Conformal electromagnetic wave propagation using primal mimetic finite elements

Elektromagnetische Wellenausbreitung bildet die physikalische Grundlage für unzählige Anwendungen in verschiedenen Bereichen der heutigen Welt. Um räumliche Szenarien zu modellieren, muss der kontinuierliche Raum in geeigneter Weise in ein Rechengebiet umgewandelt werden. Üblich diskretisierte Modelle – welche auf verschiedenen Größen beruhen – berücksichtigen die Beziehungen zwischen Feldvariablen mittels Relationen, welche durch partielle Differentialgleichungen repräsentiert werden. Um mathematische Beziehungen zwischen abhängigen Variablen in zweckdienlicher Art nachzubilden, schaffen hyperkomplexe Zahlensysteme ein passendes alternatives Rahmenwerk. Dieser Ansatz bezweckt das Einbinden bestimmter Systemeigenschaften und umfasst zusätzlich zur Modellierung von Feldproblemen, bei denen alle Variablen vorkommen, auch vereinfachte Modelle. Um eine wettbewerbsfähige Alternative zur üblichen numerischen Behandlung elektromagnetischer Felder in beobachtungsorientierter Weise darzubieten, wird das elektrische und magnetische Feld elektromagnetischer Wellenfelder als eine zusammengefasste Feldgröße, eingebettet im Funktionenraum, verstanden. Dieses Vorgehen ist intuitiv, da beide Felder in der Elektrodynamik gemeinsam auftreten und direkt messbar sind. Der Schwerpunkt dieser Arbeit ist in zwei Ziele untergliedert. Auf der einen Seite wird ein umformuliertes Maxwell-System in einer metrikfreien Umgebung mittels dem sogenannten „bikomplexen Ansatz“ umfassend untersucht. Auf der anderen Seite wird eine mögliche numerische Implementierung hinsichtlich der Finite-Elemente-Methode auf modernem Wege durch Nutzung der diskreten äußeren Analysis mit Fokus auf Genauigkeitsbelange bewertet. Hinsichtlich der numerischen Genauigkeitsbewertung wird demonstriert, dass der vorgelegte Ansatz grundsätzlich eine höhere Exaktheit zeigt, wenn man ihn mit Formulierungen vergleicht, welche auf der Helmholtz-Gleichung beruhen. Diese Dissertation trägt eine generalisierte hyperkomplexe alternative Darstellung von gewöhnlichen elektrodynamischen Ausdrucksweisen zum Themengebiet der Wellenausbreitung bei. Durch die Nutzung einer direkten Formulierung des elektrischen Feldes in Verbindung mit dem magnetischen Feld wird die Rechengenauigkeit von Randwertproblemen erhöht. Um diese Genauigkeitserhöhung zu erreichen, wird eine geeignete Erweiterung der de Rham-Kohomologie unterbreitet.Electromagnetic wave propagation provides the physical basis for countless applications in various subjects of today’s world. In order to model spatial scenarios, the continuous space must be converted to an appropriate computational domain. Ordinarily discretized models – which are based on distinct quantities – consider the connection between field variables by relations which are represented by partial differential equations. To reproduce mathematical relationships between dependent variables in a convenient manner, hypercomplex number systems build a suitable alternative framework. This approach aims to incorporate certain system properties and covers, in addition to the modeling of field problems where all variables are present, also simplified models. To provide a competitive alternative to the ordinary numerical handling of electromagnetic fields in an observation-based way, the electric and magnetic field of electromagnetic wave fields is understood as only one combined field variable embedded in the function space. This procedure is intuitive since both fields occur together in electrodynamics and are directly measureable. The focus of this thesis is twofold. On the one side, a reformulated Maxwell system is broadly investigated in a metric-free environment by the use of the so-called ”bicomplex approach”. On the other side, a possible numerical implementation concerning the Finite Element Method is evaluated in a modern way by the use of discrete exterior calculus with focus on accuracy matters. Regarding the numerical accuracy evaluation, it is demonstrated that the presented approach yields a higher exactness in general when comparing it to formulations which are based on the Helmholtz equation. This thesis contributes generalized hypercomplex alternative representations of ordinary electrodynamic expressions to the topic of wave propagation. By the use of a direct formulation of the electric field in conjunction with the magnetic field, the computational accuracy of boundary value problems is improved. In order to achieve this increase of accuracy, an appropriate enhancement of the de Rham cohomology is proposed

