Pulsatile blood flow interaction with arterial walls of aorta : autoregulation and impedance pressure boundary condition and its biomedical applications

Para las decisiones urgentes sobre intervenciones quirúrgicas en el sistema cardiovascular se necesitan simulaciones computacionales con resultados fiables y que consuman un tiempo de cálculo razonable. Durante años los investigadores han trabajado en diversos métodos numéricos de cálculo que resulten atractivos para los cirujanos. Estos métodos, precisos pero costosos desde el punto de vista del coste computacional, crean un desajuste entre la oferta de los ingenieros que realizan las simulaciones y los médicos que operan en el quirófano. Por otra parte, los métodos de cálculo más simplificados reducen el tiempo de cálculo pero pueden proporcionar resultados no realistas. El objetivo de esta tesis es combinar los conceptos de autorregulación e impedancia del sistema circulatorio, la interacción flujo sanguíneo-pared arterial y modelos geométricos idealizados tridimensionales de las arterias pero sin pérdida de realismo, con objeto de proponer una metodología de simulación que proporcione resultados correctos y completos, con tiempos de cálculo moderados. En las simulaciones numéricas, las condiciones de contorno basadas en historias de presión presentan inconvenientes por ser difícil conocerlas con detalle, y porque los resultados son muy sensibles ante pequeñas variaciones de dichas historias. La metodología propuesta se basa en los conceptos de autorregulación, para imponer la demanda de flujo aguas abajo del modelo en el ciclo cardiaco, y la impedancia, para representar el efecto que ejerce el flujo en el resto del sistema circulatorio sobre las arterias modeladas. De este modo las historias de presión en el contorno son resultados del cálculo, que se obtienen de manera iterativa. El método propuesto se aplica en una geometría idealizada del arco aórtico sin patologías y en otra geometría correspondiente a una disección Stanford de tipo A, considerando la interacción del flujo pulsátil con las paredes arteriales. El efecto de los tejidos circundantes también se incorpora en los modelos. También se hacen aplicaciones considerando la interacción en una geometría especifica de un paciente anciano que proviene de una tomografía computarizada. Finalmente se analiza una disección Stanford tipo B con tres modelos que incluyen la fenestración del saco. Clinicians demand fast and reliable numerical results of cardiovascular biomechanic simulations for their urgent pre-surgery decissions. Researchers during many years have work on different numerical methods in order to attract the clinicians' confidence to their colorful contours. Though precise but expensive and time-consuming methodologies create a gap between numerical biomechanics and hospital personnel. On the other hand, simulation simplifications with the aim of reduction in computational time may cause in production of unrealistic outcomes. The main objective of the current investigation is to combine ideas such as autoregulation, impedance, fluid-solid interaction and idealized geometries in order to propose a computationally cheap methodology without excessive or unrealistic simplifications. The pressure boundary conditions are critical and polemic in numerical simulations of cardiovascular system, in which a specific arterial site is of interest and the rest of the netwrok is neglected but represented by a boundary condition. The proposed methodology is a pressure boundary condition which takes advantage of numerical simplicity of application of an imposed pressure boundary condition on outlets, while it includes more sophisticated concepts such as autoregulation and impedance to gain more realistic results. Incorporation of autoregulation and impedance converts the pressure boundary conditions to an active and dynamic boundary conditions, receiving feedback from the results during the numerical calculations and comparing them with the physiological requirements. On the other hand, the impedance boundary condition defines the shapes of the pressure history curves applied at outlets. The applications of the proposed method are seen on idealized geometry of the healthy arotic arch as well as idealized Stanford type A dissection, considering the interaction of the arterial walls with the pulsatile blood flow. The effect of surrounding tissues is incorporated and studied in the models. The simulations continue with FSI analysis of a patient-specific CT scanned geometry of an old individual. Finally, inspiring of the statistic results of mortality rates in Stanford type B dissection, three models of fenestrated dissection sac is studied and discussed. Applying the developed boundary condition, an alternative hypothesis is proposed by the author with respect to the decrease in mortality rates in patients with fenestrations.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

