Microfluidic device and interfacial transport: application to biomolecules and nanostructures

The aim of my dissertation is to provide new knowledge and applications of microfluidics in a variety of problems, from materials science, devices, and biomedicine, where the control on the fluid dynamics and the local concentration of the solutions containing the relevant molecules (either materials, precursors, or biomolecules) is crucial. The control of interfacial phenomena occurring in solutions at dierent length scales is compelling in nanotechnology for devising new sensors, molecular electronics devices, memories. Microfluidic devices were fabricated and integrated with organic electronics devices. The transduction involves the species in the solution which infills the transistor channel and confined by the microfluidic device. This device measures what happens on the surface, at few nanometers from the semiconductor channel. Soft-lithography was adopted to fabricate platinum electrodes, starting from platinum carbonyl precursor. I proposed a simple method to assemble these nanostructures in periodic arrays of microstripes, and form conductive electrodes with characteristic dimension of 600 nm. The conductivity of these sub-microwires is compared with the values reported in literature and bulk platinum. The process is suitable for fabricating thin conductive patterns for electronic devices or electrochemical cells, where the periodicity of the conductive pattern is comparable with the diusion length of the molecules in solution. The ordering induced among artificial nanostructures is of particular interest in science. I show that large building blocks, like carbon nanotubes or core-shell nanoparticles, can be ordered and self-organised on a surface in patterns due to capillary forces. The eective probability of inducing order with microfluidic flow is modeled with finite element calculation on the real geometry of the microcapillaries, in soft-lithographic process. The oligomerization of A40 peptide in microconfined environment represents a new investigation of the extensively studied peptide aggregation. The added value of the approach I devised is the precise control on the local concentration of peptides together with the possibility to mimick cellular crowding. Four populations of oligomers where distinguished, with diameters ranging from 15 to 200 nm. These aggregates could not be addresses separately in fluorescence. The statistical analysis on the atomic force microscopy images together with a model of growth reveal new insights on the kinetics of amyloidogenesis as well as allows me to identify the minimum stable nucleus size. This is an important result owing to its implications in the understanding and early diagnosis and therapy of the Alzheimer’s disease

Bonded structures for enhanced damage tolerant pressurized fuselages

Adhesive bonding provides solutions to realize cost effective and low weight aircraft fuselage structures, in particular where the Damage Tolerance (DT) is the design criterion. Bonded structures that combine Metal Laminates (MLs) and eventually Selective Reinforcements can guarantee slow crack propagation, crack arrest and large damage capability. To optimize the design exploiting the benefit of bonded structures incorporating selective reinforcement requires reliable analysis tools. The effect of bonded doublers / selective reinforcements is very difficult to be predicted numerically or analytically due to the complexity of the underlying mechanisms and failures modes acting. Reliable predictions of crack growth and residual strength can only be based on sound empirical and phenomenological considerations strictly related to the specific structural concept. Large flat stiffened panels that combine MLs and selective reinforcements have been tested with the purpose of investigating solutions applicable to pressurized fuselages. The large test campaign (for a total of 35 stiffened panels) has quantitatively investigated the role of the different metallic skin concepts (monolithic vs. MLs) of the aluminum, titanium and glass-fiber reinforcements, of the stringers material and cross sections and of the geometry and location of doublers / selective reinforcements. Bonded doublers and selective reinforcements confirmed to be outstanding tools to improve the DT properties of structural elements with a minor weight increase. However the choice of proper materials for the skin and the stringers must be not underestimated since they play an important role as well. A fuselage structural concept has been developed to exploit the benefit of a metal laminate design concept in terms of high Fatigue and Damage Tolerance (F&DT) performances. The structure used laminated skin (0.8mm thick), bonded stringers, two different splicing solutions and selective reinforcements (glass prepreg embedded in the laminate) under the circumferential frames. To validate the design concept a curved panel was manufactured and tested under loading conditions representative of a single aisle fuselage: cyclic internal pressurization plus longitudinal loads. The geometry of the panel, design and loading conditions were tailored for the requirements of the upper front fuselage. The curved panel has been fatigue tested for 60 000 cycles before the introduction of artificial damages (cracks in longitudinal and circumferential directions). The crack growth of the artificial damages has been investigated for about 85 000 cycles. At the end a residual strength test has been performed with a “2 bay over broken frame” longitudinal crack. The reparability of this innovative concept has been taken into account during design and demonstrated with the use of an external riveted repair. The F&DT curved panel test has confirmed that a long fatigue life and high damage tolerance can be achieved with a hybrid metal laminate low weight configuration. The superior fatigue life from metal laminates and the high damage tolerance characteristics provided by integrated selective reinforcements are the key concepts that provided the excellent performances. The weight comparison between the innovative bonded concept and a conventional monolithic riveted design solution showed a significant potential weight saving but the weight advantages shall be traded off with the additional costs.

