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We introduce a new class of nonreflecting boundary conditions for lattice models, which minimizes reflections at artificial boundaries. Exact integrodifferential boundary conditions for finite chains and half-spaces are obtained by means of Green's functions for initial value problems. Truncating the resulting integrals in time, we obtain absorbing boundary conditions. Numerical tests illustrate the ability of these conditions to suppress reflections., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper, the characteristics of the induced ground motion are studied for two pile installation methods. Specifically, the classical axial vibratory driving is compared with the Gentle Driving of Piles (GDP) method, to investigate the effect of high-frequency torsional excitation in the soil response. For that purpose, a non-linear 3-D axisymmetric pile-soil interaction model - benchmarked against field data for both methods - is used to perform the numerical study. The friction redirection mechanism, that is mobilized due to the torsional excitation in GDP, leads to a different wavefield in the soil medium compared to axial vibro-driving. In the latter only SV-P wave motions are elicited, whereas torsion introduces SH wave motions as well. For the numerical study, the model is comprised by a thin cylindrical shell coupled with a linear elastic layered half-space through a history-dependent frictional interface. The Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) is employed to accurately describe the wave motion in the soil medium. Comparisons in terms of the peak particle velocities (PPVs) and soil particle trajectories showcase significant motion reduction due to redirection of the soil friction forces, which elicits high-frequency SH waves and reduces the SV-P wave motion., Dynamics of Structures, Offshore Engineering, Engineering Structures

The ambitious goals towards the decarbonization of the global energy sector have amplified the demand for renewable energy resources. Amongst the renewables, offshore wind possesses a pivotal role in this endeavour, showcasing remarkable growth in recent years. However, this rapid expansion has been accompanied by a series of technical challenges. Foundation installation comprises one of the most critical phases in the construction of an offshore wind farm and engineering advancements in this topic are vital to accommodate this developmental pace. Bottom-fixed foundations are primarily used to support offshore wind turbines and amongst the available concepts, the monopile is the foremost one. The installation of these substructures is most commonly performed via impact hammering. Notwithstanding the robustness and efficacy of this technique, major environmental concerns have been raised due to the significant levels of underwater noise pollution during driving. In view of this alarming issue, alternative and sustainable pile installation techniques have been progressively drawing attention during the last decade and an increasing number of research projects focus on their investigation and development. At present, the offshore wind industry is increasingly adopting vibratory pile driving. The previous method has been successfully employed in onshore projects for decades, albeit its wider use in the offshore environment is hindered due to the incompleteness of available field observations. To boost the improvement of vibratory installation methods, a new technology has been recently proposed by the Delft University of Technology, namely the Gentle Driving of Piles (GDP). The preceding method aims to enhance the installation performance of vibratory driving for tubular (mono)piles and to reduce the associated noise emissions, via the simultaneous application of low-frequency/axial and high-frequency/torsional vibrations. Naturally, the shift to these technol, Dynamics of Structures

Gentle Driving of Piles (GDP) is a new vibratory installation technology for tubular (mono)piles. It is characterized by the simultaneous application of low-frequency axial and high-frequency torsional vibrations, envisaged to achieve both high installation performance and reduced underwater noise emissions. The concept of GDP has been demonstrated experimentally in a medium-scale onshore field campaign, showcasing the potential of the method in terms of installation and post-installation performances. To further comprehend the mechanics of the GDP method, the driving process is studied by means of a novel pile–soil model; this framework has been recently developed and successfully applied to the problem of axial vibratory driving. In particular, the pile is treated as a thin cylindrical shell via a Semi-analytical Finite Element (SAFE) approach and a linear elastic layered soil half-space is considered via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs). The pile–soil coupling is realized through a hereditary frictional interface and an elasto-plastic tip formulation, both characterized by standard geotechnical in-situ measurements. The comparison of numerical results with field data is favourable for drivability purposes, showcasing the potential of the numerical framework for the analysis of GDP. Conclusively, the mechanics of the installation process are deciphered and the redirection of the friction force vector – induced by high-frequency torsion – is identified as the main driving mechanism of GDP., Dynamics of Structures, Offshore Engineering, Engineering Structures

This paper presents a computationally efficient model for vibratory pile installation. A semi-analytical finite element (SAFE) model for thin cylindrical shells is derived to represent the pile. The linear dynamic response of the soil medium is described by means of Green's functions via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) to account for the underlying elastic half-space. Furthermore, the non-linear pile–soil interaction is addressed through a history-dependent frictional interface and a visco-elasto-plastic tip reaction model that can be characterized on the basis of standard geotechnical in-situ measurements. The solution to the non-linear dynamic pile–soil interaction problem is based on the sequential application of the Harmonic Balance Method (HBM). The constituent components of the model are first benchmarked against established numerical schemes. Subsequently, model predictions are compared with experimental data collected from field tests. It is demonstrated that the proposed model amalgamates rigorous theoretical elements and promising prediction capabilities in a computationally efficient framework, applicable to engineering practice., Dynamics of Structures, Offshore Engineering, Engineering Structures

An integral equation technique for the analysis of multiport H‐plane microwave circuits composed of an unlimited number of arbitrarily shaped metallic and/or dielectric elements is proposed. The structure under study is divided into different regions after the application of the surface equivalence principle. Following this approach, the access waveguide ports are modelled by means of parallel plate Green's functions, whereas the central region is characterised by 2D rectangular cavity Green's functions. The use of this kind of Green's functions represents a novelty for solving H‐plane integral equation problems. For the first time, the Ewald method has been employed in order to accelerate the computation of the 2D rectangular cavity Green's functions and their derivatives, needed in the integral equation. In addition, convergence studies show the numerical convenience of using the Ewald method to achieve a fast and accurate evaluation of these Green's functions. Results show that the analysis can be very efficient if the structure is segmented in a proper way based on fitting the cavity resonator within the geometry of the structure under analysis. In fact, all the walls of the structure that are coincident with the auxiliary resonator need not to be discretised during the numerical solution. Finally, several simulation examples of practical inductive microwave circuits are presented and discussed, showing a good agreement and higher computational efficiency when compared to results provided by commercial full‐wave software tools and measurements.

In this thesis we employ the non-equilibrium Green’s function (NEGF) method to study both finite and infinite systems. We develop a codebase capable of computing the steady state interacting NEGF in open systems, i.e. tight-binding leads contacting a central region, in both Hartree-Fock (HF) and second Born (2B) approximations of particle-particle interactions. Furthermore, we use the exact interacting Green’s function on finite re- gions to assess a method we found to compute any pair-correlation function. The method utilizes the Hellman-Feynman theorem applied to the Galitskii- Migdal formula for the total energy of a system. We find that it works well for finite systems, with and without currents, whereas for open (infinite) systems the method requires more care. Lastly, we briefly investigate a non- perturbative G1-G2 scheme; whether computing the two-particle Green’s function in a subsystem approximates the full two-particle Green’s function well. We find that the considered G1-G2 scheme provides results of variable accuracy, suggesting that our investigation is not exhaustive, and that the roles of system geometry and particle density should be further assessed., Under de senaste åren, har system vars dynamik sker ur jämvikt fått mycket uppmärksamhet, främst på grund av stora framsteg inom experimentella förverkliganden inom nanosystem som kan utnyttja kvanteffekter, och experimentella verktyg som tillåter mätningar under väldigt korta tidsfönster. I dagens samhälle där vi använder datorer och nanochip, praktiskt taget, överallt är det viktigt att förstå sig på de effekter och konsekvenser som finns när man når så små avstånd. Kvantmekaniken introducerar många nya fenomen i nanovärlden, många av dem inte välkomna. Det är därför viktigt att kunna studera, rent teoretiskt, nanosystem och dess dynamik med stor noggrannhet för att kunna förutse och förhindra oönskade effekter. I det här verket, använder vi så kallade “Green’s functions” för att studera kvanttransportgeometrier, system i vilka elektroner kan transporteras. De fyller en viktig funktion som modelleringssystem för verkliga och mer komplicerade system. Vi implementerar ett ramverk i FORTRAN, via vilket man kan beräkna Green’s functions i steady state, alltså när system har nått ett stilla tillstånd. Detta använder vi sedan för att beräkna den så kallade concurrence i ett system som består av två ihopkopplade kvantprickar som i sin tur är kopplade i en linje med ledare. Ett sådant system, är i principen oändligt, vilket såklart är omöjligt att jobba med, och vi använder därför en metod för att projicera lederna på det centrala systemet, som heter “embedding”. Vi studerar även ett ändligt system, nämligen en ring, i två syften. Främst, för att applicera en metod vi fann för att hitta korrelationsfunktioner, men dessutom för att undersöka om kan frångå den tidigare använda approximationen för interaktioner mellan partiklar, self-energy expansion, och istället beräkna den exakta två-partikels Green’s function och använda den för att beräkna en-partikels Green’s function i det hela systemet.

