La tesis estudia cinco formulaciones del método de modos acoplados para analizar guías con medios magnéticos en su interior. La formulación indirecta, de tipo general, se ha aplicado al análisis de desfasadores toroidales obteniéndose resultados similares a los obtenidos mediante un método numérico puro como es el de diferencias finitas. La tesis introduce igualmente una formulación del método de adaptación que junto con el método de modos acoplados permite analizar discontinuidades simples. La combinación de los métodos anteriores con la matriz de dispersión generalizada ha permitido analizar discontinuidades en guías de onda con ferritas transversalmente magnetizadas con discontinuidades en las tres direcciones del sistema de coordenadas.

Aquesta tesi estudia les propietats de sincronització de motius de neurones o poblacions de neurones acoblats amb retard. S'ha trobat que dos elements indirectament connectats de forma bidireccional a través d'un mediador de retransmissió dinàmica poden sincronitzar robustament la seva activitat a retard zero. L'efecte és estudiat en circuits especialment ben coneguts del cervell: xarxes corticals, circuits talamo-corticals i xarxes hipocampo-corticals. Els fonaments del mecanisme s'atribueixen a la influència de fonts ressonants: un parell d'elements directament acoblats bidireccionalment. En la presència de latència no negligible, la parella acoblada tendeix a sincronitzar en anti-fase. Aquesta propietat prevalent, intrínsecament dota a cada element amb una capacitat potencial de induir òptimament una sincronització isocrònica entre dos elements comunament conduïts. Aquest efecte, anomenat Sincronització Induïda per Ressonància, s'observa consistentment en diversos sistemes, sempre que hi hagi absència de frustració geomètrica en l'arquitectura estructural / Esta tesis estudia las propiedades de sincronización de motivos de neuronas, o de las poblaciones neuronales, acopladas con un cierto retraso. Se ha encontrado que dos elementos indirectamente conectados de forma bidireccional, a través de un mediador dinámico, pueden sincronizar de forma robusta sus actividades a tiempo cero. El efecto se estudia en circuitos del cerebro que se sabe juegan un papel fundamental: las redes corticales, circuitos tálamo-corticales y las redes hipocampo-corteza. Los fundamentos del mecanismo se atribuyen a la influencia de las fuentes de resonancia: un par de elementos bidireccionalmente acoplados. En presencia de tiempos de latencia no despreciable, el par de neuronas o poblaciones de neuronas acopladas tiende a sincronizar en oposición de fase. Esta característica predominante intrínsecamente dota a cada uno de los elementos con una capacidad potencial de inducir, de manera óptima, sincronización isócrona entre los elementos comúnmente dirigidos. Esta sincronización inducida por resonancia se observa consistentemente en varios sistemas, cuando ocurre que la frustración geométrica está ausente de la arquitectura estructural. / This thesis studies the synchronization properties of delay-coupled motifs of neurons or neuronal populations. It is found that two elements indirectly bidirectional-connected through a dynamical-relaying mediator can robustly synchronize their activity at zero-lag. The effect is studied in special well-known circuits of the brain: cortical networks, thalamocortical circuits, and hippocampal-cortical networks. The foundations of the mechanism are ascribed to the influence of resonant sources: a pair of directly bidirectional-coupled elements. In the presence of non-negligible latency, the coupled pair tends to synchronize in anti-phase. This prevalent property intrinsically endows each of the elements with a potential capability to optimally induce isochronous synchronization between commonly driven elements. This, so-called Resonance-Induced Synchronization, is consistently observed in distinct systems, whenever geometrical frustration is absent of the structural architecture

