Controllability and stabilizability of linear time-varying distributed hereditary control systems

This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varyinglinear abstract differential equation with distributed delay in the state variables. An approximate controllability propertyis established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operatorsassociated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptoticstability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximatecontrollability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes thesystem. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley &Sons, Ltd.

Non-centrosymmetric crystals of new N-benzylideneaniline derivatives as potential materials for non-linear optics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Procura espontânea de atendimento por idosos da Estratégia Saúde da Família: análise não linear do comportamento temporal das morbidades

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise das tensões em próteses implantossuportadas esplintadas, variando o tipo de conexão protética e a inclinação do implante: estudo pelo método dos elementos finitos tridimensionais não linear

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Alterations in pulmonary structure by elastase administration in a model of emphysema in mice is associated with functional disturbances

Several experimental studies of pulmonary emphysema using animal models have been described in the literature. However, only a few of these studies have focused on the assessment of ergometric function as a non-invasive technique to validate the methodology used for induction of experimental emphysema. Additionally, functional assessments of emphysema are rarely correlated with morphological pulmonary abnormalities caused by induced emphysema. The present study aimed to evaluate the effects of elastase administered by tracheal puncture on pulmonary parenchyma and their corresponding functional impairment. This was evaluated by measuring exercise capacity in C57Bl/6 mice in order to establish a reproducible and safe methodology of inducing experimental emphysema. Thirty six mice underwent ergometric tests before and 28 days after elastase administration. Pancreatic porcine elastase solution was administered by tracheal puncture, which resulted in a significantly decreased exercise capacity, shown by a shorter distance run (-30.5%) and a lower mean velocity (-15%), as well as in failure to increase the elimination of carbon dioxide. The mean linear intercept increased significantly by 50% in tracheal elastase administration. In conclusion, application of elastase by tracheal function in C57Bl/6 induces emphysema, as validated by morphometric analyses, and resulted in a significantly lower exercise capacity, while resulting in a low mortality rate. (C) 2011 Sociedade Portuguesa de Pneumologia. Published by Elsevier Espana, S.L. All rights reserved.

Ethanol and Water Adsorption on Close-Packed 3d, 4d, and 5d Transition-Metal Surfaces: A Density Functional Theory Investigation with van der Waals Correction

Nowadays, there is a great interest in the economic success of direct ethanol fuel cells; however, our atomistic understanding of the designing of stable and low-cost catalysts for the steam reforming of ethanol is still far from satisfactory, in particular due to the large number of undesirable intermediates. In this study, we will report a first-principles investigation of the adsorption properties of ethanol and water at low coverage on close-packed transition-metal (TM) surfaces, namely, Fe(110), Co(0001), Ni(111), Cu(111), Ru(0001), Rh(111), Pd(111), Ag(111), Os(0001), Ir(111), Pt(111), and Au(111), employing density functional theory (DFT) calculations. We employed the generalized gradient approximation with the formulation proposed by Perdew, Burke, and Erzenholf (PBE) to the exchange correlation functional and the empirical correction proposed by S. Grimme (DFT+D3) for the van der Waals correction. We found that both adsorbates binds preferentially near or on the on top sites of the TM surfaces through the 0 atoms. The PBE adsorption energies of ethanol and water decreases almost linearly with the increased occupation of the 4d and 5d d-band, while there is a deviation for the 3d systems. The van der Waals correction affects the linear behavior and increases the adsorption energy for both adsorbates, which is expected as the van der Waals energy due to the correlation effects is strongly underestimated by DFT-PBE for weak interacting systems. The geometric parameters for water/TM are not affected by the van der Waals correction, i.e., both DFT and DFT+D3 yield an almost parallel orientation for water on the TM surfaces; however, DFT+D3 changes drastically the ethanol orientation. For example, DFT yields an almost perpendicular orientation of the C-C bond to the TM surface, while the C-C bond is almost parallel to the surface using DFT +D3 for all systems, except for ethanol/Fe(110). Thus, the van der Waals correction decreases the distance of the C atoms to the TM surfaces, which might contribute to break the C-C bond. The work function decreases upon the adsorption of ethanol and water, and both follow the same trends, however, with different magnitude (larger for ethanol/TM) due to the weak binding of water to the surface. The electron density increases mainly in the region between the topmost layer and the adsorbates, which explains the reduction of the substrate work function.