The particular challenge for modeling wearable and implantable wireless systems for on-body communications lies in the near-field coupling of the antenna and the dissipative tissue. Hence, so far, the antennas could not be considered separately from the propagation channel in the system description. Therefore, methods for the systematic antenna design of on-body applications are developed, whereas the antennas are characterized de-embedded. First, a method for characterizing on-body antennas is developed based on physical modeling of the propagation along the tissue. Furthermore, on-body antenna parameters are derived, representing an adapted form of the standard free-space antenna parameters. Secondly, a method for modeling on-body links based on spherical wave functions (SWF) is developed. It enables obtaining separate models of the antennas and the channel at a higher level of abstraction. Since the developed on-body antenna parameters are defined closely to the standard free-space definitions, an intuitive characterization of on-body antennas is possible. Furthermore, an antenna test range is developed for assessing the defined on-body antenna parameters for physical prototypes. As shown by the examples evaluated, the on-body antenna parameters and the determined transmission equation, analogous to the Friis equation in free-space, can also be used to model the entire wireless system. However, the difficulty lies in determining the directional channel model, which is costly and not universally possible for any application. The developed method based on SWF complements the characterization methods, as channels of any complexity can be modeled since the method could be implemented numerically. Beyond the characterization of on-body antennas and channels, the design of optimized antennas for these applications presents a substantial challenge. Based on the derived on-body transmission equation, antenna optimization can be done directly by maximizing the on-body ant, Die besondere Herausforderung bei der Modellierung von am Körper getragenen und implantierbaren drahtlosen Systemen liegt in der Nahfeldkopplung der Antenne und des dissipativen Gewebes. Daher konnten bisher die Antennen nicht getrennt vom Ausbreitungskanal in der Systembeschreibung berücksichtigt werden. Aus diesem Grund werden Methoden für die systematische Antennenentwicklung von On-Body-Anwendungen entwickelt, wobei die Antennen separat (de-embedded) charakterisiert werden können. Zunächst wird eine Methode zur Charakterisierung von On-Body-Antennen entwickelt, die auf der physikalischen Modellierung der Ausbreitung entlang des Gewebes basiert. Darüber hinaus wurden On-Body-Antennenparameter abgeleitet, die eine angepasste Form der Standardantennenparameter für den freien Raum darstellen. Desweiteren wird eine Methode zur Modellierung von On-Body-Verbindungen auf Grundlage von sphärischen Wellenfunktionen entwickelt. Diese ermöglicht es, getrennte Modelle der Antennen und des Kanals auf einer höheren Abstraktionsebene zu erhalten. Da die entwickelten On-Body-Antennenparameter in enger Anlehnung an die Standarddefinitionen für den freien Raum definiert sind, ist eine intuitive Charakterisierung von On-Body-Antennen möglich. Weiterhin wird ein Antennenmesssystem entwickelt, um die definierten Antennenparameter für physische Prototypen auswerten zu können. Wie die untersuchten Beispiele zeigen, können die On-Body-Antennenparameter und die ermittelte Übertragungsgleichung, analog zur Friis-Gleichung im Freiraum, auch zur Modellierung des gesamten Funksystems verwendet werden. Die Schwierigkeit liegt hier jedoch in der Bestimmung des Kanalmodells, die aufwändig und nicht für jede Anwendung universell möglich ist. Die entwickelte Methode auf Basis sphärischer Wellenfunktionen (SWF) ergänzt die Charakterisierungsmethoden, da aufgrund der numerischen Implementierung hiermit Kanäle beliebiger Komplexität modelliert werden können. Neben der Charakterisierung von On-Body-A

In the present work we discuss how to address the solution of electrostatic problems, in professional cycle of undergraduate course in science or engineering, using Green's functions and the Poisson's equation. For this, it is considered the structural role that mathematics, especially Green's function, has in physical thought presented in the method of images. By using this procedure and discussing the historical construction of Green's problem, it was possible to verify its relationship with the method of images as an interdisciplinary approach that is not developed in didactic physics textbooks. The possibility of analyzing Green's function as the result of two tasks, namely, the reduction of a continuous charge distribution to the one due to a point charge and the solution of the problem as the superposition of potentials due to sets of point charges continuously distributed represented by the integration of the Green's function over the electric charge density, is our account for teaching implication that shows, at the same time, epistemological ruptures and continuities to teaching-learning processes., En el presente trabajo discutimos cómo abordar la solución de problemas electrostáticos, en ciclos profesionales de licenciatura en ciencias o ingeniería, utilizando las funciones de Green y la ecuación de Poisson. Para ello, se considera el papel estructural que tiene la matemática, en especial la función de Green, en el pensamiento físico presentado en el método de las imágenes. Al utilizar este procedimiento y discutir la construcción histórica del problema de Green, fue posible verificar su relación con el método de las imágenes como un enfoque interdisciplinario que no se desarrolla en los libros de texto de física didáctica. Se representa la posibilidad de analizar la función de Green como resultado de dos tareas, a saber, la reducción de una distribución de carga continua a la debida a una carga puntual y la solución del problema como la superposición de potenciales debido a conjuntos de cargas puntuales distribuidas de forma continua. por la integración de la función de Green sobre la densidad de carga eléctrica, es nuestra explicación de la implicación docente que muestra, al mismo tiempo, rupturas epistemológicas y continuidades en los procesos de enseñanza-aprendizaje.