Typischerweise sind Plasmen extrem heiß - diese hohen Energien sind nötig, um die Ionisationsschwelle der Atome zu überwinden und damit einen stabilen Plasmazustand zu gewährleisten. Folglich werden die physikalischen Eigenschaften dieser Plasmen für gewöhnlich durch die thermischen Energie der Plasmateilchen bestimmt, während Korrelationen zwischen den Ladungen eine untergeordnete Rolle spielen. Durch die rasanten Fortschritte auf dem Gebiet der ultrakalten Gase ist es jedoch ebenso möglich, Plasmen bei extrem tiefen Temperaturen zu erzeugen, indem lasergekühlte Atome photoionisiert werden. In diesen ultrakalten Plasmen (UKP) lassen sich aufgrund der niedrigen Temperaturen bereits deutliche Auswirkungen von Korrelationen beobachten, die zu gänzlich anderer Dynamik führen können als aus dem Bereich der heißen schwach gekoppelten Plasmen bekannt. Ähnliche Prozesse werden auch in dichten Plasmen beobachtet, in denen durch extrem kurzen Teilchenabstände die Wechselwirkungsenergie auch bei Temperaturen von über 10000 Kelvin die kinetische Energie dominiert. Dichte Plasmen spielen eine wichtige Rolle für technische Anwendungen wie die Trägheitsfusion. Im Gegensatz zu diesen dichten Plasmen realisieren UKP starke Korrelationen jedoch bei sehr viel geringen Dichten von ρ ∼ 10^9 cm^{−3} . Die daraus resultierende langsame Dynamik ist experimentell wesentlich besser zugänglich und macht diese System deshalb besonders interessant, um Korrelationseffekte in stark gekoppelten Plasmen zu studieren. Diese Arbeit beschäftigt sich mit Effekten von starken Korrelationen auf verschiedene Relaxationsprozesse, die insbesondere, aber nicht ausschließlich in UKP eine bedeutende Rolle spielen. Neben dem fundamentalen Interesse an diesen Prozessen gilt ein Augenmerk auch möglichen experimentellen Tests der getroffenen Vorhersagen. Da die Theorie der schwach gekoppelten Plasmen Korrelationen größtenteils vernachlässigt, ist sie im Regime der UKP nur eingeschränkt anwendbar. Zur Berücksichtigung der starken Korrelationen werden in dieser Arbeit umfangreiche molekulardynamischen Simulationen eingesetzt, die teilweise mit quantenmechanischen Beschreibungen kombiniert werden, um den in UKP relevanten atomphysikalischen Aspekten gerecht zu werden. Im Rahmen dieser Rechnungen wird zunächst die seit langem ungeklärte Frage der Atombildung bei tiefen Temperaturen beantwortet. Dieser Prozess ist für UKP besonders relevanten, da die Rekombination die Lebensdauer des Plasmas bestimmt. Die konventionelle Theorie für Rekombination basiert auf der Annahme von von isolierten Drei-Körper-Stößen. Die daraus resultierende Rate divergiert mit abnehmender Temperatur und verliert daher ihre Gültigkeit im ultrakalten Bereich. In dieser Arbeit wird die Beschreibung der Rekombination mit Hilfe aufwendiger Vielteilchen-Simulationen auf den stark gekoppelte Bereich ausgebaut. Hierbei zeigt sich, dass die Rekombinationsrate im Bereich tiefer Temperaturen auf einen konstanten Wert konvergiert, so dass das Problem der divergierenden Rate gelöst werden kann. Ein weiteres, seit langem kontrovers diskutiertes Problem, stellt die Relaxation aufgrund von elastischen Stößen in stark gekoppelten Plasmen dar. Auch hier gilt, dass die konventionelle Theorie für heiße Plasmen, die auf Landau und Spitzer zurückgeht, aufgrund der Vernachlässigung von Korrelationen im Regime starker Kopplung unzureichend wird. Bisher waren keine experimentellen Ergebnisse verfügbar, um die verschiedenen Vorschläge zur Erweiterung der Landau-Spitzer-Beschreibung auf den stark gekoppelten Bereich zu beurteilen. In enger Zusammenarbeit mit der Gruppe von Prof. T. C. Killian (Rice University, Houston, USA) können im Rahmen dieser Arbeit nun erstmals Relaxationsraten in stark gekoppelten Plasmen gemessen werden. Dazu wird mittels eines Pump-Probe-Verfahren die Relaxation der ionischen Geschwindigkeitsverteilung in UKP beobachtet. In dieser Arbeit konnte eine Methode zur Interpretation der experimentellen Daten entwickelt und durch semiklassische Simulationen der Parameterbereich enorm erweitert werden. Unsere Ergebnisse zeigen, dass die Landau-Spitzer-Theorie bereits bei geringen Kopplungsstärken deutliche Defizite aufweist und liefern erstmalig Vorhersagen im stark gekoppelten Bereich. Bei der Untersuchung der ionischen Relaxation wird deutlich, dass insbesondere experimentelle Ergebnisse bei hohen Kopplungsstärken von Interesse sind. Derzeit sind typische UKP-Experimente jedoch auf mäßige Kopplungsstärken limitiert. Ursache hierfür ist, dass das Plasma in einem Zustand weit entfernt vom Gleichgewicht erzeugt wird. Bei der Relaxation ins Gleichgewicht kommt es zu einer Ausbildung von Korrelationen und damit zu einer Umwandlung von potentieller in kinetische Energie. In dieser Arbeit wird deshalb ein neues Plasmaherstellungsverfahren vorgeschlagen, das für die Ionen dieses „Korrrelationsheizen“ stark unterdrücken kann. Durch eine kollektive Anregung kalter Atome in Rydberg-Zustände werden vor der Photoionsation der Atome Korrelationen im atomaren Gas induziert. Es wird gezeigt, dass diese Korrelationen durch eine selektive Ionisation der Rydberg-Atome mit Hilfe von Mikrowellen an das Plasma weitergegeben werden können. Dadurch verringert sich das Korrelationsheizen und eröffnet neue Perspektiven für Untersuchungen ultrakalter Plasmen tief im stark gekoppelten Regime.