Multivariate gene expression analysis reveals functional connectivity changes between normal/tumoral prostates

Abstract Background Prostate cancer is a leading cause of death in the male population, therefore, a comprehensive study about the genes and the molecular networks involved in the tumoral prostate process becomes necessary. In order to understand the biological process behind potential biomarkers, we have analyzed a set of 57 cDNA microarrays containing ~25,000 genes. Results Principal Component Analysis (PCA) combined with the Maximum-entropy Linear Discriminant Analysis (MLDA) were applied in order to identify genes with the most discriminative information between normal and tumoral prostatic tissues. Data analysis was carried out using three different approaches, namely: (i) differences in gene expression levels between normal and tumoral conditions from an univariate point of view; (ii) in a multivariate fashion using MLDA; and (iii) with a dependence network approach. Our results show that malignant transformation in the prostatic tissue is more related to functional connectivity changes in their dependence networks than to differential gene expression. The MYLK, KLK2, KLK3, HAN11, LTF, CSRP1 and TGM4 genes presented significant changes in their functional connectivity between normal and tumoral conditions and were also classified as the top seven most informative genes for the prostate cancer genesis process by our discriminant analysis. Moreover, among the identified genes we found classically known biomarkers and genes which are closely related to tumoral prostate, such as KLK3 and KLK2 and several other potential ones. Conclusion We have demonstrated that changes in functional connectivity may be implicit in the biological process which renders some genes more informative to discriminate between normal and tumoral conditions. Using the proposed method, namely, MLDA, in order to analyze the multivariate characteristic of genes, it was possible to capture the changes in dependence networks which are related to cell transformation.

Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Supramolecular functional assemblies with photo or chemical addressability

Supramolecular self-assembly represents a key technology for the spontaneous construction of nanoarchitectures and for the fabrication of materials with enhanced physical and chemical properties. In addition, a significant asset of supramolecular self-assemblies rests on their reversible formation, thanks to the kinetic lability of their non-covalent interactions. This dynamic nature can be exploited for the development of “self-healing” and “smart” materials towards the tuning of their functional properties upon various external factors. One particular intriguing objective in the field is to reach a high level of control over the shape and size of the supramolecular architectures, in order to produce well-defined functional nanostructures by rational design. In this direction, many investigations have been pursued toward the construction of self-assembled objects from numerous low-molecular weight scaffolds, for instance by exploiting multiple directional hydrogen-bonding interactions. In particular, nucleobases have been used as supramolecular synthons as a result of their efficiency to code for non-covalent interaction motifs. Among nucleobases, guanine represents the most versatile one, because of its different H-bond donor and acceptor sites which display self-complementary patterns of interactions. Interestingly, and depending on the environmental conditions, guanosine derivatives can form various types of structures. Most of the supramolecular architectures reported in this Thesis from guanosine derivatives require the presence of a cation which stabilizes, via dipole-ion interactions, the macrocyclic G-quartet that can, in turn, stack in columnar G-quadruplex arrangements. In addition, in absence of cations, guanosine can polymerize via hydrogen bonding to give a variety of supramolecular networks including linear ribbons. This complex supramolecular behavior confers to the guanine-guanine interactions their upper interest among all the homonucleobases studied. They have been subjected to intense investigations in various areas ranging from structural biology and medicinal chemistry – guanine-rich sequences are abundant in telomeric ends of chromosomes and promoter regions of DNA, and are capable of forming G-quartet based structures– to material science and nanotechnology. This Thesis, organized into five Chapters, describes mainly some recent advances in the form and function provided by self-assembly of guanine based systems. More generally, Chapter 4 will focus on the construction of supramolecular self-assemblies whose self-assembling process and self-assembled architectures can be controlled by light as external stimulus. Chapter 1 will describe some of the many recent studies of G-quartets in the general area of nanoscience. Natural G- quadruplexes can be useful motifs to build new structures and biomaterials such as self-assembled nanomachines, biosensors, therapeutic aptamer and catalysts. In Chapters 2-4 it is pointed out the core concept held in this PhD Thesis, i.e. the supramolecular organization of lipophilic guanosine derivatives with photo or chemical addressability. Chapter 2 will mainly focus on the use of cation-templated guanosine derivatives as a potential scaffold for designing functional materials with tailored physical properties, showing a new way to control the bottom-up realization of well-defined nanoarchitectures. In section 2.6.7, the self-assembly properties of compound 28a may be considered an example of open-shell moieties ordered by a supramolecular guanosine architecture showing a new (magnetic) property. Chapter 3 will report on ribbon-like structures, supramolecular architectures formed by guanosine derivatives that may be of interest for the fabrication of molecular nanowires within the framework of future molecular electronic applications. In section 3.4 we investigate the supramolecular polymerizations of derivatives dG 1 and G 30 by light scattering technique and TEM experiments. The obtained data reveal the presence of several levels of organization due to the hierarchical self-assembly of the guanosine units in ribbons that in turn aggregate in fibrillar or lamellar soft structures. The elucidation of these structures furnishes an explanation to the physical behaviour of guanosine units which display organogelator properties. Chapter 4 will describe photoresponsive self-assembling systems. Numerous research examples have demonstrated that the use of photochromic molecules in supramolecular self-assemblies is the most reasonable method to noninvasively manipulate their degree of aggregation and supramolecular architectures. In section 4.4 we report on the photocontrolled self-assembly of modified guanosine nucleobase E-42: by the introduction of a photoactive moiety at C8 it is possible to operate a photocontrol over the self-assembly of the molecule, where the existence of G-quartets can be alternately switched on and off. In section 4.5 we focus on the use of cyclodextrins as photoresponsive host-guest assemblies: αCD–azobenzene conjugates 47-48 (section 4.5.3) are synthesized in order to obtain a photoresponsive system exhibiting a fine photocontrollable degree of aggregation and self-assembled architecture. Finally, Chapter 5 contains the experimental protocols used for the research described in Chapters 2-4.

