem Stand der Forschung. / Converter transformers of HVDC transmission systems connect HVDC and HVAC systems. To ensure a reliable operation during the entire lifetime, their oil-paper-insulation system must be designed appropriately. An optimized dielectric design demands a fundamental understanding of the dielectric stresses as well as a reliable modeling of the insulation system both under operating voltages and under superimposed, transient overvoltages. Hence, in this work the dielectric behavior of the oil-paper-insulation system is investigated. Based on dielectric tests the investigations are performed under DC voltage stress and a composite voltage stress of a DC voltage in stationary conditions superimposed by a lightning impulse voltage. The comparison of numerical calculations using a charge-carrier-based approach according to Poisson-Nernst-Planck (PNP) with breakdown experiments clarifies the dielectric stress of the oil-paper-insulation system. Furthermore, the comparison with results determined by the established, resistive-capacitive calculation models shows that it is mandatory to take the influence of the charge carrier accumulation into account. The presented results, which were obtained at oil-paper-insulated arrangements which represent the dielectic stress of real arrangements, show the influence of the charge carriers accumulating at interfaces or in the paper insulationon on the dielectric stress. The results confirm the calculations and the assumptions according to the charge-carrier-based model as well. Due to the charge carrier accumulation, the highest dielectric stress occurs in the mineral oil and not in the paper insulation. In contrast, the findings obtained assuming an ohmic conductivity would results in a higher dielectric stress of the oil-paperinsulated arrangements. Furthermore, polarity effects in homogeneous but asymmetrical, paper-insulated electrode arrangements or the influence of the surrounding oil in the test vessel demonstrate the effects of the charge carriers. Under composite voltage stresses it is also shown, that the applied superimposed voltage as well as the fast polarity reversal does not lead to a higher dielectric stress of the arrangements compared to the pure DC voltage stress. Commonly used calculation models would determine higher stresses due to the fast polarity reversal instead. Consequently, the applicability of the charge-carrier-based PNP calculation model is verified qualitatively in the presented investigations. Furthermore, it is demonstrated that the simplified assumptions of the commonly used calculation models cannot simulate the dielectric stresses under DC voltage stress and under the investigated superimposed voltage stresses. Hence, the determination of the dielectric stresses of oil-paper-insulation systems under DC voltage stress according to the commonly used calculation models assuming an ohmic conductivity does not correspond to the current state of research.

Electrolytic solutions contain mobile ions that can pass current, and are essential components of any solution-phase electrochemical system. The Nernst–Planck–Poisson equations describe the electrodynamics and transport dynamics of electrolytic solutions. This thesis applies modern numerical and mathematical techniques in order to solve these equations, and hence determine the behaviour of electrochemical systems involving charge transport. The following systems are studied: a liquid junction where a concentration gradient causes charge transport; an ideally polarisable electrode where an applied potential difference causes charge transport; and an electrochemical cell where electrolysis causes charge transport. The nanometre Debye length and nanosecond Debye time scales are shown to control charge separation in electrolytic solutions. At equilibrium, charge separation is confined to within a Debye length scale of a charged electrode surface. Non-equilibrium charge separation is compensated in solution on a Debye time scale following a perturbation, whereafter electroneutrality dictates charge transport. The mechanism for the recovery of electroneutrality involves both migration and diffusion, and is non-linear for larger electrical potentials. Charge separation is an extremely important consideration on length scales comparable to the Debye length. The predicted features of capacitive charging and electrolysis at nanoelectrodes are shown to differ qualitatively from the behaviour of larger electrodes. Nanoscale charge separation can influence the behaviour of a larger system if it limits the overall rate of mass transport or electron transfer. This thesis advocates the use of numerical methods to solve the Nernst–Planck–Poisson equations, in order to avoid the simplifying approximations required by traditional analytical methods. As this thesis demonstrates, this methodology can reveal the behaviour of increasingly elaborate electrochemical systems, while illustrating the self-consistency and generality of fundamental theories concerning charge transport.

Electrodialysis performance strongly depends on the boundary layer near ion exchange membranes. The thickness of the boundary layer has not been clearly evaluated due to its substantial fluctuation around the spacer geometry. In this study, the boundary layer thickness was defined with three statistical parameters: the mean, standard deviation, and correlation coefficient between the two boundary layers facing across the spacer. The relationship between the current and potential under conditions of the competitive transport between mono- and di-valent cations was used to estimate the statistical parameters. An uncertainty model was developed for the steady-state ionic transport in a two-dimensional cell pair. Faster ionic separations were achieved with smaller means, greater standard deviations, and more positive correlation coefficients. With the increasing flow velocity from 1.06 to 4.24 cm/s in the bench-scale electrodialyzer, the best fit values for the mean thickness reduced from 40 to less than 10 μm, and the standard deviation was in the same order of magnitude as the mean. For the partitioning of mono- and di-valent cations, a CMV membrane was examined in various KCl and CaCl₂ mixtures. The equivalent fraction correlation and separation factor responded sensitively to the composition of the mixture; however, the selectivity coefficient was consistent over the range of aqueous-phase ionic contents between 5 and 100 mN and the range of equivalent fractions of each cation between 0.2 and 0.8. It was shown that small analytic errors in measuring the concentration of the mono-valent cation are amplified when estimating the selectivity coefficient. To minimize the effects of such error propagation, a novel method employing the least square fitting was proposed to determine the selectivity coefficient. Each of thermodynamic factors, such as the aqueous- and membrane-phase activity coefficients, water activity, and standard state, was found to affect the magnitude of the selectivity coefficient. The overlimiting current, occurring beyond the electroneutral limit, has not been clearly explained because of the difficulty in solving the singularly perturbed Nernst-Planck-Poisson equations. The steady-state Nernst-Planck-Poisson equations were converted into the Painlevé equation of the second kind (P[subscript II] equation). The converted model domain is explicitly divided into the space charge and electroneutral regions. Given this property, two mathematical formulae were proposed for the limiting current and the width of the space charge region. The Airy solution of the P[subscript II] equation described the ionic transport in the space charge region. By using a hybrid numerical scheme including the fixed point iteration and Newton Raphson methods, the P[subscript II] equation was successfully solved for the ionic transport in the space charge and electroneutral regions as well as their transition zone. Above the limiting current, the sum of the ionic charge in the aqueous-phase electric double layer and in the space charge region remains stationary. Thus, growth of the space charge region involves shrinkage of the aqueous-phase electric double layer. Based on this observation, a repetitive mechanism of expansion and shrinkage of the aqueous-phase electric double layer was suggested to explain additional current above the limiting current. / text

Two computational fluid dynamics models are developed to predict the performance of a solid oxide fuel cell stack, a detailed and a simplified model. In the detailed model, the three dimensional momentum, heat, and species transport equations are coupled with electrochemistry. In the simplified model, the diffusion terms in the transport equations are selectively replaced by rate terms within the core region of the stack. This allows much coarser meshes to be employed at a fraction of the computational cost. Following the mathematical description of the problem, results for single-cell and multi-cell stacks are presented. Comparisons of local current density, temperature, and cell voltage indicate that good agreement is obtained between the detailed and simplified models, verifying the latter as a practical option in stack design. Then, the simplified model is used to determine the effects of utilization on the electrochemical performance and temperature distributions of a 10 cell stack. The results are presented in terms of fluid flow, pressure, species mass fraction, temperature, voltage and current density distributions. The effects of species and flow distributions on electrochemical performance and temperature are then analyzed for a 100 cell stack. The discussion highlights the importance of manifold design on performance and thermal management of large stacks. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-09-30 15:55:18.627