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

Proton coupled electron transfer reactions often involve tyrosine residues, because when oxidized, the phenolic side chain deprotonates. Tyrosine Z (YZ) is responsible for extracting electrons in a stepwise fashion from the oxygen evolving-complex in order to build enough potential to oxidize water. This process requires that each step YZ must deprotonate and reprotonate in order to maintain the high midpoint potential that is necessary to oxidize the oxygen-evolving complex, which makes YZ highly involved in proton coupled electron transfer reactions. In this thesis YZ has been studied within oxygen-evolving photosystem II utilizing electron paramagnetic resonance spectroscopy to monitor the tyrosyl radical that is formed upon light excitation. Kinetic analysis of YZ has shed light on the factors that are important for PSII to carry out water oxidation at the oxygen-evolving complex. Most notably the strong hydrogen-bonding network and the midpoint potential of YZ have been shown to be integral aspects of the water splitting reactions of PSII. By studying YZ within oxygen-evolving PSII, conclusions are readily applied to the native system.

This thesis discusses and develops one approach to solve parabolic partial differential equations with random input data. The stochastic problem is firstly transformed into a parametrized one by using finite dimensional noise assumption and the truncated Karhunen-Loeve expansion. The approach, Monte Carlo discontinuous Galerkin (MCDG) method, randomly generates $M$ realizations of uncertain coefficients and approximates the expected value of the solution by averaging M numerical solutions. This approach is applied to two numerical examples. The first example is a two-dimensional parabolic partial differential equation with random convection term and the second example is a benchmark problem coupling flow and transport equations. I first apply polynomial kernel principal component analysis of second order to generate M realizations of random permeability fields. They are used to obtain M realizations of random convection term computed from solving the flow equation. Using this approach, I solve the transport equation M times corresponding to M velocity realizations. The MCDG solution spreads toward the whole domain from the initial location and the contaminant does not leave the initial location completely as time elapses. The results show that MCDG solution is realistic, because it takes the uncertainty in velocity fields into consideration. Besides, in order to correct overshoot and undershoot solutions caused by the high level of oscillation in random velocity realizations, I solve the transport equation on meshes of finer resolution than of the permeability, and use a slope limiter as well as lower and upper bound constraints to address this difficulty. Finally, future work is proposed.

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

In modern low pressure plasma discharges, the electron mean free path often exceeds the device dimensions. Under such conditions the electron velocity distribution function may significantly deviate from Maxwellian, which strongly affects the discharge properties. The description of such plasmas has to be kinetic and often requires the use of numerical methods. This thesis presents the study of kinetic effects in inductively coupled plasmas and Hall thrusters carried out by means of particle-in-cell simulations. The important result and the essential part of the research is the development of particle-in-cell codes. <p>An advective electromagnetic 1d3v particle-in-cell code is developed for modelling the inductively coupled plasmas. An electrostatic direct implicit 1d3v particle-in-cell code EDIPIC is developed for plane geometry simulations of Hall thruster plasmas. The EDIPIC code includes several physical effects important for Hall thrusters: collisions with neutral atoms, turbulence, and secondary electron emission. In addition, the narrow sheath regions crucial for plasma-wall interaction are resolved in simulations. The code is parallelized to achieve fast run times. <p>Inductively coupled plasmas sustained by the external RF electromagnetic field are widely used in material processing reactors and electrodeless lighting sources. In a low pressure inductive discharge, the collisionless electron motion strongly affects the absorption of the external electromagnetic waves and, via the ponderomotive force, the density profile. The linear theory of the anomalous skin effect based on the linear electron trajectories predicts a strong decrease of the ponderomotive force for warm plasmas. Particle-in-cell simulations show that the nonlinear modification of electron trajectories by the RF magnetic field partially compensates the effects of electron thermal motion. As a result, the ponderomotive force in warm collisionless plasmas is stronger than predicted by linear kinetic theory. <p>Hall thrusters, where plasma is maintained by the DC electric field crossed with the stationary magnetic field, are efficient low-thrust devices for spacecraft propulsion. The energy exchange between the plasma and the wall in Hall thrusters is enhanced by the secondary electron emission, which strongly affects electron temperature and, subsequently, thruster operation. Particle-in-cell simulations show that the effect of secondary electron emission on electron cooling in Hall thrusters is quite different from predictions of previous fluid studies. Collisionless electron motion results in a strongly anisotropic, nonmonotonic electron velocity distribution function, which is depleted in the loss cone, subsequently reducing the electron wall losses compared to Maxwellian plasmas. Secondary electrons form two beams propagating between the walls of a thruster channel in opposite radial directions. The secondary electron beams acquire additional energy in the crossed external electric and magnetic fields. The energy increment depends on both the field magnitudes and the electron flight time between the walls. <p>A new model of secondary electron emission in a bounded plasma slab, allowing for emission due to the counter-propagating secondary electron beams, is developed. It is shown that in bounded plasmas the average energy of plasma bulk electrons is far less important for the space charge saturation of the sheath than it is in purely Maxwellian plasmas. A new regime with relaxation oscillations of the sheath has been identified in simulations. Recent experimental studies of Hall thrusters indirectly support the simulation results with respect to the electron temperature saturation and the channel width effect on the thruster discharge.