On Designing Compliant Actuators Based On Dielectric Elastomers

Dielectric Elastomers (DE) are incompressible dielectrics which can experience deviatoric (isochoric) finite deformations in response to applied large electric fields. Thanks to the strong electro-mechanical coupling, DE intrinsically offer great potentialities for conceiving novel solid-state mechatronic devices, in particular linear actuators, which are more integrated, lightweight, economic, silent, resilient and disposable than equivalent devices based on traditional technologies. Such systems may have a huge impact in applications where the traditional technology does not allow coping with the limits of weight or encumbrance, and with problems involving interaction with humans or unknown environments. Fields such as medicine, domotic, entertainment, aerospace and transportation may profit. For actuation usage, DE are typically shaped in thin films coated with compliant electrodes on both sides and piled one on the other to form a multilayered DE. DE-based Linear Actuators (DELA) are entirely constituted by polymeric materials and their overall performance is highly influenced by several interacting factors; firstly by the electromechanical properties of the film, secondly by the mechanical properties and geometry of the polymeric frame designed to support the film, and finally by the driving circuits and activation strategies. In the last decade, much effort has been focused in the devolvement of analytical and numerical models that could explain and predict the hyperelastic behavior of different types of DE materials. Nevertheless, at present, the use of DELA is limited. The main reasons are 1) the lack of quantitative and qualitative models of the actuator as a whole system 2) the lack of a simple and reliable design methodology. In this thesis, a new point of view in the study of DELA is presented which takes into account the interaction between the DE film and the film supporting frame. Hyperelastic models of the DE film are reported which are capable of modeling the DE and the compliant electrodes. The supporting frames are analyzed and designed as compliant mechanisms using pseudo-rigid body models and subsequent finite element analysis. A new design methodology is reported which optimize the actuator performances allowing to specifically choose its inherent stiffness. As a particular case, the methodology focuses on the design of constant force actuators. This class of actuators are an example of how the force control could be highly simplified. Three new DE actuator concepts are proposed which highlight the goodness of the proposed method.

Oberflächenplasmonen-artige Resonanzen auf metallischen Gittern

Die Geometrie einer Metalloberfläche bestimmt die Wechselwirkung zwischen der Oberflächenplasmonenresonanz und anderen Energieformen wie Photonen, anderen Oberflächenplasmonen und molekularen Anregungen. In dieser Arbeit wird der Einfluss dieser Effekte auf die optischen Eigenschaften von metallischen Reliefgittern untersucht.Aufgrund von Modellrechungen werden auf tiefen Gitterstrukturen Resonanzen erwartet, die sich als selbstgekoppelte Oberflächenplasmonen interpretieren lassen. Diese Resonanzen wurden aufgrund der Symmetrie des elektromagnetischen Feldes klassifiziert. Es wurden tiefe Gitter mit unterschiedlichen Profilformen hergestellt, die die experimentelle Beobachtung von drei gekoppelten Resonanzen erlauben. Variationen in der Tiefe und Asymmetrie der Gitter sowie in der experimentellen Geometrie zeigen die theoretisch vorausgesagten Effekte.Fluoreszenzfarbstoffe können mit elektromagnetischen Oberflächenresonanzen Energie austauschen. Die Lokalisierung des elektrischen Feldes von gekoppelten Resonanzen führt zu einer Ortsabhängigkeit der Kopplung, die bei 'freien' Oberflächenplasmonen nicht beobachtet wird. Ein theoretisches Modell ist in der Lage, die experimentellen Befunde weitgehend zu beschreiben. Die Ortsabhägigkeit der photochemischen Zerstörungsrate erlaubt die Anwendung dieses Effektes zur Messung von Diffusionsphänomenen in dünnen Filmen.Des weiteren wurde die Polarisationsabhängigkeit der Anregung von Oberflächenplasmonen wurde in konischer Reflexionsgeometrie und die Rolle der Oberflächenplasmonen in der thermisch induzierten Lichtemission untersucht. Ferner wurde eine vereinfachte Auswertungsroutine zur Anwendung von Gittern in der Untersuchung von dünnen dielektrischen Filmen entwickelt.