In this paper, we introduce a two-point nonlinear boundary value problem for a finite fractional difference equation. An associated Green’s function is constructed as a series of functions and some of its properties are obtained. Some existence results are deduced from fixed point theory and lower and upper solutions

In the present work we discuss how to address the solution of electrostatic problems, in professional cycle of undergraduate course in science or engineering, using Green's functions and the Poisson's equation. For this, it is considered the structural role that mathematics, especially Green's function, has in physical thought presented in the method of images. By using this procedure and discussing the historical construction of Green's problem, it was possible to verify its relationship with the method of images as an interdisciplinary approach that is not developed in didactic physics textbooks. The possibility of analyzing Green's function as the result of two tasks, namely, the reduction of a continuous charge distribution to the one due to a point charge and the solution of the problem as the superposition of potentials due to sets of point charges continuously distributed represented by the integration of the Green's function over the electric charge density, is our account for teaching implication that shows, at the same time, epistemological ruptures and continuities to teaching-learning processes., En el presente trabajo discutimos cómo abordar la solución de problemas electrostáticos, en ciclos profesionales de licenciatura en ciencias o ingeniería, utilizando las funciones de Green y la ecuación de Poisson. Para ello, se considera el papel estructural que tiene la matemática, en especial la función de Green, en el pensamiento físico presentado en el método de las imágenes. Al utilizar este procedimiento y discutir la construcción histórica del problema de Green, fue posible verificar su relación con el método de las imágenes como un enfoque interdisciplinario que no se desarrolla en los libros de texto de física didáctica. Se representa la posibilidad de analizar la función de Green como resultado de dos tareas, a saber, la reducción de una distribución de carga continua a la debida a una carga puntual y la solución del problema como la superposición de potenciales debido a conjuntos de cargas puntuales distribuidas de forma continua. por la integración de la función de Green sobre la densidad de carga eléctrica, es nuestra explicación de la implicación docente que muestra, al mismo tiempo, rupturas epistemológicas y continuidades en los procesos de enseñanza-aprendizaje.

This paper presents a new method of describing the electronic spectrum and electrical conductivity of disordered crystals based on the Hamiltonian of electrons and phonons. Electronic states of a system are described by the tight-binding model. Expressions for Green’s functions and electrical conductivity are derived using the diagram method. Equations are obtained for the vertex parts of the mass operators of the electron–electron and electron–phonon interactions. A system of exact equations is obtained for the spectrum of elementary excitations in a crystal. This makes it possible to perform numerical calculations of the energy spectrum and to predict the properties of the system with a predetermined accuracy. In contrast to other approaches, in which electron correlations are taken into account only in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. The cluster expansion is obtained for the density of states and electrical conductivity of disordered systems. We show that the contribution of the electron scattering processes to clusters is decreasing, along with increasing the number of sites in the cluster, which depends on a small parameter.

This paper presents a new method of describing the electronic spectrum and electrical conductivity of disordered crystals based on the Hamiltonian of electrons and phonons. Electronic states of a system are described by the tight-binding model. Expressions for Green’s functions and electrical conductivity are derived using the diagram method. Equations are obtained for the vertex parts of the mass operators of the electron–electron and electron–phonon interactions. A system of exact equations is obtained for the spectrum of elementary excitations in a crystal. This makes it possible to perform numerical calculations of the energy spectrum and to predict the properties of the system with a predetermined accuracy. In contrast to other approaches, in which electron correlations are taken into account only in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. The cluster expansion is obtained for the density of states and electrical conductivity of disordered systems. We show that the contribution of the electron scattering processes to clusters is decreasing, along with increasing the number of sites in the cluster, which depends on a small parameter.

In this thesis we employ the non-equilibrium Green’s function (NEGF) method to study both finite and infinite systems. We develop a codebase capable of computing the steady state interacting NEGF in open systems, i.e. tight-binding leads contacting a central region, in both Hartree-Fock (HF) and second Born (2B) approximations of particle-particle interactions. Furthermore, we use the exact interacting Green’s function on finite re- gions to assess a method we found to compute any pair-correlation function. The method utilizes the Hellman-Feynman theorem applied to the Galitskii- Migdal formula for the total energy of a system. We find that it works well for finite systems, with and without currents, whereas for open (infinite) systems the method requires more care. Lastly, we briefly investigate a non- perturbative G1-G2 scheme; whether computing the two-particle Green’s function in a subsystem approximates the full two-particle Green’s function well. We find that the considered G1-G2 scheme provides results of variable accuracy, suggesting that our investigation is not exhaustive, and that the roles of system geometry and particle density should be further assessed., Under de senaste åren, har system vars dynamik sker ur jämvikt fått mycket uppmärksamhet, främst på grund av stora framsteg inom experimentella förverkliganden inom nanosystem som kan utnyttja kvanteffekter, och experimentella verktyg som tillåter mätningar under väldigt korta tidsfönster. I dagens samhälle där vi använder datorer och nanochip, praktiskt taget, överallt är det viktigt att förstå sig på de effekter och konsekvenser som finns när man når så små avstånd. Kvantmekaniken introducerar många nya fenomen i nanovärlden, många av dem inte välkomna. Det är därför viktigt att kunna studera, rent teoretiskt, nanosystem och dess dynamik med stor noggrannhet för att kunna förutse och förhindra oönskade effekter. I det här verket, använder vi så kallade “Green’s functions” för att studera kvanttransportgeometrier, system i vilka elektroner kan transporteras. De fyller en viktig funktion som modelleringssystem för verkliga och mer komplicerade system. Vi implementerar ett ramverk i FORTRAN, via vilket man kan beräkna Green’s functions i steady state, alltså när system har nått ett stilla tillstånd. Detta använder vi sedan för att beräkna den så kallade concurrence i ett system som består av två ihopkopplade kvantprickar som i sin tur är kopplade i en linje med ledare. Ett sådant system, är i principen oändligt, vilket såklart är omöjligt att jobba med, och vi använder därför en metod för att projicera lederna på det centrala systemet, som heter “embedding”. Vi studerar även ett ändligt system, nämligen en ring, i två syften. Främst, för att applicera en metod vi fann för att hitta korrelationsfunktioner, men dessutom för att undersöka om kan frångå den tidigare använda approximationen för interaktioner mellan partiklar, self-energy expansion, och istället beräkna den exakta två-partikels Green’s function och använda den för att beräkna en-partikels Green’s function i det hela systemet.

The particular challenge for modeling wearable and implantable wireless systems for on-body communications lies in the near-field coupling of the antenna and the dissipative tissue. Hence, so far, the antennas could not be considered separately from the propagation channel in the system description. Therefore, methods for the systematic antenna design of on-body applications are developed, whereas the antennas are characterized de-embedded. First, a method for characterizing on-body antennas is developed based on physical modeling of the propagation along the tissue. Furthermore, on-body antenna parameters are derived, representing an adapted form of the standard free-space antenna parameters. Secondly, a method for modeling on-body links based on spherical wave functions (SWF) is developed. It enables obtaining separate models of the antennas and the channel at a higher level of abstraction. Since the developed on-body antenna parameters are defined closely to the standard free-space definitions, an intuitive characterization of on-body antennas is possible. Furthermore, an antenna test range is developed for assessing the defined on-body antenna parameters for physical prototypes. As shown by the examples evaluated, the on-body antenna parameters and the determined transmission equation, analogous to the Friis equation in free-space, can also be used to model the entire wireless system. However, the difficulty lies in determining the directional channel model, which is costly and not universally possible for any application. The developed method based on SWF complements the characterization methods, as channels of any complexity can be modeled since the method could be implemented numerically. Beyond the characterization of on-body antennas and channels, the design of optimized antennas for these applications presents a substantial challenge. Based on the derived on-body transmission equation, antenna optimization can be done directly by maximizing the on-body ant, Die besondere Herausforderung bei der Modellierung von am Körper getragenen und implantierbaren drahtlosen Systemen liegt in der Nahfeldkopplung der Antenne und des dissipativen Gewebes. Daher konnten bisher die Antennen nicht getrennt vom Ausbreitungskanal in der Systembeschreibung berücksichtigt werden. Aus diesem Grund werden Methoden für die systematische Antennenentwicklung von On-Body-Anwendungen entwickelt, wobei die Antennen separat (de-embedded) charakterisiert werden können. Zunächst wird eine Methode zur Charakterisierung von On-Body-Antennen entwickelt, die auf der physikalischen Modellierung der Ausbreitung entlang des Gewebes basiert. Darüber hinaus wurden On-Body-Antennenparameter abgeleitet, die eine angepasste Form der Standardantennenparameter für den freien Raum darstellen. Desweiteren wird eine Methode zur Modellierung von On-Body-Verbindungen auf Grundlage von sphärischen Wellenfunktionen entwickelt. Diese ermöglicht es, getrennte Modelle der Antennen und des Kanals auf einer höheren Abstraktionsebene zu erhalten. Da die entwickelten On-Body-Antennenparameter in enger Anlehnung an die Standarddefinitionen für den freien Raum definiert sind, ist eine intuitive Charakterisierung von On-Body-Antennen möglich. Weiterhin wird ein Antennenmesssystem entwickelt, um die definierten Antennenparameter für physische Prototypen auswerten zu können. Wie die untersuchten Beispiele zeigen, können die On-Body-Antennenparameter und die ermittelte Übertragungsgleichung, analog zur Friis-Gleichung im Freiraum, auch zur Modellierung des gesamten Funksystems verwendet werden. Die Schwierigkeit liegt hier jedoch in der Bestimmung des Kanalmodells, die aufwändig und nicht für jede Anwendung universell möglich ist. Die entwickelte Methode auf Basis sphärischer Wellenfunktionen (SWF) ergänzt die Charakterisierungsmethoden, da aufgrund der numerischen Implementierung hiermit Kanäle beliebiger Komplexität modelliert werden können. Neben der Charakterisierung von On-Body-A