A time-domain finite element method for seakeeping and wave resistance problems

El objetivo de la tesis es la investigación de algoritmos numéricos para el desarrollo de herramientas numéricas para la simulación de problemas tanto de comportamiento en la mar como de resistencia al avance de buques y estructuras flotantes. La primera herramienta desarrollada resuelve el problema de difracción y radiación de olas. Se basan en el método de los elementos finitos (MEF) para la resolución de la ecuación de Laplace, así como en esquemas basados en MEF, integración a lo largo de líneas de corriente, y en diferencias finitas desarrollados para la condición de superficie libre. Se han desarrollado herramientas numéricas para la resolución de la dinámica de sólido rígido en sistemas multicuerpos con ligaduras. Estas herramientas han sido integradas junto con la herramienta de resolución de olas difractadas y radiadas para la resolución de problemas de interacción de cuerpos con olas. También se han diseñado algoritmos de acoplamientos con otras herramientas numéricas para la resolución de problemas multifísica. En particular, se han realizado acoplamientos con una herramienta numérica basada de cálculo de estructuras con MEF para problemas de interacción fluido-estructura, otra de cálculo de líneas de fondeo, y con una herramienta numérica de cálculo de flujos en tanques internos para problemas acoplados de comportamiento en la mar con “sloshing”. Se han realizado simulaciones numéricas para la validación y verificación de los algoritmos desarrollados, así como para el análisis de diferentes casos de estudio con aplicaciones diversas en los campos de la ingeniería naval, oceánica, y energías renovables marinas. ABSTRACT The objective of this thesis is the research on numerical algorithms to develop numerical tools to simulate seakeeping problems as well as wave resistance problems of ships and floating structures. The first tool developed is a wave diffraction-radiation solver. It is based on the finite element method (FEM) in order to solve the Laplace equation, as well as numerical schemes based on FEM, streamline integration, and finite difference method tailored for solving the free surface boundary condition. It has been developed numerical tools to solve solid body dynamics of multibody systems with body links across them. This tool has been integrated with the wave diffraction-radiation solver to solve wave-body interaction problems. Also it has been tailored coupling algorithms with other numerical tools in order to solve multi-physics problems. In particular, it has been performed coupling with a MEF structural solver to solve fluid-structure interaction problems, with a mooring solver, and with a solver capable of simulating internal flows in tanks to solve couple seakeeping-sloshing problems. Numerical simulations have been carried out to validate and verify the developed algorithms, as well as to analyze case studies in the areas of marine engineering, offshore engineering, and offshore renewable energy.

VHDL-based system design of a cognitive sensorimotor loop (CSL) for haptic Human-Machine Interaction (HMI)

