The nuclear electric quadrupole moment of hafnium from the molecular method

The molecular method is used to obtain nuclear electric quadrupole moment (NQM) values for hafnium through electric field gradients (EFGs) at this nucleus in HfO and HfS. Dirac-Coulomb calculations with the Coupled Cluster approach, DC-CCSD (T) and DC-CCSD-T, were carried out to achieve the most accurate estimates of these EFGs. Higher order corrections are also added. Hence, the most reliable values for 177Hf and 179Hf determined here are 3319(33) and 3750(37) mbarn, respectively, in nice accordance with the best currently accepted NQMs for this element. (C) 2012 Elsevier B.V. All rights reserved.

Microstructural characterization of as-cast hf-b alloys

An accurate knowledge of several metal-boron phase diagrams is important to evaluation of higher order systems such as metal-silicon-boron ternaries. The refinement and reassessment of phase diagram data is a continuous work, thus the reevaluation of metal-boron systems provides the possibility to confirm previous data from an investigation using higher purity materials and better analytical techniques. This work presents results of rigorous microstructural characterization of as-cast hafnium-boron alloys which are significant to assess the liquid composition associated to most of the invariant reactions of this system. Alloys were prepared by arc melting high purity hafnium (minimum 99.8%) and boron (minimum 99.5%) slices under argon atmosphere in water-cooled copper crucible with non consumable tungsten electrode and titanium getter. The phases were identified by scanning electron microscopy, using back-scattered electron image mode and X-ray diffraction. In general, a good agreement was found between our data and those from the currently accepted Hafnium-Boron phase diagram. The phases identified are αHfSS and B-RhomSS, the intermediate compounds HfB and HfB2 and the liquide L. The reactions are the eutectic L ⇔ αHfSS + HfB and L ⇔ HfB2 + B-Rhom, the peritectic L + HfB2 ⇔ HfB and the congruent formation of HfB2.

Design methodology of piezoelectric energy-harvesting skin using topology optimization

Abstract This paper describes a design methodology for piezoelectric energy harvester s that thinly encapsulate the mechanical devices and expl oit resonances from higher- order vibrational modes. The direction of polarization determines the sign of the pi ezoelectric tensor to avoid cancellations of electric fields from opposite polarizations in the same circuit. The resultant modified equations of state are solved by finite element method (FEM). Com- bining this method with the solid isotropic material with penalization (SIMP) method for piezoelectric material, we have developed an optimization methodology that optimizes the piezoelectric material layout and polarization direc- tion. Updating the density function of the SIMP method is performed based on sensitivity analysis, the sequen- tial linear programming on the early stage of the opti- mization, and the phase field method on the latter stage

User interaction widgets for interactive theorem proving

Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using a script for storing textual commands for the system. In the tradition of LCF, the proof language of Matita is procedural and relies on tactic and tacticals to proceed toward proof completion. The interaction paradigm offered to the user is based on the script management technique at the basis of the popularity of the Proof General generic interface for interactive theorem provers: while editing a script the user can move forth the execution point to deliver commands to the system, or back to retract (or “undo”) past commands. Matita has been developed from scratch in the past 8 years by several members of the Helm research group, this thesis author is one of such members. Matita is now a full-fledged proof assistant with a library of about 1.000 concepts. Several innovative solutions spun-off from this development effort. This thesis is about the design and implementation of some of those solutions, in particular those relevant for the topic of user interaction with theorem provers, and of which this thesis author was a major contributor. Joint work with other members of the research group is pointed out where needed. The main topics discussed in this thesis are briefly summarized below. Disambiguation. Most activities connected with interactive proving require the user to input mathematical formulae. Being mathematical notation ambiguous, parsing formulae typeset as mathematicians like to write down on paper is a challenging task; a challenge neglected by several theorem provers which usually prefer to fix an unambiguous input syntax. Exploiting features of the underlying calculus, Matita offers an efficient disambiguation engine which permit to type formulae in the familiar mathematical notation. Step-by-step tacticals. Tacticals are higher-order constructs used in proof scripts to combine tactics together. With tacticals scripts can be made shorter, readable, and more resilient to changes. Unfortunately they are de facto incompatible with state-of-the-art user interfaces based on script management. Such interfaces indeed do not permit to position the execution point inside complex tacticals, thus introducing a trade-off between the usefulness of structuring scripts and a tedious big step execution behavior during script replaying. In Matita we break this trade-off with tinycals: an alternative to a subset of LCF tacticals which can be evaluated in a more fine-grained manner. Extensible yet meaningful notation. Proof assistant users often face the need of creating new mathematical notation in order to ease the use of new concepts. The framework used in Matita for dealing with extensible notation both accounts for high quality bidimensional rendering of formulae (with the expressivity of MathMLPresentation) and provides meaningful notation, where presentational fragments are kept synchronized with semantic representation of terms. Using our approach interoperability with other systems can be achieved at the content level, and direct manipulation of formulae acting on their rendered forms is possible too. Publish/subscribe hints. Automation plays an important role in interactive proving as users like to delegate tedious proving sub-tasks to decision procedures or external reasoners. Exploiting the Web-friendliness of Matita we experimented with a broker and a network of web services (called tutors) which can try independently to complete open sub-goals of a proof, currently being authored in Matita. The user receives hints from the tutors on how to complete sub-goals and can interactively or automatically apply them to the current proof. Another innovative aspect of Matita, only marginally touched by this thesis, is the embedded content-based search engine Whelp which is exploited to various ends, from automatic theorem proving to avoiding duplicate work for the user. We also discuss the (potential) reusability in other systems of the widgets presented in this thesis and how we envisage the evolution of user interfaces for interactive theorem provers in the Web 2.0 era.

