Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber-reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three-dimensional solid approach and first-order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright (C) 2012 John Wiley & Sons, Ltd.

Local Structure of Hydrogen-Bonded Liquids

Ordinary yet unique, water is the substance on which life is based. Water seems, at first sight, to be a very simple molecule, consisting of two hydrogen atoms attached to one oxygen. Its small size belies the complexity of its action and its numerous anomalies, central to a broad class of important phenomena, ranging from global current circulation, terrestrial water and CO2 cycles to corrosion and wetting. The explanation of this complex behavior comes from water's unique ability to form extensive three-dimensional networks of hydrogen-bonds, whose nature and structures, in spite of a great deal of efforts involving a plethora of experimental and theoretical techniques, still lacks a complete scientific understanding. This thesis is devoted to the study of the local structure of hydrogen-bonded liquids, with a particular emphasis on water, taking advantage of a combination of core-level spectroscopies and density functional theory spectra calculations. X-ray absorption, in particular, is found to be sensitive to the local hydrogen-bond environment, thus offering a very promising tool for spectroscopic identification of specific structural configurations in water, alcohols and aqueous solutions. More specifically, the characteristic spectroscopic signature of the broken hydrogen-bond at the hydrogen side is used to analyze the structure of bulk water, leading to the finding that most molecules are arranged in two hydrogen-bond configurations, in contrast to the picture provided by molecular dynamics simulations. At the liquid-vapor interface, an interplay of surface sensitive measurements and theoretical calculations enables us to distinguish a new interfacial species in equilibrium with the gas. In a similar approach the cluster form of the excess proton in highly concentrated acid solutions and the different coordination of methanol at the vacuum interface and in the bulk can also be clearly identified. Finally the ability of core-level spectroscopies, aided by sophisticated density functional theory calculations, to directly probe the valence electronic structure of a system is used to observe the nature of the interaction between water molecules and solvated ions in solution. Water around transition metal ions is found to interact with the solute via orbital mixing with the metal d-orbitals. The hydrogen-bond between water molecules is explained in terms of electrostatic interactions enhanced by charge rehybridization in which charge transfer between connecting molecules is shown to be fundamental.

Longitudinal bar buckling behavior

Reinforced concrete columns might fail because of buckling of the longitudinal reinforcing bar when exposed to earthquake motions. Depending on the hoop stiffness and the length-over-diameter ratio, the instability can be local (in between two subsequent hoops) or global (the buckling length comprises several hoop spacings). To get insight into the topic, an extensive literary research of 19 existing models has been carried out including different approaches and assumptions which yield different results. Finite element fiberanalysis was carried out to study the local buckling behavior with varying length-over-diameter and initial imperfection-over-diameter ratios. The comparison of the analytical results with some experimental results shows good agreement before the post buckling behavior undergoes large deformation. Furthermore, different global buckling analysis cases were run considering the influence of different parameters; for certain hoop stiffnesses and length-over-diameter ratios local buckling was encountered. A parametric study yields an adimensional critical stress in function of a stiffness ratio characterized by the reinforcement configuration. Colonne in cemento armato possono collassare per via dell’instabilità dell’armatura longitudinale se sottoposte all’azione di un sisma. In funzione della rigidezza dei ferri trasversali e del rapporto lunghezza d’inflessione-diametro, l’instabilità può essere locale (fra due staffe adiacenti) o globale (la lunghezza d’instabilità comprende alcune staffe). Per introdurre alla materia, è proposta un’esauriente ricerca bibliografica di 19 modelli esistenti che include approcci e ipotesi differenti che portano a risultati distinti. Tramite un’analisi a fibre e elementi finiti si è studiata l’instabilità locale con vari rapporti lunghezza d’inflessione-diametro e imperfezione iniziale-diametro. Il confronto dei risultati analitici con quelli sperimentali mostra una buona coincidenza fino al raggiungimento di grandi spostamenti. Inoltre, il caso d’instabilità globale è stato simulato valutando l’influenza di vari parametri; per certe configurazioni di rigidezza delle staffe e lunghezza d’inflessione-diametro si hanno ottenuto casi di instabilità locale. Uno studio parametrico ha permesso di ottenere un carico critico adimensionale in funzione del rapporto di rigidezza dato dalle caratteristiche dell’armatura.