Thin functional conducting polymer films

In the present study, thin functional conducting polyaniline (PANI) films, either doped or undoped, patterned or unpatterned, were prepared by different approaches. The properties of the obtained PANI films were investigated in detail by a combination of electrochemistry with several other techniques, such as SPR, QCM, SPFS, diffraction, etc. The sensing applications (especially biosensing applications) of the prepared PANI films were explored. Firstly, the pure PANI films were prepared by the electropolymerisation method and their doping/dedoping properties in acidic conditions were investigated in detail by a combination of electrochemistry with SPR and QCM. Dielectric constants of PANI at different oxidation states were obtained quantitatively. The results obtained here laid a good foundation for the following investigations of PANI films in neutral pH conditions. Next, PANI multilayer films doped by a variety of materials were prepared by the layer-by-layer method in order to explore their biosensing applications, because of the loss of redox activity of pure PANI in neutral pH conditions. The dopants used include not only the traditionally used linear polyelectrolytes, but also, for the first tim, some other novel materials, like modified gold nanoparticles or modified carbon nanotubes. Our results showed that all the used dopants could form stable multilayer films with PANI. All the obtained PANI multilayer films showed good redox activity in a neutral pH environment, which makes them feasible for bioassays. We found that all the prepared PANI multilayer films can electrocatalyze the oxidation of NADH in neutral conditions at a low potential, although their catalytic efficiencies are different. Among them, PANI/carbon nanotube system showed the highest catalytic efficiency toward the oxidation of NADH, which makes it a good candidate as a NADH sensor. Besides, because some of the prepared PANI multilayer systems were end-terminated with –COOH groups (like PANI/Au nanoparticles system), which can be utilized to easily link biomolecules for biosensing applications. Here, we demonstrated, for the first time, to use the prepared PANI multilayer films for the DNA hybridisation detection. The detection event was monitored either by direct electrochemical method, or by enzyme-amplified electrochemical method, or by surface plasmon enhanced fluorescence spectroscopic method. All the methods can effectively differentiate non-complementary DNA from the complementary ones, even at the single-base mismatch level. It should also be noted that, our success in fabricating PANI multilayer films with modified Au nanoparticles or carbon nanotubes also offered another novel method for incorporating such novel materials into (conducting) polymers. Because of the unique electrochemical and optical properties of each component of the obtained PANI multilayer films, they should also find potential applications in many other fields such as microelectronics, or for electrochromic and photovoltaic devices. Finally, patterned PANI films were fabricated by the combination of several patterning techniques, such as the combination of electrocopolymerization with micromolding in capillaries (EP-MIMIC), the combination of microcontact printing with the layer-by-layer technique (µCP-LBL), and the polystyrene (PS) template induced electropolymerisation method. Using the obtained stripe-shaped PANI/PSS film, a redox-switchable polymer grating based on the surface-plasmon-enhanced mode was constructed and its application in the field of biosensing was explored. It was found that the diffraction efficiency (DE) of the grating was very sensitive to the applied potential (i.e. redox state of the film) as well as the pH environment of the dielectric medium. Moreover, the DE could also be effectively tuned by an electrocatalytic event, such as the electrocatalytic oxidation of NADH by the grating film. By using PS colloidal crystal assemblies as templates, well-ordered 3D interconnected macroporous PANI arrays (PANI inverse opals) were fabricated via electropolymerisation method. The quality of the obtained inverse opals was much higher than those reported by chemical synthesis method. By electrochemical method, the structures of the prepared inverse opals can be easily controlled. To explore the possible biosensing applications of PANI inverse opals, efforts were also done toward the fabrication of PANI composite inverse opals. By selecting proper dopants, high quality inverse opals of PANI composites were fabricated for the first time. And the obtained opaline films remained redox-active in neutral pH conditions, pointing to their possible applications for electrobioassays.

