Cordas cósmicas e gravitação planar de ordem superior

The possibility of generalizing gravity in 2+1 dimensions to include higher-derivative terms, thereby allowing for a dynamical theory, opens up a variety of new interesting questions. This is in great contrast with pure Einstein gravity which is a generally covariant theory that has no degrees of freedom - a peculiarity that, in a sense, renders it a little insipid and odorless. The research on gravity of particles moving in a plane, that is, living in flatland, within the context of higher-derivative gravity, leads to novel and interesting effects. For instance, the generation of gravity, antigravity, and gravitational shielding by the interaction of massive scalar bosons via a graviton exchange. In addition, the gravitational deffection angle of a photon, unlike that of Einstein gravity, is dependent of the impact parameter. On the other hand, the great drawback to using linearized general relativity for describing a gravitating string is that this description leads to some unphysical results such as: (i) lack of a gravity force in the nonrelativistic limit; (ii) gravitational deffection independent of the impact parameter. Interesting enough, the effective cure for these pathologies is the replacement of linearized gravity by linearized higher-derivative gravity. We address these issues here

Damage detection in beams by using artificial neural networks and dynamical parameters

In this paper is presented a multilayer perceptron neural network combined with the Nelder-Mead Simplex method to detect damage in multiple support beams. The input parameters are based on natural frequencies and modal flexibility. It was considered that only a number of modes were available and that only vertical degrees of freedom were measured. The reliability of the proposed methodology is assessed from the generation of random damages scenarios and the definition of three types of errors, which can be found during the damage identification process. Results show that the methodology can reliably determine the damage scenarios. However, its application to large beams may be limited by the high computational cost of training the neural network.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

The photosynthetic bacterial reaction center in native and artificial envirnoments: effects on light-induced electron transfer

In this thesis we focussed on the characterization of the reaction center (RC) protein purified from the photosynthetic bacterium Rhodobacter sphaeroides. In particular, we discussed the effects of native and artificial environment on the light-induced electron transfer processes. The native environment consist of the inner antenna LH1 complex that copurifies with the RC forming the so called core complex, and the lipid phase tightly associated with it. In parallel, we analyzed the role of saccharidic glassy matrices on the interplay between electron transfer processes and internal protein dynamics. As a different artificial matrix, we incorporated the RC protein in a layer-by-layer structure with a twofold aim: to check the behaviour of the protein in such an unusual environment and to test the response of the system to herbicides. By examining the RC in its native environment, we found that the light-induced charge separated state P+QB - is markedly stabilized (by about 40 meV) in the core complex as compared to the RC-only system over a physiological pH range. We also verified that, as compared to the average composition of the membrane, the core complex copurifies with a tightly bound lipid complement of about 90 phospholipid molecules per RC, which is strongly enriched in cardiolipin. In parallel, a large ubiquinone pool was found in association with the core complex, giving rise to a quinone concentration about ten times larger than the average one in the membrane. Moreover, this quinone pool is fully functional, i.e. it is promptly available at the QB site during multiple turnover excitation of the RC. The latter two observations suggest important heterogeneities and anisotropies in the native membranes which can in principle account for the stabilization of the charge separated state in the core complex. The thermodynamic and kinetic parameters obtained in the RC-LH1 complex are very close to those measured in intact membranes, indicating that the electron transfer properties of the RC in vivo are essentially determined by its local environment. The studies performed by incorporating the RC into saccharidic matrices evidenced the relevance of solvent-protein interactions and dynamical coupling in determining the kinetics of electron transfer processes. The usual approach when studying the interplay between internal motions and protein function consists in freezing the degrees of freedom of the protein at cryogenic temperature. We proved that the “trehalose approach” offers distinct advantages with respect to this traditional methodology. We showed, in fact, that the RC conformational dynamics, coupled to specific electron transfer processes, can be modulated by varying the hydration level of the trehalose matrix at room temperature, thus allowing to disentangle solvent from temperature effects. The comparison between different saccharidic matrices has revealed that the structural and dynamical protein-matrix coupling depends strongly upon the sugar. The analyses performed in RCs embedded in polyelectrolyte multilayers (PEM) structures have shown that the electron transfer from QA - to QB, a conformationally gated process extremely sensitive to the RC environment, can be strongly modulated by the hydration level of the matrix, confirming analogous results obtained for this electron transfer reaction in sugar matrices. We found that PEM-RCs are a very stable system, particularly suitable to study the thermodynamics and kinetics of herbicide binding to the QB site. These features make PEM-RC structures quite promising in the development of herbicide biosensors. The studies discussed in the present thesis have shown that, although the effects on electron transfer induced by the native and artificial environments tested are markedly different, they can be described on the basis of a common kinetic model which takes into account the static conformational heterogeneity of the RC and the interconversion between conformational substates. Interestingly, the same distribution of rate constants (i.e. a Gamma distribution function) can describe charge recombination processes in solutions of purified RC, in RC-LH1 complexes, in wet and dry RC-PEM structures and in glassy saccharidic matrices over a wide range of hydration levels. In conclusion, the results obtained for RCs in different physico-chemical environments emphasize the relevance of the structure/dynamics solvent/protein coupling in determining the energetics and the kinetics of electron transfer processes in a membrane protein complex.