A new insight in stress recovery tecniques and hessian reconstruction methods

Stress recovery techniques have been an active research topic in the last few years since, in 1987, Zienkiewicz and Zhu proposed a procedure called Superconvergent Patch Recovery (SPR). This procedure is a last-squares fit of stresses at super-convergent points over patches of elements and it leads to enhanced stress fields that can be used for evaluating finite element discretization errors. In subsequent years, numerous improved forms of this procedure have been proposed attempting to add equilibrium constraints to improve its performances. Later, another superconvergent technique, called Recovery by Equilibrium in Patches (REP), has been proposed. In this case the idea is to impose equilibrium in a weak form over patches and solve the resultant equations by a last-square scheme. In recent years another procedure, based on minimization of complementary energy, called Recovery by Compatibility in Patches (RCP) has been proposed in. This procedure, in many ways, can be seen as the dual form of REP as it substantially imposes compatibility in a weak form among a set of self-equilibrated stress fields. In this thesis a new insight in RCP is presented and the procedure is improved aiming at obtaining convergent second order derivatives of the stress resultants. In order to achieve this result, two different strategies and their combination have been tested. The first one is to consider larger patches in the spirit of what proposed in [4] and the second one is to perform a second recovery on the recovered stresses. Some numerical tests in plane stress conditions are presented, showing the effectiveness of these procedures. Afterwards, a new recovery technique called Last Square Displacements (LSD) is introduced. This new procedure is based on last square interpolation of nodal displacements resulting from the finite element solution. In fact, it has been observed that the major part of the error affecting stress resultants is introduced when shape functions are derived in order to obtain strains components from displacements. This procedure shows to be ultraconvergent and is extremely cost effective, as it needs in input only nodal displacements directly coming from finite element solution, avoiding any other post-processing in order to obtain stress resultants using the traditional method. Numerical tests in plane stress conditions are than presented showing that the procedure is ultraconvergent and leads to convergent first and second order derivatives of stress resultants. In the end, transverse stress profiles reconstruction using First-order Shear Deformation Theory for laminated plates and three dimensional equilibrium equations is presented. It can be seen that accuracy of this reconstruction depends on accuracy of first and second derivatives of stress resultants, which is not guaranteed by most of available low order plate finite elements. RCP and LSD procedures are than used to compute convergent first and second order derivatives of stress resultants ensuring convergence of reconstructed transverse shear and normal stress profiles respectively. Numerical tests are presented and discussed showing the effectiveness of both procedures.

Confocal microscopy applied to the study of single entity fluorescence and light scattering