Molecular architecture of fur binding to iron-induced and - repressed genes in Helicobacter pylori

The ferric uptake regulator protein Fur regulates iron-dependent gene expression in bacteria. In the human pathogen Helicobacter pylori, Fur has been shown to regulate iron-induced and iron-repressed genes. Herein we investigate the molecular mechanisms that control this differential iron-responsive Fur regulation. Hydroxyl radical footprinting showed that Fur has different binding architectures, which characterize distinct operator typologies. On operators recognized with higher affinity by holo-Fur, the protein binds to a continuous AT-rich stretch of about 20 bp, displaying an extended protection pattern. This is indicative of protein wrapping around the DNA helix. DNA binding interference assays with the minor groove binding drug distamycin A, point out that the recognition of the holo-operators occurs through the minor groove of the DNA. By contrast, on the apo-operators, Fur binds primarily to thymine dimers within a newly identified TCATTn10TT consensus element, indicative of Fur binding to one side of the DNA, in the major groove of the double helix. Reconstitution of the TCATTn10TT motif within a holo-operator results in a feature binding swap from an holo-Fur- to an apo-Fur-recognized operator, affecting both affinity and binding architecture of Fur, and conferring apo-Fur repression features in vivo. Size exclusion chromatography indicated that Fur is a dimer in solution. However, in the presence of divalent metal ions the protein is able to multimerize. Accordingly, apo-Fur binds DNA as a dimer in gel shift assays, while in presence of iron, higher order complexes are formed. Stoichiometric Ferguson analysis indicates that these complexes correspond to one or two Fur tetramers, each bound to an operator element. Together these data suggest that the apo- and holo-Fur repression mechanisms apparently rely on two distinctive modes of operator-recognition, involving respectively the readout of a specific nucleotide consensus motif in the major groove for apo-operators, and the recognition of AT-rich stretches in the minor groove for holo-operators, whereas the iron-responsive binding affinity is controlled through metal-dependent shaping of the protein structure in order to match preferentially the major or the minor groove.

Quadraturformeln für das Qualokationsverfahren

Im Mittelpunkt dieser Arbeit steht Beweis der Existenz- und Eindeutigkeit von Quadraturformeln, die für das Qualokationsverfahren geeignet sind. Letzteres ist ein von Sloan, Wendland und Chandler entwickeltes Verfahren zur numerischen Behandlung von Randintegralgleichungen auf glatten Kurven (allgemeiner: periodische Pseudodifferentialgleichungen). Es erreicht die gleichen Konvergenzordnungen wie das Petrov-Galerkin-Verfahren, wenn man durch den Operator bestimmte Quadraturformeln verwendet. Zunächst werden die hier behandelten Pseudodifferentialoperatoren und das Qualokationsverfahren vorgestellt. Anschließend wird eine Theorie zur Existenz und Eindeutigkeit von Quadraturformeln entwickelt. Ein wesentliches Hilfsmittel hierzu ist die hier bewiesene Verallgemeinerung eines Satzes von Nürnberger über die Existenz und Eindeutigkeit von Quadraturformeln mit positiven Gewichten, die exakt für Tschebyscheff-Räume sind. Es wird schließlich gezeigt, dass es stets eindeutig bestimmte Quadraturformeln gibt, welche die in den Arbeiten von Sloan und Wendland formulierten Bedingungen erfüllen. Desweiteren werden 2-Punkt-Quadraturformeln für so genannte einfache Operatoren bestimmt, mit welchen das Qualokationsverfahren mit einem Testraum von stückweise konstanten Funktionen eine höhere Konvergenzordnung hat. Außerdem wird gezeigt, dass es für nicht-einfache Operatoren im Allgemeinen keine Quadraturformel gibt, mit der die Konvergenzordnung höher als beim Petrov-Galerkin-Verfahren ist. Das letzte Kapitel beinhaltet schließlich numerische Tests mit Operatoren mit konstanten und variablen Koeffizienten, welche die theoretischen Ergebnisse der vorangehenden Kapitel bestätigen.