Tesis por compendio, [EN] The dimensionality of the system plays a decisive role in the behavior of the electronic dynamics of interacting electrons. In particular, the quasi-2D dimensionality is responsible for the unusual behavior observed in graphene-like materials and layered van-der-Waal systems. Moreover, such effects are also observed for superconducting materials of high critical temperature, even in the normal state, due to their low-dimensionality. The experimental study of graphene triggered a growing attention to respective electronic properties, because the honeycomb lattice defines a band structure with two nodal points in the Brillouin zone which determines a relativistic Dirac-type electronic dynamics. Within a theoretical framework, many properties of single-layer graphene have been studied to allow further characterization of this material. These properties are unconventional due to the unique band structure of graphene, which is described in terms of Dirac fermions, creating links with certain theories of particle physics. In fact, several theoretical groups have employed phenomenological models inspired in quantum cromodynamics (i.e. Nambu-Jona Lassino and Gross-Neveu models) applied to the study of graphene properties. These properties are responsible for the unusual phenomena, such as the fractional Hall effect, which allows the possibility for magnetic catalysis of an excitonic gap, ferromagnetism and superconductivity. The research of high critical temperature superconductors with impurity centers is significant for understanding the underlying physics of such disordered systems. While the cuprate family present insulating properties in the pristine state, the undoped iron pnictides (i.e. LaOFeAs) show a semi-metallic behavior. Inspite these diferences, both compounds are layered structures, where the superconducting state is supported by a quasi-2D square lattice. While for iron pnictides this state is formed by the FeAs layer, the cuprate superconducting state, [ES] La dimensionalidad de un sistema juega un papel fundamental en la conducta de la dinámica de los electrones que interactúan. En particular, la dimensionalidad cuasi-2D es responsable del comportamiento inusual observado en materiales de tipo grafeno y sistemas laminares basados en enlaces de tipo van der Waals. Además, estos efectos también se observan en materiales superconductores de alta temperatura crítica, incluso en el estado normal, debido a su baja dimensionalidad. El estudio experimental del grafeno provocó una atención creciente a sus propie-dades electrónicas, porque su estructura en forma de panal de abejas da lugar a una estructura de bandas con dos puntos nodales en la zona de Brillouin que determina una dinámica electrónica relativista de tipo Dirac. En el plano teórico, muchas propiedades del grafeno de una sola capa se han estudiado para permitir una mayor caracterización de este material. Estas propiedades son poco convencionales debido a la singular estructura de bandas del grafeno, que se describe en términos de fermiones de Dirac, lo que crea vínculos con ciertas teorías de la física de partículas. De hecho, varios grupos teóricos han empleado modelos fenomenológicos inspirados en la cromodinámica cuántica (es decir, los modelos Nambu-Jona Lassino y Gross-Neveu) aplicados al estudio de las propiedades del grafeno. Estas propiedades son responsables de inusuales fenómenos, como el efecto Hall fraccionario, que permite la posibilidad de catálisis magnética de un gap excitónico, ferromagnetismo y superconductividad. La investigación de superconductores de alta temperatura crítica con centros de impurezas es importante para comprender la física subyacente de tales sistemas desordenados. Mientras que la familia de los cupratos presenta propiedades aislantes en estado prístino, los pnictogenuros de hierro sin dopar (es decir, LaOFeAs) muestran un comportamiento semimetálico. A pesar de estas diferencias, ambos compuestos son estructuras en capas, [CAT] La dimensionalitat d'un sistema juga un paper fonamental en la conducta de la dinámica dels electrons que interactúen. En particular, la dimensionalitat cuasi-2D és responsable del comportament inusual observat a materials de tipus grafè i sistemes laminars basats en enllaços de tipus van der Waals. A més a més, aquestos efectes també s'observen a materials superconductors d'alta temperatura crítica, inclús al seu estat normal, degut a la seua baixa dimensionalitat. L'estudi experimental del grafè va produir una atenció creixent a les seues propietats electròniques, perque la seua estructura en forma de panal d'abelles dona lloc a una estructura de bandes amb dos punts nodals a la zona de Brillouin que determinen una dinámica electrónica relativista de tipus Dirac. Al planol teòric, moltes propietats del grafè d'una sola capa s'han estudiat per a permetre una major caracterizació d'aquest material. Aquestes propietat són poc convencionals degut a la singular estructura de bandes del grafè, que es descriu mitjançant fermions de Dirac. Aquestos fermions permeten establir víncles amb certes teories de la física de particles. De fet, alguns grups teòrics han empleat models fenomenològics inspirats a la cromodinàmica quàntica (es a dir, els models Nambu-Jona Lassino i Gross-Neveu) aplicats a l'estudi de les propietats del grafè. Aquestes propietats són responsables d'inusuals fenómens, com l'efecte Hall fraccionari, que permet la possibilitat de catálisi magnètica d'un gap excitònic, ferromagnetisme i superconductivitat. La investigació de superconductors d'alta temperatura crítica amb centres d'impureses és important per a comprendre la física subjacent de tals sistemes desordenats. Mentre que la família dels cuprats presenta propietats aïllants en estat pristí, els pnictogenurs de ferro sense dopar (és a dir, LaOFeAs) mostren un comportament semimetálico. Malgrat aquestes diferències, tots dos compostos són estructures en capes, on l'estat superconductor està rec

Closed-form time-domain (TD) analytical expressions describing the electromagnetic (EM) signal transfer between two vertical dipoles through a thin, highly contrasting layer with combined magneto-dielectric properties are derived via the Cagniard–DeHoop (CdH) technique with the TD saltus-type conditions. The TD EM-field coupling between the antennas in the absence of the layer is discussed, including its near-field asymptotic solution. It is demonstrated both analytically and numerically that under certain circumstances the combined sheet behaves virtually as a transparent sheet the transition across which inverts the polarity of the received signal., Accepted author manuscript, Electrical Engineering Education