A sample scanning confocal optical microscope (SCOM) was designed and constructed in order to perform local measurements of fluorescence, light scattering and Raman scattering. This instrument allows to measure time resolved fluorescence, Raman scattering and light scattering from the same diffraction limited spot. Fluorescence from single molecules and light scattering from metallic nanoparticles can be studied. First, the electric field distribution in the focus of the SCOM was modelled. This enables the design of illumination modes for different purposes, such as the determination of the three-dimensional orientation of single chromophores. Second, a method for the calculation of the de-excitation rates of a chromophore was presented. This permits to compare different detection schemes and experimental geometries in order to optimize the collection of fluorescence photons. Both methods were combined to calculate the SCOM fluorescence signal of a chromophore in a general layered system. The fluorescence excitation and emission of single molecules through a thin gold film was investigated experimentally and modelled. It was demonstrated that, due to the mediation of surface plasmons, single molecule fluorescence near a thin gold film can be excited and detected with an epi-illumination scheme through the film. Single molecule fluorescence as close as 15nm to the gold film was studied in this manner. The fluorescence dynamics (fluorescence blinking and excited state lifetime) of single molecules was studied in the presence and in the absence of a nearby gold film in order to investigate the influence of the metal on the electronic transition rates. The trace-histogram and the autocorrelation methods for the analysis of single molecule fluorescence blinking were presented and compared via the analysis of Monte-Carlo simulated data. The nearby gold influences the total decay rate in agreement to theory. The gold presence produced no influence on the ISC rate from the excited state to the triplet but increased by a factor of 2 the transition rate from the triplet to the singlet ground state. The photoluminescence blinking of Zn0.42Cd0.58Se QDs on glass and ITO substrates was investigated experimentally as a function of the excitation power (P) and modelled via Monte-Carlo simulations. At low P, it was observed that the probability of a certain on- or off-time follows a negative power-law with exponent near to 1.6. As P increased, the on-time fraction reduced on both substrates whereas the off-times did not change. A weak residual memory effect between consecutive on-times and consecutive off-times was observed but not between an on-time and the adjacent off-time. All of this suggests the presence of two independent mechanisms governing the lifetimes of the on- and off-states. The simulated data showed Poisson-distributed off- and on-intensities, demonstrating that the observed non-Poissonian on-intensity distribution of the QDs is not a product of the underlying power-law probability and that the blinking of QDs occurs between a non-emitting off-state and a distribution of emitting on-states with different intensities. All the experimentally observed photo-induced effects could be accounted for by introducing a characteristic lifetime tPI of the on-state in the simulations. The QDs on glass presented a tPI proportional to P-1 suggesting the presence of a one-photon process. Light scattering images and spectra of colloidal and C-shaped gold nano-particles were acquired. The minimum size of a metallic scatterer detectable with the SCOM lies around 20 nm.

Computer simulations of charged systems in partially periodic geometries

This work presents algorithms for the calculation of the electrostatic interaction in partially periodic systems. The framework for these algorithms is provided by the simulation package ESPResSo, of which the author was one of the main developers. The prominent features of the program are listed and the internal structure is described. In the following, algorithms for the calculation of the Coulomb sum in three dimensionally periodic systems are described. These methods are the foundations for the algorithms for partially periodic systems presented in this work. Starting from the MMM2D method for systems with one non-periodic coordinate, the ELC method for these systems is developed. This method consists of a correction term which allows to use methods for three dimensional periodicity also for the case of two periodic coordinates. The computation time of this correction term is neglible for large numbers of particles. The performance of MMM2D and ELC are demonstrated by results from the implementations contained in ESPResSo. It is also discussed, how different dielectric constants inside and outside of the simulation box can be realized. For systems with one periodic coordinate, the MMM1D method is derived from the MMM2D method. This method is applied to the problem of the attraction of like-charged rods in the presence of counterions, and results of the strong coupling theory for the equilibrium distance of the rods at infinite counterion-coupling are checked against results from computer simulations. The degree of agreement between the simulations at finite coupling and the theory can be characterized by a single parameter gamma_RB. In the special case of T=0, one finds under certain circumstances flat configurations, in which all charges are located in the rod-rod plane. The energetically optimal configuration and its stability are determined analytically, which depends on only one parameter gamma_z, similar to gamma_RB. These findings are in good agreement with results from computer simulations.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

A sampling method for detecting buried objects using electromagnetic scattering

We consider a simple (but fully three-dimensional) mathematical model for the electromagnetic exploration of buried, perfect electrically conducting objects within the soil underground. Moving an electric device parallel to the ground at constant height in order to generate a magnetic field, we measure the induced magnetic field within the device, and factor the underlying mathematics into a product of three operations which correspond to the primary excitation, some kind of reflection on the surface of the buried object(s) and the corresponding secondary excitation, respectively. Using this factorization we are able to give a justification of the so-called sampling method from inverse scattering theory for this particular set-up.

Evaluation of Human Exposure to Magnetic Fields Generated by Electric Power Systems in Complex Configurations

The international growing concern for the human exposure to magnetic fields generated by electric power lines has unavoidably led to imposing legal limits. Respecting these limits, implies being able to calculate easily and accurately the generated magnetic field also in complex configurations. Twisting of phase conductors is such a case. The consolidated exact and approximated theory regarding a single-circuit twisted three-phase power cable line has been reported along with the proposal of an innovative simplified formula obtained by means of an heuristic procedure. This formula, although being dramatically simpler, is proven to be a good approximation of the analytical formula and at the same time much more accurate than the approximated formula found in literature. The double-circuit twisted three-phase power cable line case has been studied following different approaches of increasing complexity and accuracy. In this framework, the effectiveness of the above-mentioned innovative formula is also examined. The experimental verification of the correctness of the twisted double-circuit theoretical analysis has permitted its extension to multiple-circuit twisted three-phase power cable lines. In addition, appropriate 2D and, in particularly, 3D numerical codes for simulating real existing overhead power lines for the calculation of the magnetic field in their vicinity have been created. Finally, an innovative ‘smart’ measurement and evaluation system of the magnetic field is being proposed, described and validated, which deals with the experimentally-based evaluation of the total magnetic field B generated by multiple sources in complex three-dimensional arrangements, carried out on the basis of the measurement of the three Cartesian field components and their correlation with the field currents via multilinear regression techniques. The ultimate goal is verifying that magnetic induction intensity is within the prescribed limits.

Entwicklung eines pharmakologischen Modells zur Prüfung immuntherapeutischer Antikörper mit dreidimensionalen Tumorzellkulturen in vitro

In den letzten Jahren hat die Tumorbehandlung mit immunologischen Präparaten an Bedeutung gewonnen. Der allgemeine Ablauf der Testung eines Arzneimittelkandidaten sieht vor, zunächst in Zellkulturversuchen und Tierversuchen Wirkweise und Sicherheit, sowie voraussichtliche Abbauwege und mögliche Gefahren so beurteilen zu können, dass sie für einen Einsatz im Menschen in Frage kommen. Zur präklinischen in vitro-Testung werden dabei in der Regel Monolayer-Zellkulturen oder Einzelzellsuspensionen eingesetzt. Der Einsatz von 3D-Zellkulturmodellen, welche den Aufbau von Mikrometastasen oder intervaskuläre Areale in Tumoren exakter widerspiegeln, führt zu wesentlich besseren Voraussagen bezüglich der klinischen Wirksamkeit neuer Präparate. Das Ziel dieser Arbeit war daher die Entwicklung und Anwendung eines neuen 3D-Zellkulturbasierten Systems zur Testung trifunktionaler bispezifischer Antikörper für die Tumorbehandlung, welches sich auch auf andere vergleichbare Präparate übertragen lässt.rnIn meiner Arbeit konnte ich mehrere humane Tumorzelllinien definieren, mit denen es gelang, stabile Co-Kulturen von Multi Cellular Tumour Spheroids (MCTS) mit Peripheral Blood Mononuclear Cells (PBMC) in miniaturisierten Spinner-Flaschen zu etablieren. Spinner-Flaschen, in denen die im Kulturmedium befindlichen Immunzellen, MCTS und Therapeutika ständig frei zirkulieren, sind besonders für eine wirklichkeitsnahe Nachbildung der in vivo-Simulation mit disseminierten Tumorzellen oder mit malignem Aszites geeignet. Diese Art der Kultivierung erlaubte Beobachtungszeiten von ≥20 Tagen für eine große Bandbreite Analysemethoden. Zu den mit dem erstellten Protokoll standardmäßig durchführbaren Analysemethoden zählen unter anderem immunhistochemische Färbungen an Sphäroid-Gefrierschnitten, Vitalitätstest, Untersuchung der Plattierungs-Effizienz, Bestimmung der Sphäroidvolumina, Zytokinbestimmungen aus dem Medienüberstand mit Cytokine Bead Arrays, PCR-Analysen immunzellspezifischer Antigene, sowie durchflusszytometrische Analysen. Diese Methodenkombination erlaubt einen sehr detaillierten Einblick in die Wirkweise und Effizienz neuer Immuntherapeutika aus verschiedensten Blickwinkeln und stellt ein reproduzierbares Testsystem zur präklinischen Testung von Immuntherapeutika dar, das zukünftig als Bindeglied zwischen Monolayer-Zellkulturen und klinischen Prüfungen einen festen Platz einnehmen könnte.rnMit dem beschriebenen 3D-Zellkultur-System wurden in der vorliegenden Arbeit die trifunktionalen bispezifischen Antikörper catumaxomab (unter dem Handelsnamen Removab® für die Behandlung maligner Ascites zugelassen) und ertumaxomab (derzeit in klinischen Prüfungen) hinsichtlich ihrer Wirkweise untersucht. Die Antikörper besitzen im Gegensatz zu herkömmlichen monoklonalen Antikörpern zwei verschiedene Bindungsarme, einer gegen CD3 auf T-Zellen, der zweite gegen EpCAM respektive Her2/neu - beides weit verbreitete Tumorantigene - gerichtet. An ihrem Fc-Teil besitzen sie eine dritte Bindungskapazität, über welche sie an Fcγ RI, -IIa und -III positive akzessorische Zellen binden. Diese Kombination ermöglicht theoretisch die Ausbildung eines Tri-Zell-Komplexes aus T-Zelle, Tumorzelle und akzessorischer Zelle. Dies stellt eine wirkungsvolle Therapieoption unter Ausnutzung der körpereigenen, immunologischen Abwehr dar. rnIm Rahmen dieser Arbeit wurde gezeigt, dass beide Antikörper eine Größenreduktion der Sphäroide mit den entsprechenden Tumorantigenen in gleichem Maße bewirkten und die Plattierungseffizienz durch ertumaxomab dosisabhängig reduziert wurde. Mit dem erstellten Testsystem konnte der Wirkmechanismus von catumaxomab auf Sphäroide der Zelllinie FaDu (Kopf-Hals-Plattenepithelkarzinom) detaillierter gezeigt werden: catumaxomab wirkte dosisabhängig auf die Reduktion der Sphäroidvolumina und die zunehmende Infiltration von CD45+ Zellen, die als T-, NK- und/oder dendritische Zellen identifiziert wurden. Des Weiteren rief die catumaxomab-Gabe eine verstärkte Ausschüttung der Zytokine IL-2, IFN-γ und TNF-α hervor. Diese Ergebnisse sprechen dafür, dass catumaxomab die zelluläre Immunantwort aktiviert.rnDie Standard-Tumorbehandlung beinhaltet die Gabe von Chemotherapeutika. Oft werden dafür Zytostatika mit dem unerwünschten Nebeneffekt auch gesunde proliferierende Zellen anzugreifen verwendet. Dies kann prinzipiell auch die Wirksamkeit der Antikörper-Therapie beeinflussen. Aus diesem Grund wurden in dieser Arbeit zusätzlich vergleichende Kombinations-Versuche mit catumaxomab und einem gängigen Zytostatikum - Cisplatin - durchgeführt. Mit Untersuchungen der Sphäroidvolumina, Vitalitätstests und Plattierungseffizienz konnte gezeigt werden, dass die Wirkung von catumaxomab bei gleichzeitiger Anwendung beider Therapeutika aufrecht erhalten bleibt und diese sogar additiv verstärkt wird. Eine Kombinationstherapie im Menschen ist daher denkbar.rnrn