Procedura di progettazione di protesi a basso costo per l'arto inferiore

L'attività di ricerca descritta in questa tesi fornisce linee guida per la progettazione di arti protesici inferiori, con particolare riferimento alla progettazione di protesi a basso costo. La necessità di efficienti protesi a basso costo risulta infatti sentita nei Paesi in via di sviluppo ma anche dalle fasce meno abbienti dei paesi occidentali. Al fine di comprendere le strategie adottate dall'apparato locomotorio per muoversi con le protesi sono analizzati il cammino fisiologico, le protesi presenti sul mercato ed infine le modalità con cui le loro prestazioni sono valutate. Con il presente lavoro, dopo aver osservato la presenza di una scarsa strutturazione della metodologia di progettazione che riguarda specialmente il settore del basso costo, si propone una metodologia il più possibile oggettiva e ripetibile tesa ad individuare quali sono gli aspetti essenziali di una protesi per garantire al paziente una buona qualità di vita. Solo questi aspetti dovranno essere selezionati al fine di ottenere la massima semplificazione della protesi e ridurre il più possibile i costi. Per la simulazione delle attività di locomozione, in particolare del cammino, è stato elaborato un apposito modello spaziale del cammino. Il modello proposto ha 7 membri rigidi (corrispondenti a piedi, tibie, femori e bacino) e 24 gradi di libertà. Le articolazioni e l'appoggio dei piedi al suolo sono modellati con giunti sferici. La pianta del piede consente tre possibili punti di appoggio. I criteri di realizzazione delle simulazioni possono comprendere aspetti energetici, cinematici e dinamici considerati come obiettivo dall'apparato locomotorio. In questa tesi vengono trattati in particolare gli aspetti cinematici ed è mostrata un'applicazione della procedura nella quale vengono dapprima identificati i riferimenti fisiologici del cammino e quindi simulato il cammino in presenza di una menomazione al ginocchio (eliminazione della flessione in fase di appoggio). Viene quindi lasciato a sviluppi futuri il completamento della procedura e la sua implementazione in un codice di calcolo.

Sostanzialismo e relazionalismo dello spaziotempo alla luce della relatività generale