This document is a summary of the Bachelor thesis titled “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” written by Pablo de Miguel Morales, Electronics Engineering student at the Universidad Politécnica de Madrid (UPM Madrid, Spain) during an Erasmus+ Exchange Program at the Beuth Hochschule für Technik (BHT Berlin, Germany). The tutor of this project is Dr. Prof. Hild. This project has been developed inside the Neurobotics Research Laboratory (NRL) in close collaboration with Benjamin Panreck, a member of the NRL, and another exchange student from the UPM Pablo Gabriel Lezcano. For a deeper comprehension of the content of the thesis, a deeper look in the document is needed as well as the viewing of the videos and the VHDL design. In the growing field of automation, a large amount of workforce is dedicated to improve, adapt and design motor controllers for a wide variety of applications. In the specific field of robotics or other machinery designed to interact with humans or their environment, new needs and technological solutions are often being discovered due to the existing, relatively unexplored new scenario it is. The project consisted of three main parts: Two VHDL-based systems and one short experiment on the haptic perception. Both VHDL systems are based on a Cognitive Sensorimotor Loop (CSL) which is a control loop designed by the NRL and mainly developed by Dr. Prof. Hild. The CSL is a control loop whose main characteristic is the fact that it does not use any external sensor to measure the speed or position of the motor but the motor itself. The motor always generates a voltage that is proportional to its angular speed so it does not need calibration. This method is energy efficient and simplifies control loops in complex systems. The first system, named CSL Stay In Touch (SIT), consists in a one DC motor system controller by a FPGA Board (Zynq ZYBO 7000) whose aim is to keep contact with any external object that touches its Sensing Platform in both directions. Apart from the main behavior, three features (Search Mode, Inertia Mode and Return Mode) have been designed to enhance the haptic interaction experience. Additionally, a VGA-Screen is also controlled by the FPGA Board for the monitoring of the whole system. This system has been completely developed, tested and improved; analyzing its timing and consumption properties. The second system, named CSL Fingerlike Mechanism (FM), consists in a fingerlike mechanical system controlled by two DC motors (Each controlling one part of the finger). The behavior is similar to the first system but in a more complex structure. This system was optional and not part of the original objectives of the thesis and it could not be properly finished and tested due to the lack of time. The haptic perception experiment was an experiment conducted to have an insight into the complexity of human haptic perception in order to implement this knowledge into technological applications. The experiment consisted in testing the capability of the subjects to recognize different objects and shapes while being blindfolded and with their ears covered. Two groups were done, one had full haptic perception while the other had to explore the environment with a plastic piece attached to their finger to create a haptic handicap. The conclusion of the thesis was that a haptic system based only on a CSL-based system is not enough to retrieve valuable information from the environment and that other sensors are needed (temperature, pressure, etc.) but that a CSL-based system is very useful to control the force applied by the system to interact with haptic sensible surfaces such as skin or tactile screens. RESUMEN. Este documento es un resumen del proyecto fin de grado titulado “VHDL-Based System Design of a Cognitive Sensorimotor Loop (CSL) for Haptic Human-Machine Interaction (HMI)” escrito por Pablo de Miguel, estudiante de Ingeniería Electrónica de Comunicaciones en la Universidad Politécnica de Madrid (UPM Madrid, España) durante un programa de intercambio Erasmus+ en la Beuth Hochschule für Technik (BHT Berlin, Alemania). El tutor de este proyecto ha sido Dr. Prof. Hild. Este proyecto se ha desarrollado dentro del Neurorobotics Research Laboratory (NRL) en estrecha colaboración con Benjamin Panreck (un miembro del NRL) y con Pablo Lezcano (Otro estudiante de intercambio de la UPM). Para una comprensión completa del trabajo es necesaria una lectura detenida de todo el documento y el visionado de los videos y análisis del diseño VHDL incluidos en el CD adjunto. En el creciente sector de la automatización, una gran cantidad de esfuerzo está dedicada a mejorar, adaptar y diseñar controladores de motor para un gran rango de aplicaciones. En el campo específico de la robótica u otra maquinaria diseñada para interactuar con los humanos o con su entorno, nuevas necesidades y soluciones tecnológicas se siguen desarrollado debido al relativamente inexplorado y nuevo escenario que supone. El proyecto consta de tres partes principales: Dos sistemas basados en VHDL y un pequeño experimento sobre la percepción háptica. Ambos sistemas VHDL están basados en el Cognitive Sesnorimotor Loop (CSL) que es un lazo de control creado por el NRL y cuyo desarrollador principal ha sido Dr. Prof. Hild. El CSL es un lazo de control cuya principal característica es la ausencia de sensores externos para medir la velocidad o la posición del motor, usando el propio motor como sensor. El motor siempre genera un voltaje proporcional a su velocidad angular de modo que no es necesaria calibración. Este método es eficiente en términos energéticos y simplifica los lazos de control en sistemas complejos. El primer sistema, llamado CSL Stay In Touch (SIT), consiste en un sistema formado por un motor DC controlado por una FPGA Board (Zynq ZYBO 7000) cuyo objetivo es mantener contacto con cualquier objeto externo que toque su plataforma sensible en ambas direcciones. Aparte del funcionamiento básico, tres modos (Search Mode, Inertia Mode y Return Mode) han sido diseñados para mejorar la interacción. Adicionalmente, se ha diseñado el control a través de la FPGA Board de una pantalla VGA para la monitorización de todo el sistema. El sistema ha sido totalmente desarrollado, testeado y mejorado; analizando su propiedades de timing y consumo energético. El segundo sistema, llamado CSL Fingerlike Mechanism (FM), consiste en un mecanismo similar a un dedo controlado por dos motores DC (Cada uno controlando una falange). Su comportamiento es similar al del primer sistema pero con una estructura más compleja. Este sistema no formaba parte de los objetivos iniciales del proyecto y por lo tanto era opcional. No pudo ser plenamente desarrollado debido a la falta de tiempo. El experimento de percepción háptica fue diseñado para profundizar en la percepción háptica humana con el objetivo de aplicar este conocimiento en aplicaciones tecnológicas. El experimento consistía en testear la capacidad de los sujetos para reconocer diferentes objetos, formas y texturas en condiciones de privación del sentido del oído y la vista. Se crearon dos grupos, en uno los sujetos tenían plena percepción háptica mientras que en el otro debían interactuar con los objetos a través de una pieza de plástico para generar un hándicap háptico. La conclusión del proyecto fue que un sistema háptico basado solo en sistemas CSL no es suficiente para recopilar información valiosa del entorno y que debe hacer uso de otros sensores (temperatura, presión, etc.). En cambio, un sistema basado en CSL es idóneo para el control de la fuerza aplicada por el sistema durante la interacción con superficies hápticas sensibles tales como la piel o pantallas táctiles.