La via Emilia tra Rimini e Forlì. Ruolo e immagine della strada

Abstract Il tema delle infrastrutture, intese come parte dell’architettura dello spazio urbano e del territorio, assume un ruolo centrale in molti progetti contemporanei e costituisce la ragione di questa ricerca. E’ preso in esame, in particolare, il tracciato extraurbano della via Emilia, antica strada consolare romana la cui definizione risale al II sec. a.C., nel tratto compreso tra le città di Rimini e Forlì. Studiare la strada nel suo rapporto con il territorio locale ha significato in primo luogo prendere in considerazione la via Emilia in quanto manufatto, ma anche in quanto percorso che si compie nel tempo. Si è dunque cercato di mostrare come, in parallelo all’evoluzione della sua sezione e della geometria del suo tracciato, sia cambiata anche la sua fruizione, e come si sia evoluto il modo in cui la strada viene “misurata”, denominata e gestita. All’interno di una riflessione critica sulla forma e sul ruolo della strada nel corso dei secoli la Tesi rilegge il territorio nella sua dimensione di “palinsesto”, riconoscendo e isolando alcuni momenti in cui la via Emilia ha assunto un valore “simbolico” che rimanda alla Roma imperiale. La perdita del significato via Emilia, intesa come elemento di “costruzione” del territorio, ha origine con il processo di urbanizzazione diffusa che ha investito il territorio extraurbano a partire dalla fine della seconda guerra mondiale. La condizione attuale della strada, sempre più congestionata dal traffico veicolare, costituisce la premesse per una riflessione sul futuro della sua forma e degli insediamenti che attraversa. La strategia proposta dagli Enti locali che prevede il raddoppio della strada, con la costruzione della via Emilia Bis, non garantisce solo un potenziamento infrastrutturale ma rappresenta l’occasione per sottrarre al tracciato attuale la funzione di principale asse di comunicazione extraurbana. La via Emilia potrebbe così recuperare il ruolo di itinerario narrativo, attraverso la configurazione dei suoi spazi collettivi, l’architettura dei suoi edifici, il significato dei suoi monumenti, e diventare spazio privilegiato di relazione e di aggregazione. The theme of urban infrastructures, thought as part of the design of urban space and territory, has a central role in several contemporary projects and is the reason of this research. The object of the study is the extra urban route of the via Emilia, an ancient roman road which has been defined in the II century b. C., in its stretch between the cities of Rimini and Forlì. Studying the road in its relationship with the local environment has meant first of all considering the via Emilia as an “artefact” but also as a path that takes place over time. The aim of this research was also to demonstrate how its fruition has changed together with the evolution of the section and geometry of the route, and how the road itself is measured, named and managed. Within a critical approach on the shape and on the role played by the road through the centuries, this Essay reinterprets the territory in its dimension of “palimpsest”, identifying and isolating some periods of time when the via Emilia assumed a symbolic value which recalls the Imperial Rome. The loss of the meaning of the via Emilia, intended as an element that “constitutes” the territory originates from a process of diffused urbanization, which spread in the extra urban environment from the end of the second world war. The actual condition of the road, more and more congested by traffic, is the premise of a reflection about the future of its shape and of the settlements alongside. The strategy proposed by the local authorities, that foresees to double the size of the road, building the via Emilia Bis, not only guarantees an infrastructural enhancement but also it represents an opportunity to take off from the road itself the current function of being the principal axis of extra urban connection. In this way the via Emilia could regain its role as a narrative itinerary, through the configuration of its public spaces, the architecture of its buildings, the meaning of its monuments, and then become a privileged space of relationship and aggregation.

Dall'involucro all'invaso. Lo spazio a pianta centrale nell'opera architettonica di Adalberto Libera