New path integral simulation algorithms and their application to creep in the quantum sine-Gordon chain

A path integral simulation algorithm which includes a higher-order Trotter approximation (HOA)is analyzed and compared to an approach which includes the correct quantum mechanical pair interaction (effective Propagator (EPr)). It is found that the HOA algorithmconverges to the quantum limit with increasing Trotter number P as P^{-4}, while the EPr algorithm converges as P^{-2}.The convergence rate of the HOA algorithm is analyzed for various physical systemssuch as a harmonic chain,a particle in a double-well potential, gaseous argon, gaseous helium and crystalline argon. A new expression for the estimator for the pair correlation function in the HOA algorithm is derived. A new path integral algorithm, the hybrid algorithm, is developed.It combines an exact treatment of the quadratic part of the Hamiltonian and thehigher-order Trotter expansion techniques.For the discrete quantum sine-Gordon chain (DQSGC), it is shown that this algorithm works more efficiently than all other improved path integral algorithms discussed in this work. The new simulation techniques developed in this work allow the analysis of theDQSGC and disordered model systems in the highly quantum mechanical regime using path integral molecular dynamics (PIMD)and adiabatic centroid path integral molecular dynamics (ACPIMD).The ground state phonon dispersion relation is calculated for the DQSGC by the ACPIMD method.It is found that the excitation gap at zero wave vector is reduced by quantum fluctuations. Two different phases exist: One phase with a finite excitation gap at zero wave vector, and a gapless phase where the excitation gap vanishes.The reaction of the DQSGC to an external driving force is analyzed at T=0.In the gapless phase the system creeps if a small force is applied, and in the phase with a gap the system is pinned. At a critical force, the systems undergo a depinning transition in both phases and flow is induced. The analysis of the DQSGC is extended to models with disordered substrate potentials. Three different cases are analyzed: Disordered substrate potentials with roughness exponent H=0, H=1/2,and a model with disordered bond length. For all models, the ground state phonon dispersion relation is calculated.

Use of computer algebra in the calculation of Feynman diagrams

The increasing precision of current and future experiments in high-energy physics requires a likewise increase in the accuracy of the calculation of theoretical predictions, in order to find evidence for possible deviations of the generally accepted Standard Model of elementary particles and interactions. Calculating the experimentally measurable cross sections of scattering and decay processes to a higher accuracy directly translates into including higher order radiative corrections in the calculation. The large number of particles and interactions in the full Standard Model results in an exponentially growing number of Feynman diagrams contributing to any given process in higher orders. Additionally, the appearance of multiple independent mass scales makes even the calculation of single diagrams non-trivial. For over two decades now, the only way to cope with these issues has been to rely on the assistance of computers. The aim of the xloops project is to provide the necessary tools to automate the calculation procedures as far as possible, including the generation of the contributing diagrams and the evaluation of the resulting Feynman integrals. The latter is based on the techniques developed in Mainz for solving one- and two-loop diagrams in a general and systematic way using parallel/orthogonal space methods. These techniques involve a considerable amount of symbolic computations. During the development of xloops it was found that conventional computer algebra systems were not a suitable implementation environment. For this reason, a new system called GiNaC has been created, which allows the development of large-scale symbolic applications in an object-oriented fashion within the C++ programming language. This system, which is now also in use for other projects besides xloops, is the main focus of this thesis. The implementation of GiNaC as a C++ library sets it apart from other algebraic systems. Our results prove that a highly efficient symbolic manipulator can be designed in an object-oriented way, and that having a very fine granularity of objects is also feasible. The xloops-related parts of this work consist of a new implementation, based on GiNaC, of functions for calculating one-loop Feynman integrals that already existed in the original xloops program, as well as the addition of supplementary modules belonging to the interface between the library of integral functions and the diagram generator.