Human-computer interaction based on visual hand-gesture recognition using volumetric spatiograms of local binary patterns

A more natural, intuitive, user-friendly, and less intrusive Human–Computer interface for controlling an application by executing hand gestures is presented. For this purpose, a robust vision-based hand-gesture recognition system has been developed, and a new database has been created to test it. The system is divided into three stages: detection, tracking, and recognition. The detection stage searches in every frame of a video sequence potential hand poses using a binary Support Vector Machine classifier and Local Binary Patterns as feature vectors. These detections are employed as input of a tracker to generate a spatio-temporal trajectory of hand poses. Finally, the recognition stage segments a spatio-temporal volume of data using the obtained trajectories, and compute a video descriptor called Volumetric Spatiograms of Local Binary Patterns (VS-LBP), which is delivered to a bank of SVM classifiers to perform the gesture recognition. The VS-LBP is a novel video descriptor that constitutes one of the most important contributions of the paper, which is able to provide much richer spatio-temporal information than other existing approaches in the state of the art with a manageable computational cost. Excellent results have been obtained outperforming other approaches of the state of the art.

Development of a hand-gesture recognition system for human-computer interaction

The aim of this Master Thesis is the analysis, design and development of a robust and reliable Human-Computer Interaction interface, based on visual hand-gesture recognition. The implementation of the required functions is oriented to the simulation of a classical hardware interaction device: the mouse, by recognizing a specific hand-gesture vocabulary in color video sequences. For this purpose, a prototype of a hand-gesture recognition system has been designed and implemented, which is composed of three stages: detection, tracking and recognition. This system is based on machine learning methods and pattern recognition techniques, which have been integrated together with other image processing approaches to get a high recognition accuracy and a low computational cost. Regarding pattern recongition techniques, several algorithms and strategies have been designed and implemented, which are applicable to color images and video sequences. The design of these algorithms has the purpose of extracting spatial and spatio-temporal features from static and dynamic hand gestures, in order to identify them in a robust and reliable way. Finally, a visual database containing the necessary vocabulary of gestures for interacting with the computer has been created.

Design of Mm-Wave RLSA with lossy waveguides by slot coupling control techniques

This paper discusses how to design a Radial Line Slot Antenna (RLSA) whose waveguide is filled with high loss dielectric materials. We introduce a new design for the aperture slot coupling synthesis to restrain the dielectric losses and improve the antenna gain. Based on a newly defined slot coupling, a number of RLSAs with different sizes and loss factors are analyzed and their performances are predicted. Theoretical calculations suggest that the gain is sensitive to the material losses in the radial lines. The gain enhancement by using the new coupling formula is notable for larger antenna size and higher loss factor of the dielectric material. Three prototype RLSAs are designed and fabricated at 60GHz following different slot coupling syntheses, and their measured performances consolidate our theory.