An archetype selected over the centuries Adalberto Libera wrote little, showing more inclination to use the project as the only means of verification. This study uses a survey of the project for purely compositional space in relation to the reason that most other returns with continuity and consistency throughout his work. "The fruit of a type selected over centuries", in the words of Libera, is one of the most widely used and repeated spatial archetypes present in the history of architecture, given its nature as defined by a few consolidated elements and precisely defined with characters of geometric precision and absoluteness, the central space is provided, over the course of evolution of architecture, and its construction aspects as well as symbolic, for various uses, from historical period in which it was to coincide with sacred space for excellence, to others in which it lends itself to many different expressive possibilities of a more "secular". The central space was created on assumptions of a constructive character, and the same exact reason has determined the structural changes over the centuries, calling from time to time with advances in technology, the maximum extent possible and the different applications, which almost always have coincided with the reason for the monumental space. But it’s in the Roman world that the reason for the central space is defined from the start of a series of achievements that fix the character in perpetuity. The Pantheon was seen maximum results and, simultaneously, the archetype indispensable, to the point that it becomes difficult to sustain a discussion of the central space that excludes. But the reason the space station has complied, in ancient Rome, just as exemplary, monuments, public spaces or buildings with very different implications. The same Renaissance, on which Wittkower's proving itself once and for all, the nature and interpretation of sacred space station, and thus the symbolic significance of that invaded underlying interpretations related to Humanism, fixing the space-themed drawing it with the study and direct observation by the four-sixteenth-century masters, the ruins that in those years of renewed interest in the classical world, the first big pieces of excavation of ancient Rome brought to light with great surprise of all. Not a case, the choice to investigate the architectural work of Libera through the grounds of the central space. Investigating its projects and achievements, it turns out as the reason invoked particularly evident from the earliest to latest work, crossing-free period of the war which for many authors in different ways, the distinction between one stage and another, or the final miss. The theme and the occasion for Libera always distinct, it is precisely the key through which to investigate her work, to come to discover that the first-in this case the central plan-is the constant underlying all his work, and the second reason that the quota with or at the same time, we will return different each time and always the same Libera, formed on the major works remained from ancient times, and on this building method, means consciously, that the characters of architectural works, if valid, pass the time, and survive the use and function contingent. As for the facts by which to formalize it, they themselves are purely contingent, and therefore available to be transferred from one work to another, from one project to another, using also the loan. Using the same two words-at-issue and it becomes clear now how the theme of this study is the method of Libera and opportunity to the study of the central space in his work. But there is one aspect that, with respect to space a central plan evolves with the progress of the work of Libera on the archetype, and it is the reason behind all the way, just because an area built entirely on reason centric. It 'just the "center" of space that, ultimately, tells us the real progression and the knowledge that over the years has matured and changed in Libera. In the first phase, heavily laden with symbolic superstructure, even if used in a "bribe" from Free-always ill-disposed to sacrifice the idea of architecture to a phantom-center space is just the figure that identifies the icon represents space itself: the cross, the flame or the statue are different representations of the same idea of center built around an icon. The second part of the work of clearing the space station, changed the size of the orders but the demands of patronage, grows and expands the image space centric, celebratory nature that takes and becomes, in a different way, this same symbol . You see, one in all, as the project of "Civiltà Italiana" or symbolic arch are examples of this different attitude. And at the same point of view, you will understand how the two projects formulated on the reuse of the Mausoleum of Augustus is the key to its passage from first to second phase: the Ara Pacis in the second project, making itself the center of the composition "breaks" the pattern of symbolic figure in the center, because it is itself an architecture. And, in doing so, the transition takes place where the building itself-the central space-to become the center of that space that itself creates and determines, by extending the potential and the expressiveness of the enclosure (or cover) that defines the basin centered. In this second series of projects, which will be the apex and the point of "crisis" in the Palazzo dei Congressi all'E42 received and is no longer so, the symbol at the very geometry of space, but space itself and 'action' will be determined within this; action leading a movement, in the case of the Arco simbolico and the "Civiltà Italiana" or, more frequently, or celebration, as in the great Sala dei Recevimenti all’E42, which, in the first project proposal, is represented as a large area populated by people in suits, at a reception, in fact. In other words, in this second phase, the architecture is no longer a mere container, but it represents the shape of space, representing that which "contains". In the next step-determining the knowledge from which mature in their transition to post-war-is one step that radically changes the way centric space, although formally and compositionally Libera continues the work on the same elements, compounds and relationships in a different way . In this last phase Freedom, center, puts the man in human beings, in the two previous phases, and in a latent, were already at the center of the composition, even if relegated to the role of spectators in the first period, or of supporting actors in the second, now the heart of space. And it’s, as we shall see, the very form of being together in the form of "assembly", in its different shades (up to that sacred) to determine the shape of space, and how to relate the parts that combine to form it. The reconstruction of the birth, evolution and development of the central space of the ground in Libera, was born on the study of the monuments of ancient Rome, intersected on fifty years of recent history, honed on the constancy of a method and practice of a lifetime, becomes itself, Therefore, a project, employing the same mechanisms adopted by Libera; the decomposition and recomposition, research synthesis and unity of form, are in fact the structure of this research work. The road taken by Libera is a lesson in clarity and rationality, above all, and this work would uncover at least a fragment.