Entropy, Decoherence and Spacetime Splitting

Objects in classical world model are in an "either/or" kind of state. A compass needle cannot point both north and south at the same time. The quantum world, by contrast, is "both/and" and a magnetic atom model has no trouble at pointing both directions at once. When that is the case, physicists say that a quantum object is in a "superposition" of states. In previous paper, we already discussed the major intrinsic limitations of "Science 1.0" arbitrary multi-scale (AMS) modeling and strategies to get better simulation results by "Science 2.0" approach. In 2014, Computational information conservation theory (CICT) has shown that even the most sophisticated instrumentation system is completely unable to reliably discriminate so called "random noise" (RN) from any combinatorically optimized encoded message (OECS, optimized exponential cyclic sequence), called "deterministic noise" (DN) by CICT. Unfortunately, the "probabilistic veil" can be quite opaque computationally, and misplaced precision leads to confusion. The "Science 2.0" paradigm has not yet been completely grasped by many contemporary scientific disciplines and current researchers, so that not all the implications of this big change have been realized hitherto, even less their related, vital applications. Thus, one of the key questions in understanding the quantum-classical transition is what happens to the superposition as you go up that atoms-to-apple scale. Exactly when and how does "both/and" become "either/or"? As an example, we present and discuss the observer space-time splitting case. In other words, we show spacetime mapping to classical system additive representation with entropy generation. It is exactly at this point that "both/and" becomes "either/or" representation by usual Science 1.0 approach. CICT new awareness of a discrete HG (hyperbolic geometry) subspace (reciprocal space) of coded heterogeneous hyperbolic structures, underlying the familiar Q Euclidean (direct space) surface representation can open the way to holographic information geometry (HIG) to recover system lost coherence and to overall system minimum entropy representation

Knowledge Graph Embedding: A Survey from the Perspective of Representation Spaces

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.Comment: 32 pages, 6 figure

Geometric Clifford Algebra Networks

We propose Geometric Clifford Algebra Networks (GCANs) for modeling dynamical systems. GCANs are based on symmetry group transformations using geometric (Clifford) algebras. We first review the quintessence of modern (plane-based) geometric algebra, which builds on isometries encoded as elements of the $\mathrm{Pin}(p,q,r)$ group. We then propose the concept of group action layers, which linearly combine object transformations using pre-specified group actions. Together with a new activation and normalization scheme, these layers serve as adjustable $\textit{geometric templates}$ that can be refined via gradient descent. Theoretical advantages are strongly reflected in the modeling of three-dimensional rigid body transformations as well as large-scale fluid dynamics simulations, showing significantly improved performance over traditional methods

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Quaternion-Valued Adaptive Signal Processing and Its Applications to Adaptive Beamforming and Wind Profile Prediction

Quaternion-valued signal processing has received more and more attentions in the past ten years due to the increasing need to process three or four-dimensional signals, such as colour images, vector-sensor arrays, three-phase power systems, dual-polarisation based wireless communica- tion systems, and wind profile prediction. One key operation involved in the derivation of all kinds of adaptive signal processing algorithms is the gradient operator. Although there are some derivations of this operator in literature with different level of details in the quaternion domain, it is still not fully clear how this operator can be derived in the most general case and how it can be applied to various signal processing problems. In this study, we will give a detailed derivation of the quaternion-valued gradient operator with associated properties and then apply it to different areas. In particular, it will be employed to derive the quaternion-valued LMS (QLMS) algorithm and its sparse versions for adaptive beamforming for vector sensor arrays, and another one is its application to wind profile prediction in combination with the classic computational fluid dynamics (CFD) approach. For the adaptive beamforming problem for vector sensor arrays, we consider the crossed- dipole array and the problem of how to reduce the number of sensors involved in the adap- tive beamforming process, so that reduced system complexity and energy consumption can be achieved, whereas an acceptable performance can still be maintained, which is particularly use- ful for large array systems. The quaternion-valued steering vector model for crossed-dipole arrays will be employed, and a reweighted zero attracting (RZA) QLMS algorithm is then pro- posed by introducing a RZA term to the cost function of the original QLMS algorithm. The RZA term aims to have a closer approximation to the l0 norm so that the number of non-zero valued coefficients can be reduced more effectively in the adaptive beamforming process. For wind profile prediction, it can be considered as a signal processing problem and we can solve it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,wind flow analysis is also a classical problem in the CFD field, which employs various simulation methods and models to calculate the speed of wind flow at different time. It is accurate but time-consuming with high computational cost. To tackle the problem, a combined approach based on synergies between the statistical signal processing approach and the CFD approach is proposed. There are different ways of combining the signal processing approach and the CFD approach to obtain a more effective and efficient method for wind profile prediction. In the combined method, the signal processing part employs the QLMS algorithm, while for the CFD part, large eddy simulation (LES) based on the Smagorinsky subgrid-scale (SGS) model will be employed so that more efficient wind profile prediction can be achieved