The increasingly competitive market is forcing the industry to develop higher-quality products more quickly and less expensively. Engineering analysis, at the same time, plays an important role in helping designers evaluate the performance of the designed product against design requirements. In the context of automated CAD/FEA integration, the domain-dependent engineers different usage views toward product models cause an information gap between CAD and FEA models, which impedes the interoperability among these engineering tools and the automatic transformation from an idealized design model into a solvable FEA model. Especially in highly coupled variable topology multi-body (HCVTMB) problems, this transformation process is usually very labor-intensive and time-consuming. In this dissertation, a knowledge-based FEA modeling method, which consists of three information models and the transformation processes between these models, is presented. An Analysis Building Block (ABB) model represents the idealized analytical concepts in a FEA modeling process. Solution Method Models (SMMs) represent these analytical concepts in a solution technique-specific format. When FEA is used as the solution technique, an SMM consists of a Ready to Mesh Model (RMM) and a Control Information Model (CIM). An RMM is obtained from an ABB through geometry manipulation so that the quality mesh can be automatically generated using FEA tools. CIMs contain information that controls the FEA modeling and solving activities. A Solution Tool Model (STM) represents an analytical model at the tool-specific level to guide the entire FEA modeling process. Two information transformation processes are presented between these information models. A solution method mapping transforms an ABB into an RMM through a complex cell decomposition process and an attribute association process. A solution tool mapping transforms an SMM into an STM by mimicking an engineers selection of FEA modeling operations. Four HCVTMB industrial FEA modeling cases are presented for demonstration and validation. These involve thermo-mechanical analysis scenarios: a simple chip package, a Plastic Ball Grid Array (PBGA), and an Enhanced Ball Grid Array (EBGA), as well as a thermal analysis scenario: another PBGA. Compared to traditional methods, results indicate that this method provides better knowledge capture and decreases the modeling time from days/hours to hours/minutes.

Critical infrastructure systems are essential for the continuous functionality of modern global societies. Some examples of these systems include electric energy, potable water, oil and gas, telecommunications, and the internet. Different topologies underline the structure of these networked systems. Each topology (i.e., physical layout) conditions the way in which networks transmit and distribute their flow. Also, their ability to absorb unforeseen natural or intentional disruptions depends on complex relations between network topology and optimal flow patterns. Most of the current research on large networks is focused on understanding their properties using statistical physics, or on developing advanced models to capture network dynamics. Despite these important research efforts, almost all studies concentrate on specific networks. This network-specific approach rules out a fundamental phenomenon that may jeopardize the performance predictions of current sophisticated models: network response is in general interdependent, and its performance is conditioned on the performance of additional interacting networks. Although there are recent conceptual advances in network interdependencies, current studies address the problem from a high-level point of view. For instance, they discuss the problem at the macro-level of interacting industries, or utilize economic input-output models to capture entire infrastructure interactions. This study approaches the problem of network interdependence from a more fundamental level. It focuses on network topology, flow patterns within the networks, and optimal interdependent system performance. This approach also allows for probabilistic response characterization of interdependent networked systems when subjected to disturbances of internal nature (e.g., aging, malfunctioning) or disruptions of external nature (e.g., coordinated attacks, seismic hazards). The methods proposed in this study can identify the role that each network element has in maintaining interdependent network connectivity and optimal flow. This information is used in the selection of effective pre-disaster mitigation and post-disaster recovery actions. Results of this research also provide guides for growth of interacting infrastructure networks and reveal new areas for research on interdependent dynamics. Finally, the algorithmic structure of the proposed methods suggests straightforward implementation of interdependent analysis in advanced computer software applications for multi-hazard loss estimation.