This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation of the Dirichlet conditions by considering a homogeneous Dirichlet-type condition at one extreme of the interval and an integral operator on the other one. We obtain the expression of the Green’s function related to the linear part of the equation and characterize its constant sign. Such a property will be fundamental to deduce the existence of solutions of the nonlinear problem. The results hold from fixed point theory applied to related operators defined on suitable cones

Closed-form time-domain (TD) analytical expressions describing the electromagnetic (EM) signal transfer between two vertical dipoles through a thin, highly contrasting layer with combined magneto-dielectric properties are derived via the Cagniard–DeHoop (CdH) technique with the TD saltus-type conditions. The TD EM-field coupling between the antennas in the absence of the layer is discussed, including its near-field asymptotic solution. It is demonstrated both analytically and numerically that under certain circumstances the combined sheet behaves virtually as a transparent sheet the transition across which inverts the polarity of the received signal., Accepted author manuscript, Electrical Engineering Education

In this review are summarized about 20 years of theoretical research with applications in the field of many-body physics for strongly correlated fermions with Rowe's equation of motion (R-EOM) method and extended RPA equations. One major goal is to set up, via EOM, RPA equations with a correlated ground state. Since the correlations depend on the RPA amplitudes, it follows that RPA becomes a selfconsistency problem which is called Self-Consistent RPA (SCRPA). This then also improves very much the Pauli principle violated with standard RPA. The method was successfully applied to several non trivial problems, like the nuclear pairing Hamiltonian in the particle–particle channel (pp-RPA) and the Hubbard model of condensed matter. The SCRPA has several nice properties, as for instance, it can be formulated in such a way that all very appreciated qualities of standard RPA as, e.g., appearance of zero (Goldstone) modes in the case of broken symmetries, conservation laws, Ward identities, etc. are maintained. For the Goldstone mode an explicit example of a model case is presented. The formalism has its sound theoretical basis in the fact that an extension of the usual RPA operator has been found which exactly annihilates the Coupled Cluster Doubles (CCD) ground state wave function. This has been a longstanding problem for all RPA practitioners from the beginning. There exists a rather simplified version of SCRPA which is the so-called renormalized RPA (r-RPA) where only the correlated occupation numbers are involved in the selfconsistent cycle. Because its numerical solution is rather similar to standard RPA, it has known quite a number of applications, like beta and double beta decays, which are reviewed in this article. In this review also an extended version of second RPA (ERPA)is described. This ERPA maintains all appreciable properties of standard RPA. Several realistic applications for, e.g., the damping of giant resonances are presented. Another important aspect of

Исследовано поглощение мощности электромагнитного поля тканями головы человека в микроволновом диапазоне. Расчет электрического поля в тканях головы, индуцированного элементарной антенной, основано на применении функций Грина слоистых сред. Два вида излучателей, таких как полуволновый диполь и петлевая антенна сравниваются с точки зрения глубины проникновения электромагнитной энергии. Рассчитана мощность, поглощаемая в различных слоях модели головы человека. В заключении сделан вывод о преимуществе применения криволинейных токов, таких, как формируемых плоской спиралью. Рассмотрено влияние проводящего экрана на эффективность излучения антенны. Полученные результаты предполагается использовать при разработке эффективных сенсоров для микроволновой радиометрии мозга., The power absorbed by human head tissues in the microwave range is investigated. Calculation of the electric field induced in the head tissues by antenna probe is based on the use of the Green’s functions of the stratified media. Two types of emitters such as a half-wave dipole and a loop antenna are compared in terms of the depth of electromagnetic energy penetration. The power absorbed by different layers of the human head model is calculated. The conclusion is made on the best efficiency of antenna with an annular current, such as a flat helix. The effect of the conducting screen on the efficiency of the antenna is studied. The data were obtained for designing effective field sensors for the microwave radiometry of the brain.

We present a multiscale model based on many-body Green's functions theory in the GW approximation and the Bethe–Salpeter equation (GW-BSE) for the simulation of singlet and triplet exciton transport in molecular materials. Dynamics of coupled electron–hole pairs are modeled as a sequence of incoherent tunneling and decay events in a disordered morphology obtained at room temperature from molecular dynamics. The ingredients of the rates associated to the events, i.e. reorganization energies, site energies, lifetimes, and coupling elements, are determined from a combination of GW-BSE and classical polarizable force field techniques. Kinetic Monte Carlo simulations are then employed to evaluate dynamical properties such as the excitonic diffusion tensor and diffusion lengths. Using DCV5T-Me(3,3), a crystalline organic semiconductor, we demonstrate how this multiscale approach provides insight into the fundamental factors driving the transport processes. Comparing the results obtained via different calculation models, we investigate in particular the effects of charge-transfer mediated high exciton coupling and the influence of internal site energy disorder due to conformational variations. We show that a small number of high coupling elements indicative of delocalized exciton states does not impact the overall dynamics perceptively. Molecules with energies in the tail of the excitonic density of states dominate singlet decay, independent of the level of disorder taken into account in the simulation. Overall, our approach yields singlet diffusion lengths on the order of 10 nm as expected for energetically disordered molecular materials.

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D-3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D-3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D-3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level.

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D-3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D-3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D-3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level.

We present a multiscale model based on many-body Green's functions theory in the GW approximation and the Bethe–Salpeter equation (GW-BSE) for the simulation of singlet and triplet exciton transport in molecular materials. Dynamics of coupled electron–hole pairs are modeled as a sequence of incoherent tunneling and decay events in a disordered morphology obtained at room temperature from molecular dynamics. The ingredients of the rates associated to the events, i.e. reorganization energies, site energies, lifetimes, and coupling elements, are determined from a combination of GW-BSE and classical polarizable force field techniques. Kinetic Monte Carlo simulations are then employed to evaluate dynamical properties such as the excitonic diffusion tensor and diffusion lengths. Using DCV5T-Me(3,3), a crystalline organic semiconductor, we demonstrate how this multiscale approach provides insight into the fundamental factors driving the transport processes. Comparing the results obtained via different calculation models, we investigate in particular the effects of charge-transfer mediated high exciton coupling and the influence of internal site energy disorder due to conformational variations. We show that a small number of high coupling elements indicative of delocalized exciton states does not impact the overall dynamics perceptively. Molecules with energies in the tail of the excitonic density of states dominate singlet decay, independent of the level of disorder taken into account in the simulation. Overall, our approach yields singlet diffusion lengths on the order of 10 nm as expected for energetically disordered molecular materials.

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D-3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D-3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D-3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level.

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D-3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D-3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D-3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level.

In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower-dimensional sources. In this work, we consider a coupled 1D-3D flow model, in which the well is modelled as a line source in the reservoir domain and endowed with its own 1D flow equation. The flow between well and reservoir can then be modelled in a fully coupled manner by applying a linear filtration law. The line source induces a logarithmic-type singularity in the reservoir pressure that is difficult to resolve numerically. We present here a singularity removal method for the model equations, resulting in a reformulated coupled 1D-3D flow model in which all variables are smooth. The singularity removal is based on a solution splitting of the reservoir pressure, where it is decomposed into two terms: an explicitly given, lower-regularity term capturing the solution singularity and some smooth background pressure. The singularities can then be removed from the system by subtracting them from the governing equations. Finally, the coupled 1D-3D flow equations can be reformulated so they are given in terms of the well pressure and the background reservoir pressure. As these variables are both smooth (i.e. non-singular), the reformulated model has the advantage that it can be approximated using any standard numerical method. The reformulation itself resembles a Peaceman well correction performed at the continuous level.