Synthesis of hexa-peri-hexabenzocoronenes - from building blocks to functional materials

Discotic hexa-peri-hexabenzocoronene (HBC) derivatives have attracted intensive scientific interest due to their unique optoelectronic properties, which depends, to a large extend, upon the attached functional groups. The presented work covers the synthesis of novel HBC building blocks and new HBC derivatives as functional materials. The traditional preparation of HBC derivatives requires elaborate synthetic techniques and tremendous effort. Especially, more than 10 synthetic steps are usually necessary to approach HBCs with lower symmetries. In order to simplify the synthetic work and reduce the high costs, a novel synthetic strategy involving only four steps was developed based on 2,3,5,6-tetraphenyl-1,4-diiodobenzene intermediates and palladium catalyzed Suzuki cross coupling reactions. In order to introduce various functionalities and expand the diversity of multi-functionalizations, a novel C2v-symmetric dihalo HBC building block 2-47, which contains one iodine and one bromine in para positions, was prepared following the traditional intermolecular [4+2] Diels-Alder reaction route. The outstanding chemical selectivity between iodo and bromo groups in this compound consequently leads to lots of HBC derivatives bearing different functionalities. Directly attached heteroatoms will improve the material properties. According to the application of intramolecular Scholl reaction to a para-dimethoxy HPB, which leads to a meta-dimethoxy HBC, a phenomenon of phenyl group migration was discovered. Thereby, several interesting mechanistic details involving arenium cation intermediates were discussed. With a series of dipole functionalized HBCs, the molecular dynamics of this kind of materials was studied in different phases by DSC, 2D WAXD, solid state NMR and dielectric spectroscopies. High charge carrier mobility is an important parameter for a semiconductive material and depends on the degree of intramolecular order of the discotic molecules in thin films for HBC derivatives. Dipole – dipole interaction and hydrogen bonds were respectively introduced in order to achieve highly ordered supramolecular structure. The self-assembly behavior of these materials were investigated both in solution and solid state. Depending upon the different functionalities, these novel materials show either gelating or non-linear optical properties, which consequently broaden their applications as functional materials. In the field of conceivable electronic devices at a molecular level, HBCs hold high promise. Differently functionalized HBCs have been used as active component in the studies of single-molecular CFET and metal-SAMs-metal junctions. The outstanding properties shown in these materials promise their exciting potential applications in molecular devices.