Molekulardynamik-Simulation zur Struktur von SiO 2-Oberflächen mit adsorbiertem Wasser

In der vorliegenden Arbeit werdenMolekulardynamik-Simulationen zur Untersuchung derstatischen Eigenschaften von amorphenSiliziumdioxidoberflächen (Siliziumdioxid) durchgeführt. Da das von van Beest, Kramer und van Santen vorgeschlagene,sogenannte BKS-Potential für Bulksysteme optimiert wurde und an Oberflächen deutlichandere Ladungsverteilungenauftreten als im Bulk, ist die Anwendbarkeit diesesPotentials für Oberflächensystemefraglich. Aus diesem Grund haben wir untersucht, inwieweitsich die Oberflächeneigenschaften von Systemen, die mit Hilfe des BKS-Potentials äquilibriertwurden, durch ein Nachrelaxieren mit einer ab-initio-Simulation (Car-Parrinello-Methode)ändern. Mit Hilfe der Kombination aus BKS- und Car-Parrinello-Methode (CPMD)konnten wir feststellen, daß sich die Systeme aufgrund des Nachrelaxierens in z-Richtungweiter ausdehnen. Desweiteren zeigte sich insbesondere bei kleinen Ringen (kommen nur ander Oberfläche vor), daß es deutliche Abweichungen in den Geometrien (Atomabstände,Winkel usw.) zwischen der reinen BKS- und der kombinierten BKS-CPMD-Methode gibt. Anhand vonCPMD-Simulationen konnten wir zeigen, daß es durch die Wechselwirkung eines Wassermolekülsmit einem 2er-Ring zum Aufbrechen dieser Ringstruktur und zur Bildung von zweiSilanolgruppen (SiOH) kommt. Desweiteren stellten wir fest, daß es sich hierbei um eineexotherme Reaktion (Energiedifferenz 1.6 eV) handelt, für die eineEnergiebarriere von 1.1 eV überwunden werden muß. Ferner ergab sich, daß die an der Bildung des2er-Ringes beteiligten, stark deformierten Tetraeder nach dem Aufbrechen dieserRingstruktur eine nahezu ideale Tetraederform annehmen.

Polyelectrolytes and their counterions studied by EPR spectroscopy

In this thesis methods of EPR spectroscopy were used to investigate polyion-counterion interactions in polyelectrolyte solutions. The fact that EPR techniques are local methods is exploited and by employing spin-carrying (i.e., EPR-active) probe ions it is possible to examine polyelectrolytes from the counterions’ point of view. It was possible to gain insight into i) the dynamics and local geometry of counterion attachment, ii) conformations and dynamics of local segments of the polyion in an indirect manner, and iii) the spatial distribution of spin probe ions that surround polyions in solution. Analysis of CW EPR spectra of dianion nitroxide spin probe Fremy’s salt (FS, potassium nitrosodisulfonate) in solutions of cationic PDADMAC polyelectrolyte revealed that FS ions and PDADMAC form transient ion pairs with a lifetime of less than 1 ns. This effect was termed as dynamic electrostatic attachment (DEA). By spectral simulation taking into account the rotational dynamics as a uniaxial Brownian reorientation, also the geometry of the attached state could be characterized. By variation of solvent, the effect of solvent viscosity and permittivity were investigated and indirect information of the polyelectrolyte chain motion was obtained. Furthermore, analysis of CW EPR data also indicates that in mixtures of organic solvent/water PDADMAC chains are preferentially solvated by the organic solvent molecules, while in purely aqueous mixtures the PDADMAC chain segments were found in different conformations depending on the concentration ratio R of FS counterions to PDADMAC repeat units.Broadenings in CW EPR spectra of FS ions were assigned to spin-exchange interaction and hence contain information on the local concentrations and distributions of the counterions. From analysis of these broadenings in terms of a modified cylindrical cell approach of polyelectrolyte theory, radial distribution functions for the FS ions in the different solvents were obtained. This approach breaks down in water above a threshold value of R, which again indicates that PDADMAC chain conformations are altered as a function of R. Double electron-electron resonance (DEER) measurements of FS ions were carried out to probe the distribution of attached counterions along polyelectrolyte chains. For a significant fraction of FS spin probes in solution with a rigid-rod model polyelectrolyte containing charged Ru2+-centers, a bimodal distance distribution was found that nicely reproduced the spacings of direct and next-neighbor Ru2+-centers along the polyelectrolyte: 2.35 and 4.7 nm. For the system of FS/PDADMAC, DEER data could be simulated by assuming a two-state distribution of spin probes, one state corresponding to a homogeneous (3-dimensional) distribution of spin probes in the polyelectrolyte bulk and the other to a linear (1-dimensional) distribution of spin probes that are electrostatically condensed along locally extended PDADMAC chain segments. From this analysis it is suggested that the PDADMAC chains form locally elongated structures of a size of at least ~5 nm.