Until recently the debate on the ontology of spacetime had only a philosophical significance, since, from a physical point of view, General Relativity has been made "immune" to the consequences of the "Hole Argument" simply by reducing the subject to the assertion that solutions of Einstein equations which are mathematically different and related by an active diffeomorfism are physically equivalent. From a technical point of view, the natural reading of the consequences of the "Hole Argument” has always been to go further and say that the mathematical representation of spacetime in General Relativity inevitably contains a “superfluous structure” brought to light by the gauge freedom of the theory. This position of apparent split between the philosophical outcome and the physical one has been corrected thanks to a meticulous and complicated formal analysis of the theory in a fundamental and recent (2006) work by Luca Lusanna and Massimo Pauri entitled “Explaining Leibniz equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events”. The main result of this article is that of having shown how, from a physical point of view, point-events of Einstein empty spacetime, in a particular class of models considered by them, are literally identifiable with the autonomous degrees of freedom of the gravitational field (the Dirac observables, DO). In the light of philosophical considerations based on realism assumptions of the theories and entities, the two authors then conclude by saying that spacetime point-events have a degree of "weak objectivity", since they, depending on a NIF (non-inertial frame), unlike the points of the homogeneous newtonian space, are plunged in a rich and complex non-local holistic structure provided by the “ontic part” of the metric field. Therefore according to the complex structure of spacetime that General Relativity highlights and within the declared limits of a methodology based on a Galilean scientific representation, we can certainly assert that spacetime has got "elements of reality", but the inevitably relational elements that are in the physical detection of point-events in the vacuum of matter (highlighted by the “ontic part” of the metric field, the DO) are closely dependent on the choice of the global spatiotemporal laboratory where the dynamics is expressed (NIF). According to the two authors, a peculiar kind of structuralism takes shape: the point structuralism, with common features both of the absolutist and substantival tradition and of the relationalist one. The intention of this thesis is that of proposing a method of approaching the problem that is, at least at the beginning, independent from the previous ones, that is to propose an approach based on the possibility of describing the gravitational field at three distinct levels. In other words, keeping the results achieved by the work of Lusanna and Pauri in mind and following their underlying philosophical assumptions, we intend to partially converge to their structuralist approach, but starting from what we believe is the "foundational peculiarity" of General Relativity, which is that characteristic inherent in the elements that constitute its formal structure: its essentially geometric nature as a theory considered regardless of the empirical necessity of the measure theory. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now "visible" no longer in terms of its autonomous degrees of freedom (the DO), which, in fact, do not have a tensorial and, therefore, nor geometric nature, but it is analyzable through three levels: a first one, called the potential level (which the theory identifies with the components of the metric tensor), a second one, known as the connections level (which in the theory determine the forces acting on the mass and, as such, offer a level of description related to the one that the newtonian gravitation provides in terms of components of the gravitational field) and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part” of the metric field. It is then shown how to this last level it is possible to establish a “primitive level of objectivity” of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor. The convergence towards the affirmation by Lusanna and Pauri that the existence of a holistic, non-local and relational structure from which the properties quantitatively identified of point-events depend (in addition to their own intrinsic detection), even if it is obtained from different considerations, is realized, in our opinion, in the assignment of a crucial role to the degree of curvature of spacetime that is defined by the Weyl tensor even in the case of empty spacetimes (as in the analysis conducted by Lusanna and Pauri). In the end, matter, regarded as the physical counterpart of spacetime curvature, whose expression is the Weyl tensor, changes the value of this tensor even in spacetimes without matter. In this way, going back to the approach of Lusanna and Pauri, it affects the DOs evolution and, consequently, the physical identification of point-events (as our authors claim). In conclusion, we think that it is possible to see the holistic, relational, and non-local structure of spacetime also through the "behavior" of the Weyl tensor in terms of the Riemann tensor. This "behavior" that leads to geometrical effects of curvature is characterized from the beginning by the fact that it concerns extensive domains of the manifold (although it should be pointed out that the values of the Weyl tensor change from point to point) by virtue of the fact that the action of matter elsewhere indefinitely acts. Finally, we think that the characteristic relationality of spacetime structure should be identified in this "primitive level of organization" of spacetime.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

Vibrational spectroscopy on thermally and optically switchable spin crossover compounds

Oktaedrisch koordinierte Übergangsmetalle mit der Elektronenkonfiguration [Ar]3d4 - 3d7 können in zwei unterschiedlichen elektronischen Zuständen existieren: im High-Spin (HS) oder im Low-Spin (LS) Zustand. Zum Beispiel kann Fe(II) in 1A1g (LS) oder 5T2g (HS) Konfiguration auftreten.Besonderes Interesse besteht in der Aufklärung des Mechanismus der kooperativen Wechselwirkung, die den Spinübergang im Festkörper bestimmt. Hierzu müssen zunächst die internen Freiheitsgrade der molekularen Einheiten bekannt sein. Besonders der Beitrag der molekularen Schwingungen zur Entropiedifferenz, die die Triebkraft des Spinübergangs darstellt, ist von entscheidender Bedeutung. Bisher existieren nur wenige detaillierte Untersuchungen zu den Schwingungseigenschaften der Spincrossovermoleküle.In Rahmen der vorliegenden Arbeit wurden die Schwingungseigenschaften einiger Komplexverbindungen, die Spincrossover zeigen, im Detail untersucht. Dazu wurden temperaturabhängige Raman-, Fern- und Mittel-Infrarot-Spektroskopie, Isotopensubstitution und Normalkoordinatenanalysen (NKA) in Verbindung mit Dichtefunktional-Rechnungen (DFT) verwendet.Die gewonnenen Werte der zugeordneten Schwingungsfrequenzen und die bestimmten Kraftkonstantenänderungen können nun zur Verfeinerung von theoretischen Modellen zur Beschreibung des Spinübergangs verwendet werden.

Mesonic chiral perturbation theory - odd intrinsic parity sector

In der vorliegenden Dissertation werden zwei verschiedene Aspekte des Sektors ungerader innerer Parität der mesonischen chiralen Störungstheorie (mesonische ChPT) untersucht. Als erstes wird die Ein-Schleifen-Renormierung des führenden Terms, der sog. Wess-Zumino-Witten-Wirkung, durchgeführt. Dazu muß zunächst der gesamte Ein-Schleifen-Anteil der Theorie mittels Sattelpunkt-Methode extrahiert werden. Im Anschluß isoliert man alle singulären Ein-Schleifen-Strukturen im Rahmen der Heat-Kernel-Technik. Zu guter Letzt müssen diese divergenten Anteile absorbiert werden. Dazu benötigt man eine allgemeinste anomale Lagrange-Dichte der Ordnung O(p^6), welche systematisch entwickelt wird. Erweitert man die chirale Gruppe SU(n)_L x SU(n)_R auf SU(n)_L x SU(n)_R x U(1)_V, so kommen zusätzliche Monome ins Spiel. Die renormierten Koeffizienten dieser Lagrange-Dichte, die Niederenergiekonstanten (LECs), sind zunächst freie Parameter der Theorie, die individuell fixiert werden müssen. Unter Betrachtung eines komplementären vektormesonischen Modells können die Amplituden geeigneter Prozesse bestimmt und durch Vergleich mit den Ergebnissen der mesonischen ChPT eine numerische Abschätzung einiger LECs vorgenommen werden. Im zweiten Teil wird eine konsistente Ein-Schleifen-Rechnung für den anomalen Prozeß (virtuelles) Photon + geladenes Kaon -> geladenes Kaon + neutrales Pion durchgeführt. Zur Kontrolle unserer Resultate wird eine bereits vorhandene Rechnung zur Reaktion (virtuelles) Photon + geladenes Pion -> geladenes Pion + neutrales Pion reproduziert. Unter Einbeziehung der abgeschätzten Werte der jeweiligen LECs können die zugehörigen hadronischen Strukturfunktionen numerisch bestimmt und diskutiert werden.

Über die Existenz invarianter Tori in Hamiltonschen Systemen, die bis auf eine endlich oft differenzierbare Störung analytisch und integrabel sind

Es wird die Existenz invarianter Tori in Hamiltonschen Systemen bewiesen, die bis auf eine 2n-mal stetig differenzierbare Störung analytisch und integrabel sind, wobei n die Anzahl der Freiheitsgrade bezeichnet. Dabei wird vorausgesetzt, dass die Stetigkeitsmodule der 2n-ten partiellen Ableitungen der Störung einer Endlichkeitsbedingung (Integralbedingung) genügen, welche die Hölderbedingung verallgemeinert. Bisher konnte die Existenz invarianter Tori nur unter der Voraussetzung bewiesen werden, dass die 2n-ten Ableitungen der Störung hölderstetig sind.