Modélisation bayésienne et robotique

This document describes my research around Bayesian modeling and robotics. My work started with the modeling of biological processes before evolving towards robotics. In both cases, I was interested in both perception and action. I first proposed a model of human perception of planar surfaces with optic flow which fuses in a single framework two concurrent hypotheses of the literature. I also proposed and compared several models of eye movement selection in a Multiple Object Tracking task. I was able to show that the model with explicit uncertainty was the closest to the subjects eye movements.In robotics, I worked on the state estimation of several robots with classical filtering techniques but also including fusion of multiple sources of information of various nature and characteristics. I also discuss the Iterative Closest Point algorithm for which we proposed a more rigorous method for evaluating the different variants. The last piece of work I present deals with online three-dimensional path planning and execution of a tracked robot with significant climbing capabilities.I conclude this document with perspectives on what I call situated robotics, that is robots not taken in isolation but embedded in a sensorized environment shared with humans.Ce document décrit mes travaux de recherche autour de la modélisation bayésienne et de la robotique. Mon travail a commencé par la modélisation de processus biologiques avant, dans un deuxième temps, d'évoluer vers la robotique. Dans les deux cas, je me suis intéressé à la fois à la perception et à l'action. J'ai donc proposé un modèle de la perception humaine de plans par le flux optique qui réunit deux hypothèses de la littérature dans un cadre unique. J'ai aussi proposé et comparé différents modèle de la sélection de mouvement oculaire dans une tâche de suivi multi-cibles, et montré que le modèle prenant en compte explicitement l'incertitude proposait des mouvements plus proches de ceux des sujets.Du côté robotique, j'ai travaillé sur l'estimation d'état de plusieurs robots avec des techniques classiques de filtrage mais en incluant la fusion de plusieurs sources d'informations de nature et caractéristiques différentes. Je discute aussi de l'algorithme d'Iterative Closest Point pour proposer une méthode plus rigoureuse d'évaluation des différentes variantes. Le dernier travail que je présente concerne la planification en ligne et l'exécution de chemin pour un robot à chenille avec des capacités de franchissement importantes.Je conclus ce document par des perspectives de travail sur ce que j'appelle la robotique située, c'est-à-dire des robots non plus isolés mais plongés dans un environnement équipé de capteurs et partagé avec des humains

Understanding magmatic processes and seismo-volcano source localization with multicomponent seismic arrays

Dans cette thèse, nous étudions le problème de la localisation de sources sismo-volcanique, à partir des données enregistrées par des réseaux de capteurs composés de nouveaux sismomètres à trois composantes (3C). Nous nous concentrerons sur le volcan Ubinas, l'un des plus actifs au Pérou. Nous développons une nouvelle approche (MUSIC-3C) basée sur la méthode MUSIC permetant de retourner les 3 paramètres utiles (lenteur, azimut et incidence). Pour valider notre méthodologie, nous analysons des sources synthétiques propagées en tenant compte de la topographie du volcan Ubinas. Dans cette expérience, les données synthétiques ont été générées pour plusieurs sources situées à différentes profondeurs sous le cratère Ubinas. Nous utilisons l'algorithme MUSIC-3C pour les relocaliser. Nous traitons également des données réelles provenant d'une expérience de terrain menée sur le volcan Ubinas (Pérou) en 2009 par les équipes de recherche de l'IRD-France (Institut de Recherche pour le Déveleppment), UCD l'Irlande (projet VOLUME) et l'Institut de Géophysique du Pérou (IGP). Nous utilisons l'algorithme MUSIC-3C pour localiser les événements explosifs (type vulcanien), ce qui nous permet d'identifier et d'analyser les processus physiques de ces événements, à la suite de cette analyse, nous avons trouvé deux sources pour chaque explosion situées à 300 m et 1100 m en dessous du fond du cratère actif. Basé sur les mécanismes éruptifs proposés pour d'autres volcans du même type, nous interprétons la position de ces sources ainsi que les limites du conduit éruptif impliqué dans le processus de fragmentation.In this thesis, we study the seismo-volcanic source localization using data recorded by new sensor arrays composed of three-component (3C) seismometers deployed on Ubinas stratovolcano (Peru). We develop a new framework (MUSIC-3C) of source localization method based on the well-known MUSIC algorithm. To investigate the performance of the MUSIC-3C method, we use synthetic datasets designed from eight broadband isotropic seismic sources located beneath the crater floor at different depths. The fundamental scheme of the MUSIC-3C method exploits the fact of the cross-spectral matrix of 3C array data, corresponding to the first seismic signal arrivals, provides of useful vector components (slowness, back-azimuth and incidence angle) from the seismic source. Application of the MUSIC-3C method on synthetic datasets shows the recovery of source positions. Real data used in this study was collected during seismic measurements with two seismic antennas deployed at Ubinas volcano in 2009, whose experiment conduced by volcanic teams of IRD-France (l'Institute de Recherche pour le Déveleppment), Geophysics group University College Dublin Ireland and Geophysical Institute of Peru (IGP). We apply the MUSIC-3C algorithm to investigate wave fields associated with the magmatic activity of Ubinas volcano. These analysis evidence a complex mechanism of vulcanian eruptions in which their seismic sources are found at two separated sources located at depths of 300 m and 1100 m beneath the crater floor. This implies the reproduction of similar mechanisms into the conduit. Based on the eruptive mechanisms proposed for other volcanoes of the same type, we interpret the position of this sources as the limits of the conduit portion that was involved in the fragmentation process.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF