Title: Algebraic Approaches to Elementary Excitations in Media with Broken Spatial or Time-reversal Symmetry Author: Kay Condie Erb Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: Ing. Jiří Hlinka, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Structural phase transitions with macroscopic symmetry breaking can be divided into 212 non-magnetic species according to the mutual spatial orien- tation of the point groups of both phases. Classification into the given species implies a set of universal transition properties such as the number of macroscopic domain states of the low-symmetry phase and their distinguishability by order parameter. In this work, the distinguishability of macroscopic domain states by all order pa- rameters which transform as vectors or vectorlike quantities (called bidirectors) was studied. For solving this task, a computer algorithm was designed which enabled an explicit listing of all vector and vectorlike order parameters, not only for the 212 non-magnetic species, but even for all 1602 magnetic species which includes transitions between crystallographic gray and bicolor point groups. In addition, irreducible representations of the 122 magnetic crystallographic point groups which transform as vectors or vectorlike quantities are...

L’étude de dimensionnement d’un réseau cellulaire est une phase de conception qui doit permettre de déterminer les performances d’un système dans une configuration donnée. Elle inclut l’étude de couverture et l’analyse de trafic. De complexes simulations sont possibles pour connaître les paramètres de performances d’un réseau mais seules les études analytiques fournissent des résultats rapides. Par ailleurs, pour faire face à la demande de hauts débits, à la rareté du spectre fréquentiel et à l’impossibilité d’émettre à de plus fortes puissances, de nouvelles techniques de transmissions sont apparues. Nous sommes ainsi passés d’un système classique à une seule antenne à des systèmes à multiple antennes et même à des scénarios de coopération entre stations de base. Dans cette thèse, nous proposons des modèles analytiques pour l’étude des performances, notamment en termes de probabilités de coupure, de ces évolutions des réseaux cellulaires. Dans une première phase, nous considérons des systèmes multicellulaires à une antenne émettrice et une antenne réceptrice (SISO). Nous proposons deux méthodes d’étude de l’impact conjoint de l’affaiblissement de parcours, de l’effet de masque et des évanouissements rapides. Nous étudions, par la suite, un système à large bande utilisant le retournement temporel comme technique de transmission. Dans une deuxième phase, nous considérons des systèmes multicellulaires à antennes multiple à l’émission ou à la réception (MISO/MIMO) implémentant les schémas de diversité Alamouti et de combinaison par rapport maximal (MRC). Ensuite, nous considérons un système multicellulaire multi-utilisateurs à précodage de forçage à zéro (ZFBF). / The implementation of cellular systems have aroused issues related to the design of cellular networks termed to as network dimensioning. It includes the coverage estimation and thetraffic analysis. Simple models and methods are required to reduce the time consumption of these two analysis. At the same time, the growing demand for higher data rates constrained by the scarcity of frequency spectrum, and the requirements in terms of power consumption reduction make the telecommunication community think about new transmission techniques moving from the classical single antenna systems to multiple antenna systems and even the newly envisaged cooperative systems. In this thesis, we provide analytical models to assess the performance of these different cellular network evolutions in terms of outage probabilities. In a first study, we consider multicellular single input single output (SISO) systems. First, we propose two accurate methods to study the joint impact of path-loss, shadowing and fast fading. This system has so far been studied either considering the only impact of path-loss and Rayleigh fading, or considering the same channel model as in our case but providing very complex outage probability expressions. Then, we provide an outage probability expression in a wideband communication context implementing the Time Reversal (TR) transmission technique considering the impact of fast fading. In a second study, we focus on multiple antenna systems. We study the performance of a Multiple Input Multiple Output (MIMO) system implementing a transmit and a receivediversity schemes namely the Alamouti code and the Maximum Ratio Combining (MRC).

L'objectif de la thèse a été de mettre en place dans un premier temps des modèles analytiques et statistiques permettant d'évaluer les performances d'un système à retournement temporel de fortes-puissances puis de les vérifier grâce à des mesures.Des campagnes de mesures ont alors permis de vérifier les modèles. Des simulations numériques ont aussi montrées les possibilités offertes par un tel système.En parallèle, des travaux sur l'impact des antennes dans une chambre réverbérantes ont été menés afin d'évaluer les performances d'un système ayant plusieurs sorties.Les résultats de thèses ont permis l'élaboration de nouvelles métriques des performances du système.Le développement d'un prototype a nécessité la conception et la réalisation de chacune des branches du système complet.Les premières campagnes de mesures ont permis la validation complète des modèles. / A main aspect of this work has been to develop analytical and statistical models of the power efficiency of a time-reversal amplification system (TRAS).It is also important to evaluate the efficiency of a reverberation chamber. This allows quantifying the power received by one or more antenna when the reverberation chamber is excited. This factor is important when considering construction of the most efficient chamber for time-reversal amplification.Measurements assessing the loading effect of antennas in reverberation chambers when the field can be considered diffused were also undertaken. The study focuses on the evaluation of the varying quality factor when adding loaded antennas in the chamber.Another focus of this work is to evaluate the ratios between signals during calibration and focusing phase. An important aspect of the studies presented in this work thus concerns evaluation of the maximum value of the impulse response in a complex propagation system.We also present the power gain of time-reversal techniques and its statistical advantages compared to a classic use of a reverberation chamber.The development of a prototype required the design and implementation of each of the branches of the complete systems.The first measurement campaigns allowed the complete validation of the models.