Advanced signal and receiver design for next generation OFDM systems

This thesis deal with the design of advanced OFDM systems. Both waveform and receiver design have been treated. The main scope of the Thesis is to study, create, and propose, ideas and novel design solutions able to cope with the weaknesses and crucial aspects of modern OFDM systems. Starting from the the transmitter side, the problem represented by low resilience to non-linear distortion has been assessed. A novel technique that considerably reduces the Peak-to-Average Power Ratio (PAPR) yielding a quasi constant signal envelope in the time domain (PAPR close to 1 dB) has been proposed.The proposed technique, named Rotation Invariant Subcarrier Mapping (RISM),is a novel scheme for subcarriers data mapping,where the symbols belonging to the modulation alphabet are not anchored, but maintain some degrees of freedom. In other words, a bit tuple is not mapped on a single point, rather it is mapped onto a geometrical locus, which is totally or partially rotation invariant. The final positions of the transmitted complex symbols are chosen by an iterative optimization process in order to minimize the PAPR of the resulting OFDM symbol. Numerical results confirm that RISM makes OFDM usable even in severe non-linear channels. Another well known problem which has been tackled is the vulnerability to synchronization errors. Indeed in OFDM system an accurate recovery of carrier frequency and symbol timing is crucial for the proper demodulation of the received packets. In general, timing and frequency synchronization is performed in two separate phases called PRE-FFT and POST-FFT synchronization. Regarding the PRE-FFT phase, a novel joint symbol timing and carrier frequency synchronization algorithm has been presented. The proposed algorithm is characterized by a very low hardware complexity, and, at the same time, it guarantees very good performance in in both AWGN and multipath channels. Regarding the POST-FFT phase, a novel approach for both pilot structure and receiver design has been presented. In particular, a novel pilot pattern has been introduced in order to minimize the occurrence of overlaps between two pattern shifted replicas. This allows to replace conventional pilots with nulls in the frequency domain, introducing the so called Silent Pilots. As a result, the optimal receiver turns out to be very robust against severe Rayleigh fading multipath and characterized by low complexity. Performance of this approach has been analytically and numerically evaluated. Comparing the proposed approach with state of the art alternatives, in both AWGN and multipath fading channels, considerable performance improvements have been obtained. The crucial problem of channel estimation has been thoroughly investigated, with particular emphasis on the decimation of the Channel Impulse Response (CIR) through the selection of the Most Significant Samples (MSSs). In this contest our contribution is twofold, from the theoretical side, we derived lower bounds on the estimation mean-square error (MSE) performance for any MSS selection strategy,from the receiver design we proposed novel MSS selection strategies which have been shown to approach these MSE lower bounds, and outperformed the state-of-the-art alternatives. Finally, the possibility of using of Single Carrier Frequency Division Multiple Access (SC-FDMA) in the Broadband Satellite Return Channel has been assessed. Notably, SC-FDMA is able to improve the physical layer spectral efficiency with respect to single carrier systems, which have been used so far in the Return Channel Satellite (RCS) standards. However, it requires a strict synchronization and it is also sensitive to phase noise of local radio frequency oscillators. For this reason, an effective pilot tone arrangement within the SC-FDMA frame, and a novel Joint Multi-User (JMU) estimation method for the SC-FDMA, has been proposed. As shown by numerical results, the proposed scheme manages to satisfy strict synchronization requirements and to guarantee a proper demodulation of the received signal.

Singularity-Free Fully-Isotropic Translational Parallel Manipulators

Parallel mechanisms show desirable characteristics such as a large payload to robot weight ratio, considerable stiffness, low inertia and high dynamic performances. In particular, parallel manipulators with fewer than six degrees of freedom have recently attracted researchers’ attention, as their employ may prove valuable in those applications in which a higher mobility is uncalled-for. The attention of this dissertation is focused on translational parallel manipulators (TPMs), that is on parallel manipulators whose output link (platform) is provided with a pure translational motion with respect to the frame. The first part deals with the general problem of the topological synthesis and classification of TPMs, that is it identifies the architectures that TPM legs must possess for the platform to be able to freely translate in space without altering its orientation. The second part studies both constraint and direct singularities of TPMs. In particular, special families of fully-isotropic mechanisms are identified. Such manipulators exhibit outstanding properties, as they are free from singularities and show a constant orthogonal Jacobian matrix throughout their workspace. As a consequence, both the direct and the inverse position problems are linear and the kinematic analysis proves straightforward.

Klassische und ab initio Molekulardynamik-Untersuchungen zu Germaniumdioxidschmelzen