Thiete und Bisthiete in der Heterocyclensynthese

Die vorliegende Arbeit beschäftigt sich mit der Synthese arenoanellierter Naphthothiete und Benzobisthiete, sowie mit der Umsetzung der aus diesen Thieten thermisch generierbaren Valenzisomeren (Thiochinonmethide). Diese Thiochinonmethide sind hochreaktive Diensysteme, die mit zahlreichen Dienophilen (homo- und hetero-Doppel- und Dreifachbindungssysteme) nach Diels-Alder abreagieren, die dabei entstehenden S-Heterocyclen können im Sechsring noch weitere Heteroatome (N, P, O, S) enthalten. Daraus resultiert ein großes Potential der Arenothiete zur Synthese neuer Thioheterocyclen. Durch die erstmals gelungene Synthese der beiden Benzobisthiete 2H,3H-Benzo[1,2-b:4,3-b']bisthiet und 1H,4H-Benzo[2,1-b:3,4-b']bisthiet mit gewinkelter Anellierungsgeometrie hat das synthetische Spektrum der aus Arenothieten darstellbaren Thioheterocyclen nochmal eine deutliche Erweiterung erfahren.

Die Darstellung der Arenothiete erfolgt in einer mehrstufigen Synthese, in deren finalem Schritt sie mittels Blitz-Vakuum-Pyrolyse aus Arylhydroxymethylthiolen gebildet werden, dabei wird das Edukt mittels molekularer Strömung in den "Reaktor" eingebracht. Da die Arylhydroxymethylthiole in der Regel nur eine sehr geringe Flüchtigkeit haben, waren die Arenothiete meist nur in geringen Mengen darstellbar. Daher wurde in dieser Arbeit sowohl die Synthese neuer Arenothiete (gewinkelte Benzobisthiete) als auch eine Optimierung der bisherigen Synthesemethode angestrebt; diese erfolgt bevorzugt durch Variation der Pyrolyseedukte in Richtung zu potentiell höherflüchtigen Verbindungen.

Im Rahmen dieser Versuche war die Darstellung zweier Arenothiete ausgehend von cyclischen O,S-Acetalen als alternative Pyrolysevorstufen erfolgreich.

Ein besonderes Interesse speziell an Benzobisthieten begründet sich in ihrer generellen Fähigkeit zum Aufbau von bandartigen Strukturen durch Oligo- und Poly-Diels-Alder-Reaktionen. Durch die Synthese einiger Modellverbindungen konnte ihre prinzipielle Eignung zum Aufbau von Bandstrukturen auch für die beiden Benzobisthiete belegt werden.

Eduard Study (1862-1930) - ein mathematischer Mephistopheles im geometrischen Gärtchen

Diese Arbeit befasst sich mit Eduard Study (1862-1930), einem der deutschen Geometer um die Jahrhundertwende, der seine Zeit zum Einen durch seine Kontakte zu Klein, Hilbert, Engel, Lie, Gordan, Halphen, Zeuthen, Einstein, Hausdorff und Weyl geprägt hat, zum Anderen in ihr aber auch für seine beißenden und stilistisch ausgefeilten Kritiken ebenso berühmt wie berüchtigt war. Da sich Study mit einer Vielzahl mathematischer Themen beschäftigt hat, führen wir zunächst in die von ihm bearbeiteten Gebiete der Geometrie des 19. Jahrhunderts ein (analytische und synthetische Geometrie im Sinne von Monge, Poncelet, Plücker und Reye, Invariantentheorie Clebsch-Gordan'scher Prägung, abzählende Geometrie von Chasles und Halphen, die Werke Lie's und Grassmann’s, Liniengeometrie sowie Axiomatik und Grundlagenkrise). In seiner darauf folgenden Biographie finden sich als zentrale Stellen seine Habilitation bei Klein über die Chasles’sche Vermutung, sein Streit mit Zeuthen darüber als eine der Debatten der Mathematischen Annalen (aus der er historisch zwar nicht, mathematisch aber tatsächlich als Gewinner hätte herausgehen müssen, wie wir an der Lösung des Problems durch van der Waerden sehen werden) und seine Auseinandersetzungen als etablierter Bonner Professor mit Engel über Lie, Weyl über Invariantentheorie, zahlreichen philosophischen Richtungen über das Raumproblem, Pasch’s Axiomatik, Hilbert’s Formalismus sowie Brouwer’s und Weyl’s Intuitionismus.

Grating coupled surface plasmon enhanced fluorescence spectroscopy

Over the last three decades, sensors based on the phenomenon of surface plasmon resonance have proven particularly suitable for real time thin film characterization, gas detection, biomolecular interaction examination and to supplement electrochemical methods. Systems based on prism coupling have been combined with fluorescence detection under the name of surface plasmon fluorescence spectroscopy to increase sensitivity even further. Alternatively, metal gratings can be employed to match photons for plasmon resonance. The real time monitoring of binding reactions not yet been reported in the combination of fluorescence detection and grating coupling. Grating-based systems promise more competitive products, because of reduced operating costs, and offer benefits for device engineering. This thesis is comprised of a comprehensive study of the suitability of grating coupling for fluorescence based analyte detection. Fundamental properties of grating coupled surface plasmon fluorescence spectroscopy are described, as well as issues related to the commercial realization of the method. Several new experimental techniques are introduced and demonstrated in order to optimize performance in certain areas and improve upon capabilities in respect to prism-based systems. Holographically fabricated gratings are characterized by atomic force microscopy and optical methods, aided by simulations and profile parameters responsible for efficient coupling are analyzed. The directional emission of fluorophores immobilized on a grating surface is studied in detail, including the magnitude and geometry of the fluorescence emission pattern for different grating constants and polarizations. Additionally, the separation between the minimum of the reflected intensity and the maximum fluorescence excitation position is examined. One of the key requirements for the commercial feasibility of grating coupling is the cheap and faithful mass production of disposable samples from a given master grating. The replication of gratings is demonstrated by a simple hot embossing method with good reproducibility to address this matter. The in-situ fluorescence detection of analyte immobilization and affinity measurements using grating coupling are described for the first time. The physical factors related to the sensitivity of the technique are assessed and the lower limit of detection of the technique is determined for an exemplary assay. Particular attention is paid to the contribution of bulk fluorophores to the total signal in terms of magnitude and polarization of incident and emitted light. Emission from the bulk can be a limiting factor for experiments with certain assay formats. For that reason, a novel optical method, based on the modulation of both polarization and intensity of the incident beam, is introduced and demonstrated to be capable of eliminating this contribution.

Quantum gravity effects in rotating black hole spacetimes

The aim of this work is to explore, within the framework of the presumably asymptotically safe Quantum Einstein Gravity, quantum corrections to black hole spacetimes, in particular in the case of rotating black holes. We have analysed this problem by exploiting the scale dependent Newton s constant implied by the renormalization group equation for the effective average action, and introducing an appropriate "cutoff identification" which relates the renormalization scale to the geometry of the spacetime manifold. We used these two ingredients in order to "renormalization group improve" the classical Kerr metric that describes the spacetime generated by a rotating black hole. We have focused our investigation on four basic subjects of black hole physics. The main results related to these topics can be summarized as follows. Concerning the critical surfaces, i.e. horizons and static limit surfaces, the improvement leads to a smooth deformation of the classical critical surfaces. Their number remains unchanged. In relation to the Penrose process for energy extraction from black holes, we have found that there exists a non-trivial correlation between regions of negative energy states in the phase space of rotating test particles and configurations of critical surfaces of the black hole. As for the vacuum energy-momentum tensor and the energy conditions we have shown that no model with "normal" matter, in the sense of matter fulfilling the usual energy conditions, can simulate the quantum fluctuations described by the improved Kerr spacetime that we have derived. Finally, in the context of black hole thermodynamics, we have performed calculations of the mass and angular momentum of the improved Kerr black hole, applying the standard Komar integrals. The results reflect the antiscreening character of the quantum fluctuations of the gravitational field. Furthermore we calculated approximations to the entropy and the temperature of the improved Kerr black hole to leading order in the angular momentum. More generally we have proven that the temperature can no longer be proportional to the surface gravity if an entropy-like state function is to exist.