This dissertation concerns the quantum many-body problem, which is the problem of predicting the properties of systems of several quantum particles from the first principles of quantum mechanics. Included under this umbrella are various problems of fundamental importance in quantum chemistry, condensed matter physics, and materials science. Of particular interest is the electronic structure problem, the problem of determining the state of the electrons in a system with fixed atomic nuclei. Since direct numerical solution of the many-body Schrödinger equation is intractable even for systems of moderate size, a diverse array of approximate methods has been developed. The broad goals of this dissertation are to improve the mathematical understanding of certain widely-used approximations, as well as to propose new methods. Roughly speaking, we consider three (overlapping) categories of methods: Green's function methods, embedding methods, and variational methods.One can understand Green's function methods in terms of many-body perturbation theory, which computes series expansions of physical quantities about a non-interacting reference system. These expansions can be expressed graphically in terms of Feynman diagrams, which can in turn be reorganized, in some cases, into an expansion in terms of so-called bold diagrams. Green's function methods can be specified by choosing a subset of bold diagrams to approximate the sum. At the same time, such methods can be understood in terms of an object known as the Luttinger-Ward (LW) functional, which admits a representation in terms of the bold diagrams. Many aspects of these constructions are purely formal, and indeed the existence of the fermionic LW functional as a single-valued functional has recently been called into question. To contribute to the understanding of these issues, we provide rigorous proofs of the combinatorial construction and analytic interpretation of the bold diagrams in the simplified setting of a classic

The unsteady heat conduction in composite planar structure, with arbitrary number of layers, using analytical approach based on Green's Functions (GF) is analyzed. The analytical solution for spatial and temporal temperature distribution is evaluated in the general form and expressed in the terms of the convolution integrals. The GF are employed in the novel approach for calculation of Thermal Response Factors (TRF) with arbitrary shape functions for unsteady heat conduction in composite planar structure. The two pairs of TRF for spatial and temporal distribution of the temperature and the thermal flux are obtained. The whole analysis is performed in the time domain. A numerical scheme for efficient evaluation of convolution integral suitable for practical application in the case of the long term measurements with lower sampling rates is developed. The in-situ measurements of inside and outside surface temperatures and outside heat flux for a building wall under real dynamical environmental conditions during the period of then days are used for validation of the presented results and to demonstrate the possible practical application. Using developed approach and recorded surface temperatures as inputs the temporal and spatial distributions of the temperature and the thermal flux are obtained. These results are compared with experimental data and numerical simulations obtained by the Finite Volume Method (FVM).

This dissertation concerns the quantum many-body problem, which is the problem of predicting the properties of systems of several quantum particles from the first principles of quantum mechanics. Included under this umbrella are various problems of fundamental importance in quantum chemistry, condensed matter physics, and materials science. Of particular interest is the electronic structure problem, the problem of determining the state of the electrons in a system with fixed atomic nuclei. Since direct numerical solution of the many-body Schrödinger equation is intractable even for systems of moderate size, a diverse array of approximate methods has been developed. The broad goals of this dissertation are to improve the mathematical understanding of certain widely-used approximations, as well as to propose new methods. Roughly speaking, we consider three (overlapping) categories of methods: Green's function methods, embedding methods, and variational methods.One can understand Green's function methods in terms of many-body perturbation theory, which computes series expansions of physical quantities about a non-interacting reference system. These expansions can be expressed graphically in terms of Feynman diagrams, which can in turn be reorganized, in some cases, into an expansion in terms of so-called bold diagrams. Green's function methods can be specified by choosing a subset of bold diagrams to approximate the sum. At the same time, such methods can be understood in terms of an object known as the Luttinger-Ward (LW) functional, which admits a representation in terms of the bold diagrams. Many aspects of these constructions are purely formal, and indeed the existence of the fermionic LW functional as a single-valued functional has recently been called into question. To contribute to the understanding of these issues, we provide rigorous proofs of the combinatorial construction and analytic interpretation of the bold diagrams in the simplified setting of a classic

A new expression for the fundamental solution is introduced, presenting three relevant characteristics: (i) it is explicit in terms of the Stroh's eigenvalues, (ii) it remains well-defined when some Stroh's eigenvalues are repeated, and (iii) it is exact. A fast and robust numerical scheme for the evaluation of the fundamental solution and its derivatives developed from double Fourier series representations is presented. The Fourier series representation is possible due to the periodic nature of the solution. The attractiveness of this series solution is that the information of the material properties is contained only in the Fourier coefficients, while the information of the dependence of the evaluation point is contained in simple trigonometric functions. This implies that any order derivatives can be determined by spatial differentiation of the trigonometric functions. Moreover, Fourier coefficients need to be obtained only once for a given material, leading to an efficient methodology. The robustness of the scheme arises from the properties (i) and (ii) of the new expression for the fundamental solution, which is used to compute the Fourier coefficients. The proposed approach combines the clean structure of the Stroh formalism with the simplicity of Fourier expansions, addressing the old drawbacks of anisotropic fundamental solutions.

In this paper, we prove the existence of solutions of nonlinear boundary value problems of arbitrary even order using the lower and upper solutions method. In particular, we point out the fact that the existence of a pair of lower and upper solutions of a considered problem could imply the existence of solution of another one with different boundary conditions. We consider Neumann, Dirichlet, mixed and periodic boundary conditions

The unsteady heat conduction in composite planar structure, with arbitrary number of layers, using analytical approach based on Green's Functions (GF) is analyzed. The analytical solution for spatial and temporal temperature distribution is evaluated in the general form and expressed in the terms of the convolution integrals. The GF are employed in the novel approach for calculation of Thermal Response Factors (TRF) with arbitrary shape functions for unsteady heat conduction in composite planar structure. The two pairs of TRF for spatial and temporal distribution of the temperature and the thermal flux are obtained. The whole analysis is performed in the time domain. A numerical scheme for efficient evaluation of convolution integral suitable for practical application in the case of the long term measurements with lower sampling rates is developed. The in-situ measurements of inside and outside surface temperatures and outside heat flux for a building wall under real dynamical environmental conditions during the period of then days are used for validation of the presented results and to demonstrate the possible practical application. Using developed approach and recorded surface temperatures as inputs the temporal and spatial distributions of the temperature and the thermal flux are obtained. These results are compared with experimental data and numerical simulations obtained by the Finite Volume Method (FVM).

The unsteady heat conduction in composite planar structure, with arbitrary number of layers, using analytical approach based on Green's Functions (GF) is analyzed. The analytical solution for spatial and temporal temperature distribution is evaluated in the general form and expressed in the terms of the convolution integrals. The GF are employed in the novel approach for calculation of Thermal Response Factors (TRF) with arbitrary shape functions for unsteady heat conduction in composite planar structure. The two pairs of TRF for spatial and temporal distribution of the temperature and the thermal flux are obtained. The whole analysis is performed in the time domain. A numerical scheme for efficient evaluation of convolution integral suitable for practical application in the case of the long term measurements with lower sampling rates is developed. The in-situ measurements of inside and outside surface temperatures and outside heat flux for a building wall under real dynamical environmental conditions during the period of then days are used for validation of the presented results and to demonstrate the possible practical application. Using developed approach and recorded surface temperatures as inputs the temporal and spatial distributions of the temperature and the thermal flux are obtained. These results are compared with experimental data and numerical simulations obtained by the Finite Volume Method (FVM).