Germaniumdioxid (GeO2) ist ein Glasbildner, der wie das homologe SiO2 ein ungeordnetes tetraedrisches Netzwerk ausbildet. In dieser Arbeit werden mit Hilfe von Molekulardynamik-Computersimulationen die Struktur und Dynamik von GeO2 in Abhängigkeit von der Temperatur untersucht. Dazu werden sowohl Simulationen mit einem klassischen Paarpotentialmodell von Oeffner und Elliott als auch ab initio-Simulationen gemäß der Car-Parrinello-Molekulardynamik (CPMD), bei der elektronische Freiheitsgrade mittels Dichtefunktionaltheorie beschrieben werden, durchgeführt. In der klassischen Simulation werden dazu ein Temperaturen zwischen 6100 K und 2530 K betrachtet. Darüberhinaus ermöglichen Abkühlläufe auf T=300 K das Studium der Struktur des Glases. Zum Vergleich werden CPMD-Simulationen für kleinere Systeme mit 60 bzw. 120 Teilchen bei den Temperaturen 3760 K und 3000 K durchgeführt. In den klassischen Simulationen kann die im Experiment bis 1700 K nachgewiesene, im Vergleich zu SiO2 starke, Temperaturabhängigkeit der Dichte auch bei höheren Temperaturen beobachtet werden. Gute Übereinstimmungen der Simulationen mit experimentellen Daten zeigen sich bei der Untersuchung verschiedener struktureller Größen, wie z.B. Paarkorrelationsfunktionen, Winkelverteilungen, Koordinationszahlen und Strukturfaktoren. Es können leichte strukturelle Abweichungen der CPMD-Simulationen von den klassischen Simulationen aufgezeigt werden: 1. Die Paarabstände in CPMD sind durchweg etwas kleiner. 2. Es zeigt sich, daß die Bindungen in den ab initio-Simulationen weicher sind, was sich auch in einer etwas stärkeren Temperaturabhängigkeit der strukturellen Größen im Vergleich zu den klassischen Simulationen niederschlägt. 3. Für CPMD kann ein vermehrtes Auftreten von Dreierringstrukturen gezeigt werden. 4. In der CPMD werden temperaturabhängige Defektstrukturen in Form von Sauerstoffpaaren beobachtet, die vor allem bei 3760 K, kaum jedoch bei 3000 K auftreten. Alle strukturellen Unterschiede zwischen klassischer und CPMD-Simulation sind eindeutig nicht auf Finite-Size-Effekte aufgrund der kleinen Systemgrößen in den CPMD-Simulationen zurückzuführen, d.h. sie sind tatsächlich methodisch bedingt. Bei der Dynamik von GeO2 wird in den klassischen Simulationen ebenfalls eine gute Übereinstimmung mit experimentellen Daten beobachtet, was ein Vergleich der Diffusionskonstanten mit Viskositätsmessungen bei hohen Temperaturen belegt. Die Diffusionskonstanten zeigen teilweise ein verschiedenes Verhalten zum homologen SiO2. Sie folgen in GeO2 bei Temperaturen unter 3000 K einem Arrheniusgesetz mit einer deutlich niedrigeren Aktivierungsenergie. Darüberhinaus werden die Möglichkeiten der Parametrisierung eines neuen klassischen Paarpotentials mittels der Kräfte entlang der CPMD-Trajektorien untersucht. Es zeigt sich, daß derartige Parametrisierungen sehr stark von den gewählten Startparametern abhängen. Ferner führen sämtliche an die Schmelze parametrisierten Potentiale zu zu hohen Dichten im Vergleich zum Experiment. Zum einen liegt dies sehr wahrscheinlich daran,daß für das System GeO2 Kraftdaten allein nicht ausreichen, um grundlegende strukturelle Größen, wie z.B. Paarkorrelationen und Winkelverteilungen, der CPMD-Simulationen gut reproduzieren zu können. Zum anderen ist wohl die Beschreibung mittels Paarpotentialen nicht ausreichend und es ist erforderlich, Merkörperwechselwirkungen in Betracht zu ziehen.

Higher-order calculations in manifestly Lorentz-invariant baryon chiral perturbation theory

This thesis is concerned with calculations in manifestly Lorentz-invariant baryon chiral perturbation theory beyond order D=4. We investigate two different methods. The first approach consists of the inclusion of additional particles besides pions and nucleons as explicit degrees of freedom. This results in the resummation of an infinite number of higher-order terms which contribute to higher-order low-energy constants in the standard formulation. In this thesis the nucleon axial, induced pseudoscalar, and pion-nucleon form factors are investigated. They are first calculated in the standard approach up to order D=4. Next, the inclusion of the axial-vector meson a_1(1260) is considered. We find three diagrams with an axial-vector meson which are relevant to the form factors. Due to the applied renormalization scheme, however, the contributions of the two loop diagrams vanish and only a tree diagram contributes explicitly. The appearing coupling constant is fitted to experimental data of the axial form factor. The inclusion of the axial-vector meson results in an improved description of the axial form factor for higher values of momentum transfer. The contributions to the induced pseudoscalar form factor, however, are negligible for the considered momentum transfer, and the axial-vector meson does not contribute to the pion-nucleon form factor. The second method consists in the explicit calculation of higher-order diagrams. This thesis describes the applied renormalization scheme and shows that all symmetries and the power counting are preserved. As an application we determine the nucleon mass up to order D=6 which includes the evaluation of two-loop diagrams. This is the first complete calculation in manifestly Lorentz-invariant baryon chiral perturbation theory at the two-loop level. The numerical contributions of the terms of order D=5 and D=6 are estimated, and we investigate their pion-mass dependence. Furthermore, the higher-order terms of the nucleon sigma term are determined with the help of the Feynman-Hellmann theorem.