Synthetical engineering of supramolecular properties of large polycyclic aromatic hydrocarbons

An important property for devices is the charge-carrier mobility values for discotic organic materials like hexa-peri-hexabenzocoronenes. A close relation exists between the degree of their columnar self-arrangement of the molecules and their mobilities. Within this first step an induction of a higher order via hydrogen-bonding was considered, which mainly pointed towards the improvement of the intracolumnar stacking of the materials. For the analytics a broad range of methods was used including differential scanning calorimetry (DSC), wide-angle X-ray diffractometry (WAXS), solid-state NMR spectroscopy and scanning tunneling microscopy (STM). Indeed, a specific influence of the hydrogen-bonds could be identified, although in several cases by the cost of a severe reduction of solubility and processability. This effect was dampened by the addition of a long alkyl chain next to the hydrogen-bond exerting functional group, which resulted in an improved columnar arrangement by retention of processability. In contrast to the before mentioned example of inducing a higher intracolumnar order by hydrogen-bonding, the focus was also be set upon larger aromatic systems. The charge-carrier mobility is also in close relation to the size of the aromatic core and larger π-areas are expected to lead to improved mobilities. For photovoltaic applications a high extinction coefficient over a broad range of the spectrum is favorable, which can also be achieved by enlarging the aromatic core component. In addition the stronger π-interactions between the aromatic core components should yield an improved columnar stability and order. However the strengthening of the π-interactions between the aromatic core components led to a reduction of the solubility and the processability due to the stronger aggregation of the molecules. This required the introduction of efficiently solubilizing features in terms of long alkyl chains in the corona of the aromatic entity, in combination of a distortion of the aromatic core moiety by bulky tert-butyl groups. By this approach not only the processing and cleaning of the materials with standard laboratory techniques became possible, but moreover the first structure-rich UV/vis and a resolved 1H-NMR spectra for an aromatic system two times larger than hexa-peri-hexabenzocoronene were recorded. The bulk properties in an extruded fiber as well as on the surface showed a columnar self-assembly including a phase in which a homeotropic alignment on a substrate was observed, which turns the material into an interesting candidate for future applications in electronic devices.

Renormalization of fermion mixing

Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by hermiticity. After analysing the complete renormalized Lagrangian in a general theory including vector and scalar bosons with arbitrary renormalizable interactions, we consider two specific models: quark mixing in the electroweak Standard Model and mixing of Majorana neutrinos in the seesaw mechanism. A counter term for fermion mixing matrices can not be fixed by only taking into account self-energy corrections or fermion field renormalization constants. The presence of unstable particles in the theory can lead to a non-unitary renormalized mixing matrix or to a gauge parameter dependence in its counter term. Therefore, we propose to determine the mixing matrix counter term by fixing the complete correction terms for a physical process to experimental measurements. As an example, we calculate the decay rate of a top quark and of a heavy neutrino. We provide in each of the chosen models sample calculations that can be easily extended to other theories.

Social learning and action understanding in human observers: contributions of sensori-motor constraints and prior information

The aim of this thesis was to investigate the respective contribution of prior information and sensorimotor constraints to action understanding, and to estimate their consequences on the evolution of human social learning. Even though a huge amount of literature is dedicated to the study of action understanding and its role in social learning, these issues are still largely debated. Here, I critically describe two main perspectives. The first perspective interprets faithful social learning as an outcome of a fine-grained representation of others’ actions and intentions that requires sophisticated socio-cognitive skills. In contrast, the second perspective highlights the role of simpler decision heuristics, the recruitment of which is determined by individual and ecological constraints. The present thesis aims to show, through four experimental works, that these two contributions are not mutually exclusive. A first study investigates the role of the inferior frontal cortex (IFC), the anterior intraparietal area (AIP) and the primary somatosensory cortex (S1) in the recognition of other people’s actions, using a transcranial magnetic stimulation adaptation paradigm (TMSA). The second work studies whether, and how, higher-order and lower-order prior information (acquired from the probabilistic sampling of past events vs. derived from an estimation of biomechanical constraints of observed actions) interacts during the prediction of other people’s intentions. Using a single-pulse TMS procedure, the third study investigates whether the interaction between these two classes of priors modulates the motor system activity. The fourth study tests the extent to which behavioral and ecological constraints influence the emergence of faithful social learning strategies at a population level. The collected data contribute to elucidate how higher-order and lower-order prior expectations interact during action prediction, and clarify the neural mechanisms underlying such interaction. Finally, these works provide/open promising perspectives for a better understanding of social learning, with possible extensions to animal models.