In this paper, a novel integral equation formulation expressed in the spatial domain is proposed for the analysis of rectangular waveguide step discontinuities. The important novelty of the proposed formulation is that which allows to easily take into account the electrical influence of a given number of arbitrarily shaped conducting and dielectric posts placed close to the waveguide discontinuity. For the sake of simplicity, and without loss of generality, the presented integral equation has been particularized and solved for inductive rectangular waveguide geometry. In this case, the integral equation mixed-potentials kernel is written in terms of parallel plate Green’s functions with an additional ground plane located on the waveguide step. Therefore, the unknowns of the problem are reduced to an equivalent magnetic surface current on the step aperture and equivalent magnetic and electric surface currents on the dielectric and conducting posts close to the discontinuity. The numerical solution of the final integral equation is efficiently computed after the application of acceleration techniques for the slowly convergent series representing the Green’s functions of the problem. The numerical method has been validated through several simulation examples of practical microwave devices, including compact size band-pass cavity filters and coupled dielectric resonators filters. The results have been compared to those provided by commercial full-wave electromagnetic simulation software packages, showing in all cases a very good agreement, and with substantially enhanced numerical efficiencies.

Wave function based electronic structure methods have became a robust and reliable tool for the prediction and interpretation of the results of chemical experiments. However, they suffer from very steep scaling behavior with respect to an increase in the size of the system as well as very slow convergence of the correlation energy with respect to the basis set size. Thus these methods are limited to small systems of up to a dozen atoms. The first of these issues can be efficiently resolved by exploiting the local nature of electron correlation effects while the second problem is alleviated by the use of explicitly correlated R12/F12 methods. Since R12/F12 methods are central to this work, we start by reviewing their modern formulation. Next, we present the explicitly correlated second-order Mo ller-Plesset (MP2-F12) method in which all nontrivial post-mean-field steps are formulated with linear computational complexity in system size [Pavov{s}evi'c et al., {em J. Chem. Phys.} {bf 144}, 144109 (2016)]. The two key ideas are the use of pair-natural orbitals for compact representation of wave function amplitudes and the use of domain approximation to impose the block sparsity. This development utilizes the concepts for sparse representation of tensors described in the context of the DLPNO-MP2 method by Neese, Valeev and co-workers [Pinski et al., {em J. Chem. Phys.} {bf 143}, 034108 (2015)]. Novel developments reported here include the use of domains not only for the projected atomic orbitals, but also for the complementary auxiliary basis set (CABS) used to approximate the three- and four-electron integrals of the F12 theory, and a simplification of the standard B intermediate of the F12 theory that avoids computation of four-index two-electron integrals that involve two CABS indices. For quasi-1-dimensional systems (n-alkanes) the bigO{N} DLPNO-MP2-F12 method becomes less expensive than the conventional bigO{N^{5}} MP2-F12 for $n$ between 10 and 15, for double- and t

This article elaborates on an extension to the classical stiffness matrix method to obtain the Green's functions for two-and-a-half dimensional (2.5D) elastodynamic problems in homogeneous and horizontally layered half-spaces. Exact expressions for the three-dimensional (3D) stiffness matrix method for isotropic layered media in Cartesian coordinates are used to determine the stiffness matrices for a system of horizontal layers underlain by an elastic half–space. In the absence of interfaces, virtual interfaces are considered at the positions of external loads. The analytic continuation is used to find the displacements at any receiver point placed within a layer. The responses of a horizontally layered half-space subjected to a unit harmonic load obtained using the present method are compared with those calculated using a well-established methodology, achieving good agreement, Postprint (author's final draft)

Показано применение аппарата функций Грина многослойных магнито-диэлектрических структур к решению задач излучения, распространения и дифракции электромагнитных волн. В качестве источников электромагнитного поля рассматриваются произвольно ориентированные сторонние электрические и магнитные токи. Для описания слоистой радиальной структуры применен метод эквивалентных электрических цепей. Для моделирования слоев и границ областей используются матрицы передачи и эквивалентные нагрузки. Модальные напряжения и токи в эквивалентных цепях ассоциируются со спектральными составляющими электромагнитного поля. Предложенный подход позволяет конструировать универсальные алгоритмы для задач распространения волн в направляющих структурах, излучения печатных и щелевых антенн, расположенных на проводящем цилиндре с укрытиями, решать задачи дифракции электромагнитных волн с произвольным числом слоев. При этом материалы слоев могут иметь произвольные значения диэлектрической и магнитной проницаемости, учитываются потери в материале. При моделировании могут рассматриваться материалы как с положительным, так и с отрицательным коэффициентом рефракции. Предложенный подход был использован для решения задач электромагнитного возбуждения структур с метаматериалами., The method of Green’s functions of layered cylindrical magnetodielectric structures is applied to solution of radiation, propagation and scattering problems. Excitation of electromagnetic field is provided by arbitrary distribution of impressed electric and magnetic currents. The model of equivalent circuits is used for description of layered structure. Transmission matrices and various kinds of loads are used for modelling layered structure and boundaries. Equivalent voltages and currents in modelling circuits are associated with spectral field components. Suggested method allows to construct universal algorithms for wave propagation, patch and slot antennas radiation and scattering problems with any number of layers made of materials of arbitrary permittivity and permeability. Positive and negative refraction index of materials may be taken into account. Suggested technique has been successfully applied to radiating structures made of metamaterials commonly used in electromagnetic designs.

A Master of Science thesis in Mathematics by Amer Mahmoud Malbanji entitled, "Solving Fourth Order Differential Non-Linear Equations, Existence and Uniqueness," submitted in May 2017. Thesis advisor is Dr. Suheil A. Khoury. Soft and hard copy available., The aim of this thesis is to present a novel numerical approach for the solution of a class of non-linear fourth-order boundary value problems. The method is based on embedding Green's function into some fixed point iteration schemes, an idea previously used in other works to investigate nonlinear boundary value problems of lower order. To this end, the thesis is divided in 6 chapters. The first chapter is a short description of the main ideas of this thesis. The second chapter represents a review on Green's functions for differential equations. In Chapter 3 some existence and uniqueness results for the fourth order boundary value problems are presented. The proposed numerical method is then explained and applied on numerical examples in Chapter 4, where a comparison with the Spline method is also given, demonstrating thus that our method yields accurate results up to 10 e-20, compared to the Spline method, where the results are accurate up to 10 e-13. The results obtained by our method were achieved within a reasonable time limit compared with other methods. Chapter 5 is concerned with the convergence analysis of our method. More precisely, some conditions which guarantees the convergence of the solution under specific conditions is given. For the proof we used the Banach-Picard theorem along with the Green's function. Finally, in Chapter 6 we present a short conclusions and a summary of the whole thesis., College of Arts and Sciences, Department of Mathematics and Statistics

The main body of this thesis describes how to calculate scanning tunneling microscopy (STM) images from first-principles methods. The theory is based on localized orbital density functional theory (DFT), whose limitations for large-vacuum STM models are resolved by propagating localized-basis wave functions close to the surface into the vacuum region in real space. A finite difference approximation is used to define the vacuum Hamiltonian, from which accurate vacuum wave functions are calculated using equations based on standard single-particle Green’s function techniques, and ultimately used to compute the conductance. By averaging over the lateral reciprocal space, the theory is compared to a series of high-quality experiments in the low- bias limit, concerning copper surfaces with adsorbed carbon monoxide (CO) species and adsorbate atoms, scanned by pure and CO-functionalized copper tips. The theory compares well to the experiments, and allows for further insights into the elastic tunneling regime. A second significant project in this thesis concerns first-principles calculations of a simple chemical reaction of a hydroxyl (oxygen-deuterium) monomer adsorbed on a copper surface. The reaction mechanism is provided by tunneling electrons that, via a finite electron-vibration coupling, trigger the deuterium atom to flip between two nearly identical configurational states along a frustrated rotational motion. The theory suggests that the reaction primarily occurs via nuclear tunneling for the deuterium atom through the estimated reaction barrier, and that over-barrier ladder climbing processes are unlikely.