The Global Positioning System (GPS) provides good precision on a global scale, but is not suitable for indoor applications. Indoor positioning systems (IPS) aim to provide high precision position information in an indoor environment. IPS has huge market opportunity with a growing number of commercial and consumer applications especially as Internet of Things (IoT) develops. This paper studies an IPS approach using audible sound and pseudo-noise (PN) based time difference of arrival (TDoA). The system’s infrastructure consists of synchronized speakers. The object to be located, or receiver, extracts TDoA information and uses multilateration to calculate its position. The proposed IPS utilizes sound waves since they travel much slower compared to electromagnetic waves, allowing for easier measurements. Additionally, the audible spectrum has a large availability of low directivity speakers and microphones allowing for a large coverage area compared to highly directive ultrasonic transceivers. This paper experimentally evaluates the feasibility of the proposed IPS.

Physics-based fluid simulation often produces unpredictable behavior that is difficult for artists to control. We present a new method for art directing smoke animation using time reversed simulation. Given a final fluid configuration, our method steps backward in time generating a sequence that, when played forward, is visually similar to traditional forward simulations. This will give artists better control by allowing them to start from any timestep of the simulation. We address a number of challenges associated with time reversal including generating a believable final configuration and reversing entropy.

Physics-based fluid simulation often produces unpredictable behavior that is difficultfor artists to control. We present a new method for art directing smoke animation using timereversed simulation. Given a final fluid configuration, our method steps backward in timegenerating a sequence that, when played forward, is visually similar to traditional forwardsimulations. This will give artists better control by allowing them to start from any timestepof the simulation. We address a number of challenges associated with time reversal includinggenerating a believable final configuration and reversing entropy.

The time reversal (TR) process manipulates a system's impulse response in order to focus a peak of acoustic energy at a specific location in space and time. This technique has been implemented in both fluid and solid media for purposes ranging from communications to source localization. This thesis will examine both the implementation and processing of TR for nondestructive evaluation in steel, specializing in nonlinear detection methods. A series of steel samples are inspected for stress corrosion cracking (SCC) using TR focusing to excite nonlinearities inherent in cracks. It is determined that SCC exists in the expected regions of the steel samples and that an induced increase in SCC corresponds to an increase in detected nonlinearity. In addition to this, a study is shown wherein TR signal processing is optimized for the detection of cracks. The TR impulse response is modified in a number of ways with the primary goal of increasing the amplitude of the TR focus. Each of these modifications is experimentally scrutinized for characteristics necessary for application to nondestructive evaluation, and ultimately one is chosen that amplifies TR focusing without increasing system nonlinearity. The optimized technique, decay compensation TR, is employed in the detection of SCC and is found to be as or perhaps even more successful than typical TR nondestructive evaluation methods.

Time reversal is a method often used to focus sound to a desired location, and works best in a reverberant environment. The effect of focus location within a reverberant environment is presented first, revealing that proximity to reflecting surfaces has a significant effect on the amplitude of the focus both experimentally and when using a modal summation model. These effects are a primary component to creating focus signals at high amplitudes. High-amplitude focusing experiments show that when multiple sources are used simultaneously to generate a focus, a peak amplitude pressure spike of 200 dB can be achieved in air. A pressure spike of this amplitude has multiple nonlinear characteristics, and an investigation into the spatiotemporal features and harmonic content of these signals was conducted. The peak amplitude of the focus signal also increases in amplitude nonlinearly as the loudspeaker volume is linearly increased. This nonlinear increase is the primary subject of investigation in this work. Experimental and computational methods are implemented in order to understand the mechanisms driving the nonlinear increases observed when the sources are combined acoustically as opposed to linear superposition of the contributions from each sound in post-processing. Finally, models of converging high-amplitude waves are generated using the k-Wave© package for MATLAB©. These show a similar nonlinear increase in amplitudes, supporting the hypothesis of a Mach wave coalescence. A COMSOL© finite element model allows visualization of the converging waves with Mach stems forming in free space to cause the nonlinear amplification.

In absence of external fields, vibrational modes of periodic systems are usually considered as linearly polarized and, as such, they do not carry angular momentum. Our work proves that non-adiabatic effects due to the electron-phonon coupling are time-reversal symmetry breaking interactions for the vibrational field in systems with non-collinear magnetism and large spin-orbit coupling. Since in these systems the deformation potential matrix elements are necessarily complex, a nonzero synthetic gauge field (Berry curvature) arises in the dynamic equations of the ionic motion. As a result, phonon modes are elliptically polarized in the non-adiabatic framework and intrinsic vibrational angular momenta occur even for non-degenerate modes and without external probes. These results are validated by performing fully relativistic ab-initio calculations on two insulating platinum clusters and a metallic manganese compound, with non-collinear magnetism. In both cases, non-adiabatic vibrational modes carry sizeable angular momenta comparable to the orbital electronic ones in itinerant ferromagnets.

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