Foliation boudinage

In this thesis foliation boudinage and related structures have been studied based on field observations and numerical modeling. Foliation boudinage occurs in foliated rocks independent of lithology contrast. The developing structures are called ‘Foliation boudinage structures (FBSs)’ and show evidence for both ductile and brittle deformation. They are recognized in rocks by perturbations in monotonous foliation adjacent to a central discontinuity, mostly filled with vein material. Foliation boudinage structures have been studied in the Çine Massif in SW-Turkey and the Furka Pass-Urseren Zone in central Switzerland. Four common types have been distinguished in the field, named after vein geometries in their boudin necks in sections normal to the boudin axis: lozenge-, crescent-, X- and double crescent- type FBSs. Lozengetype FBSs are symmetric and characterized by lozenge-shaped veins in their boudin neck with two cusps facing opposite sides. A symmetrical pair of flanking folds occurs on the two sides of the vein. Crescent-type FBSs are asymmetric with a single smoothly curved vein in the boudin neck, with vein contacts facing to one side. X- and double crescent- type FBSs are asymmetric. The geometry of the neck veins resembles that of cuspate-lobate structures. The geometry of flanking structures is related to the shape of the veins. The veins are mostly filled with massive quartz in large single crystals, commonly associated with tourmaline, feldspar and biotite and in some cases with chlorite. The dominance of large facetted single quartz crystals and spherulitic chlorite in the veins suggest that the minerals grew into open fluidfilled space. FLAC experiments show that fracture propagation during ductile deformation strongly influences the geometry of developing veins. The cusps of the veins are better developed in the case of propagating fractures. The shape of the boudin neck veins in foliation boudinage depends on the initial orientation and shape of the fracture, the propagation behaviour of the fracture, the geometry of bulk flow, and the stage at which mineral filling takes place. A two dimensional discrete element model was used to study the progressive development of foliation boudinage structures and the behavior of visco-elastic material deformed under pure shear conditions. Discrete elements are defined by particles that are connected by visco-elastic springs. Springs can break. A number of simulations was Abstract vii performed to investigate the effect of material properties (Young’s modulus, viscosity and breaking strength) and anisotropy on the developing structures. The models show the development of boudinage in single layers, multilayers and in anisotropic materials with random mica distribution. During progressive deformation different types of fractures develop from mode I, mode II to the combination of both. Voids develop along extension fractures, at intersections of conjugate shear fractures and in small pull-apart structures along shear fractures. These patterns look similar to the natural examples. Fractures are more localized in the models where the elastic constants are low and the competence contrast is high between the layers. They propagate through layers where the constants are high and the competence contrast is relatively low. Flow localize around these fractures and voids. The patterns similar to symmetric boudinage structures and extensional neck veins (e.g. lozenge type) more commonly develop in the models with lower elastic constants and anisotropy. The patterns similar to asymmetric foliation boudinage structures (e.g. X-type) develop associated with shear fractures in the models where elastic constants and anisotropy of the materials are relatively high. In these models boudin neck veins form commonly at pull-aparts along the shear fractures and at the intersection of fractures.

Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Fluorescent ionene-dye nanoparticles by electrostatic self-assembly

It is investigated that the association of linear cationic model polyelectrolytes with oppositely charged pyrenetetrasulfonate (PY) in aqueous solution. For this purpose water soluble ionenes were prepared via Menschutkin reaction from 1-4-diazabicyclo [2.2.2] octane and e.g. 1,6-dibromohexane and 1,4 dibromotransbuten. The complex formation between dye molecules PY and oppositely charged ionenes (PD4, PD6, PD4-2 and PD4coPD6) of different chemical structures in aqueous solution was studied by light scattering (LS), small angle neutron scattering (SANS), UV-Vis, fluorescence spectroscopy and atomic force microscopy (AFM). Spectrophotometric titration results revealed that PY molecules were bind to ionenes cooperative process due to π-π interaction. Cooperative binding constant KD was determined as 6.4 x 10^6 M^-1 (+ or - 10^5 M^-1). It was found that binding mode and geometry of PY is predominantly depending on inter-charge distances of corresponding ionenes. Resultant complexes have exhibited size and structure variation as a function of charge ratio (L), ionic strength, inter-charge distances. Spherical dye-ionene complexes of which radius of gyration ranging between (RG) 50 and 190 nm have been observed in PD4-PY system while this was not possible with a different ionene (PD6) or either case ionene excess. It was found that most of the PD4-PY complexes had RG / RH ~ 0.78. Based on the AFM and LS results, spherical complexes have certain colloidal stability and their size can effectively controlled by changing the L.