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

Instead of usual approach, applying displacement-displacement Green’s functions, the momentum-momentum Green’s functions will be used to calculate the diffusion tensor. These functions enter into Kubo’s formula defining diffusion properties of the system. Calculation of the diffusion tensor requires solving of the system of difference equations. It is shown that the elements of the diffusion tensor express discrete behaviour of the dispersion law of elementary excitations and, more important - that they are temperature independent., Umesto uobičajenog pristupa, primenom Grinovih funkcija tipa pomeraj-pomeraj, tenzor difuzije izračunat je primenom Grinovih funkcija tipa impuls-impuls. Ove funkcije figurišu u Kubo formuli koja definiše difuzione osobine sistema. Izračunavanje tenzora difuzije zahteva rešavanje sistema diferencnih jednačina. U radu je pokazano da elementi tenzora difuzije ukazuju na diskretnost zakona disperzije elementarnih pobuđenja, i - što je još značajnije - ne zavise od temperature. Rezultati sprovedenih izračunavanja pokazali su da je tenzor difuzije fononskog podsistema u kristalnim strukturama dijagonalan i da svojstvene vrednosti imaju više vrednosti pri nižim frekvencijama. Navedeni zaključci su od velikog značaja, jer potvrđuju makroskopske teorije toplotnog provođenja koje tvrde da je koeficijent difuzije temperaturski invarijatan. Ova činjenica, kao i posledice koji iz nje mogu proizaći, imaju ogroman potencijalni značaj za primenu fononskog inženjeringa, prvenstveno kod savremenih nanostruktura.

Instead of usual approach, applying displacement-displacement Green's functions, the momentum-momentum Green's functions will be used to calculate the diffusion tensor. With this type of Green's function we have calculated and analyzed dispersion law in film-structures. A small number of phonon energy levels along the direction of boundary surfaces joint of the film are discrete-ones and in this case standing waves could occur. This is consequence of quantum size effects. These Green's functions enter into Kubo's formula defining diffusion properties of the system and possible heat transfer direction through observed structures. Calculation of the diffusion tensor for phonons in film structure requires solving of the system of difference equations. Boundary conditions are included into mentioned system through the Hamiltonian of the film-structure. It has been shown that the diagonal elements of the diffusion tensor express discrete behavior of the dispersion law of elementary excitations. More important result is that they are temperature independent and that their values are much higher comparing with bulk structures. This result favors better heat conduction of the film, but in direction which is perpendicular to boundary film surface. In the same time this significantly favors appearance 2D superconducting surfaces inside the ultra-thin crystal structure, which are parallel to the boundary surface.

The main aim of this paper is to contribute to the construction of Green’s functions for initial boundary value problems for fourth order partial differential equations. In this paper, we consider a transversely vibrating homogeneous semi-infinite beam with classical boundary conditions such as pinned, sliding, clamped or with a non-classical boundary conditions such as dampers. This problem is of important interest in the context of the foundation of exact solutions for semi-infinite beams with boundary damping. The Green’s functions are explicitly given by using the method of Laplace transforms. The analytical results are validated by references and numerical methods. It is shown how the general solution for a semi-infinite beam equation with boundary damping can be constructed by the Green’s function method, and how damping properties can be obtained., Mathematical Physics

Metals deform plastically at the asperity level when brought in contact with a counter body even when the nominal contact pressure is small. Modeling the plasticity of solids with rough surfaces is challenging due to the multi-scale nature of surface roughness and the length-scale dependence of plasticity. While discrete-dislocation plasticity (DDP) simulations capture size-dependent plasticity by keeping track of the motion of individual dislocations, only simple two-dimensional surface geometries have so far been studied with DDP. The main computational bottleneck in contact problems modeled by DDP is the calculation of the dislocation image fields. We address this issue by combining two-dimensional DDP with Green's function molecular dynamics. The resulting method allows for an efficient boundary-value-method based treatment of elasticity in the presence of dislocations. We demonstrate that our method captures plasticity quantitatively from single to many dislocations and that it scales more favorably with system size than conventional methods. We also derive the relevant Green's functions for elastic slabs of finite width allowing arbitrary boundary conditions on top and bottom surface to be simulated., (OLD) MSE-7

The main body of this thesis describes how to calculate scanning tunneling microscopy (STM) images from first-principles methods. The theory is based on localized orbital density functional theory (DFT), whose limitations for large-vacuum STM models are resolved by propagating localized-basis wave functions close to the surface into the vacuum region in real space. A finite difference approximation is used to define the vacuum Hamiltonian, from which accurate vacuum wave functions are calculated using equations based on standard single-particle Green’s function techniques, and ultimately used to compute the conductance. By averaging over the lateral reciprocal space, the theory is compared to a series of high-quality experiments in the low- bias limit, concerning copper surfaces with adsorbed carbon monoxide (CO) species and adsorbate atoms, scanned by pure and CO-functionalized copper tips. The theory compares well to the experiments, and allows for further insights into the elastic tunneling regime. A second significant project in this thesis concerns first-principles calculations of a simple chemical reaction of a hydroxyl (oxygen-deuterium) monomer adsorbed on a copper surface. The reaction mechanism is provided by tunneling electrons that, via a finite electron-vibration coupling, trigger the deuterium atom to flip between two nearly identical configurational states along a frustrated rotational motion. The theory suggests that the reaction primarily occurs via nuclear tunneling for the deuterium atom through the estimated reaction barrier, and that over-barrier ladder climbing processes are unlikely.

We provide the explicit solution of a general second order linear difference equation via the computation of its associated Green function. This Green function is completely characterized and we obtain a closed expression for it using functions of two–variables, that we have called Chebyshev functions due to its intimate relation with the usual one–variable Chebyshev polynomials. In fact, we show that Chebyshev functions become Chebyshev polynomials if constant coefficients are considered., Peer Reviewed, Postprint (author's final draft)

This article is devoted to the study of the parameter’s set where the Green’s function related to a general linear nth-order operator, depending on a real parameter, Tn[M], coupled with many different two point boundary value conditions, is of constant sign. This constant sign is equivalent to the strongly inverse positive (negative) character of the related operator on suitable spaces related to the boundary conditions. This characterization is based on spectral theory, in fact the extremes of the obtained interval are given by suitable eigenvalues of the differential operator with different boundary conditions. Also, we obtain a characterization of the strongly inverse positive (negative) character on some sets, where non homogeneous boundary conditions are considered. To show the applicability of the results, we give some examples. Note that this method avoids the explicit calculation of the related Green’s function.

This Thesis contains a detailed collection of the different results proved by the author in her predoctoral stage. The interest of the non-linear differential equations is well-known. This is due to their applications in different fields, such as physics, economy, medicine, biology or chemistry. It is very important to make a precise study of the existence of solutions for this kind of problems, as well as their uniqueness or multiplicity. We focus on the qualitative analysis of diverse boundary value problems, both linear and non-linear ones. Indeed, in most of the cases, our aim is to prove the existence of constant sign solutions in their definition interval. This interest comes from the constant sign of many of the magnitudes which are modelled by this kind of problems.