Konstruktion und Analyse einer funktionalen Renormierungsgruppengleichung für Gravitation im Einstein-Cartan-Zugang

Während das Standardmodell der Elementarteilchenphysik eine konsistente, renormierbare Quantenfeldtheorie dreier der vier bekannten Wechselwirkungen darstellt, bleibt die Quantisierung der Gravitation ein bislang ungelöstes Problem. In den letzten Jahren haben sich jedoch Hinweise ergeben, nach denen metrische Gravitation asymptotisch sicher ist. Das bedeutet, daß sich auch für diese Wechselwirkung eine Quantenfeldtheorie konstruieren läßt. Diese ist dann in einem verallgemeinerten Sinne renormierbar, der nicht mehr explizit Bezug auf die Störungstheorie nimmt. Zudem sagt dieser Zugang, der auf der Wilsonschen Renormierungsgruppe beruht, die korrekte mikroskopische Wirkung der Theorie voraus. Klassisch ist metrische Gravitation auf dem Niveau der Vakuumfeldgleichungen äquivalent zur Einstein-Cartan-Theorie, die das Vielbein und den Spinzusammenhang als fundamentale Variablen verwendet. Diese Theorie besitzt allerdings mehr Freiheitsgrade, eine größere Eichgruppe, und die zugrundeliegende Wirkung ist von erster Ordnung. Alle diese Eigenschaften erschweren eine zur metrischen Gravitation analoge Behandlung.rnrnIm Rahmen dieser Arbeit wird eine dreidimensionale Trunkierung von der Art einer verallgemeinerten Hilbert-Palatini-Wirkung untersucht, die neben dem Laufen der Newton-Konstante und der kosmologischen Konstante auch die Renormierung des Immirzi-Parameters erfaßt. Trotz der angedeuteten Schwierigkeiten war es möglich, das Spektrum des freien Hilbert-Palatini-Propagators analytisch zu berechnen. Auf dessen Grundlage wird eine Flußgleichung vom Propertime-Typ konstruiert. Zudem werden geeignete Eichbedingungen gewählt und detailliert analysiert. Dabei macht die Struktur der Eichgruppe eine Kovariantisierung der Eichtransformationen erforderlich. Der resultierende Fluß wird für verschiedene Regularisierungsschemata und Eichparameter untersucht. Dies liefert auch im Einstein-Cartan-Zugang berzeugende Hinweise auf asymptotische Sicherheit und damit auf die mögliche Existenz einer mathematisch konsistenten und prädiktiven fundamentalen Quantentheorie der Gravitation. Insbesondere findet man ein Paar nicht-Gaußscher Fixpunkte, das Anti-Screening aufweist. An diesen sind die Newton-Konstante und die kosmologische Konstante jeweils relevante Kopplungen, wohingegen der Immirzi-Parameter an einem Fixpunkt irrelevant und an dem anderen relevant ist. Zudem ist die Beta-Funktion des Immirzi-Parameters von bemerkenswert einfacher Form. Die Resultate sind robust gegenüber Variationen des Regularisierungsschemas. Allerdings sollten zukünftige Untersuchungen die bestehenden Eichabhängigkeiten reduzieren.

Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.

Numerical and experimental investigation of turbulent dissipation

Turbulent energy dissipation is presented in the theoretical context of the famous Kolmogorov theory, formulated in 1941. Some remarks and comments about this theory help the reader understand the approach to turbulence study, as well as give some basic insights to the problem. A clear distinction is made amongst dissipation, pseudo-dissipation and dissipation surrogates. Dissipation regulates how turbulent kinetic energy in a flow gets transformed into internal energy, which makes this quantity a fundamental characteristic to investigate in order to enhance our understanding of turbulence. The dissertation focuses on experimental investigation of the pseudo-dissipation. Indeed this quantity is difficult to measure as it requires the knowledge of all the possible derivatives of the three dimensional velocity field. Once considering an hot-wire technique to measure dissipation we need to deal with surrogates of dissipation, since not all the terms can be measured. The analysis of surrogates is the main topic of this work. In particular two flows, the turbulent channel and the turbulent jet, are considered. These canonic flows, introduced in a brief fashion, are often used as a benchmark for CFD solvers and experimental equipment due to their simple structure. Observations made in the canonic flows are often transferable to more complicated and interesting cases, with many industrial applications. The main tools of investigation are DNS simulations and experimental measures. DNS data are used as a benchmark for the experimental results since all the components of dissipation are known within the numerical simulation. The results of some DNS were already available at the start of this thesis, so the main work consisted in reading and processing the data. Experiments were carried out by means of hot-wire anemometry, described in detail on a theoretical and practical level. The study of DNS data of a turbulent channel at Re=298 reveals that the traditional surrogate can be improved Consequently two new surrogates are proposed and analysed, based on terms of the velocity gradient that are easy to measure experimentally. We manage to find a formulation that improves the accuracy of surrogates by an order of magnitude. For the jet flow results from a DNS at Re=1600 of a temporal jet, and results from our experimental facility CAT at Re=70000, are compared to validate the experiment. It is found that the ratio between components of the dissipation differs between DNS and experimental data. Possible errors in both sets of data are discussed, and some ways to improve the data are proposed.

Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.