Lesion detection and classification in breast cancer: evaluation of approaches based on morphological features, tracer kinetic modelling and semi-quantitative parameters in MR functional imaging (DCE-MRI)

The diagnosis, grading and classification of tumours has benefited considerably from the development of DCE-MRI which is now essential to the adequate clinical management of many tumour types due to its capability in detecting active angiogenesis. Several strategies have been proposed for DCE-MRI evaluation. Visual inspection of contrast agent concentration curves vs time is a very simple yet operator dependent procedure, therefore more objective approaches have been developed in order to facilitate comparison between studies. In so called model free approaches, descriptive or heuristic information extracted from time series raw data have been used for tissue classification. The main issue concerning these schemes is that they have not a direct interpretation in terms of physiological properties of the tissues. On the other hand, model based investigations typically involve compartmental tracer kinetic modelling and pixel-by-pixel estimation of kinetic parameters via non-linear regression applied on region of interests opportunely selected by the physician. This approach has the advantage to provide parameters directly related to the pathophysiological properties of the tissue such as vessel permeability, local regional blood flow, extraction fraction, concentration gradient between plasma and extravascular-extracellular space. Anyway, nonlinear modelling is computational demanding and the accuracy of the estimates can be affected by the signal-to-noise ratio and by the initial solutions. The principal aim of this thesis is investigate the use of semi-quantitative and quantitative parameters for segmentation and classification of breast lesion. The objectives can be subdivided as follow: describe the principal techniques to evaluate time intensity curve in DCE-MRI with focus on kinetic model proposed in literature; to evaluate the influence in parametrization choice for a classic bi-compartmental kinetic models; to evaluate the performance of a method for simultaneous tracer kinetic modelling and pixel classification; to evaluate performance of machine learning techniques training for segmentation and classification of breast lesion.

Functional polymer coatings — My-Patterning and My-Analysis

In dieser Arbeit werden Strukturen beschrieben, die mit Polymeren auf Oberflächen erzeugt wurden. Die Anwendungen reichen von PMMA und PNIPAM Polymerbürsten, über die Restrukturierung von Polystyrol durch Lösemittel bis zu 3D-Strukturen, die aus PAH/ PSS Polyelektrolytmultischichten bestehen. Im ersten Teil werden Polymethylmethacrylat (PMMA) Bürsten in der ionischen Flüssigkeit 1-Butyl-3-Methylimidazolium Hexafluorophospat ([Bmim][PF6]) durch kontrollierte radikalische Polymerisation (ATRP) hergestellt. Kinetische Untersuchungen zeigten ein lineares und dichtes Bürstenwachstum mit einer Wachstumsrate von 4600 g/mol pro nm. Die durchschnittliche Pfropfdichte betrug 0.36 µmol/m2. Als Anwendung wurden Mikrotropfen bestehend aus der ionischen Flüssigkeit, Dimethylformamid und dem ATRP-Katalysator benutzt, um in einer definierten Geometrie Polymerbürsten auf Silizium aufzubringen. Auf diese Weise lässt sich eine bis zu 13 nm dicke Beschichtung erzeugen. Dieses Konzept ist durch die Verdampfung des Monomers Methylmethacrylat (MMA) limitiert. Aus einem 1 µl großen Tropfen aus ionischer Flüssigkeit und MMA (1:1) verdampft MMA innerhalb von 100 s. Daher wurde das Monomer sequentiell zugegeben. Der zweite Teil konzentriert sich auf die Strukturierung von Oberflächen mit Hilfe einer neuen Methode: Tintendruck. Ein piezoelektrisch betriebenes „Drop-on-Demand“ Drucksystem wurde verwendet, um Polystyrol mit 0,4 nl Tropfen aus Toluol zu strukturieren. Die auf diese Art und Weise gebildeten Mikrokrater können Anwendung als Mikrolinsen finden. Die Brennweite der Mikrolinsen kann über die Anzahl an Tropfen, die für die Strukturierung verwendet werden, eingestellt werden. Theoretisch und experimentell wurde die Brennweite im Bereich von 4,5 mm bis 0,21 mm ermittelt. Der zweite Strukturierungsprozess nutzt die Polyelektrolyte Polyvinylamin-Hydrochlorid (PAH) und Polystyrolsulfonat (PSS), um 3D-Strukturen wie z.B. Linien, Schachbretter, Ringe, Stapel mit einer Schicht für Schicht Methode herzustellen. Die Schichtdicke für eine Doppelschicht (DS) liegt im Bereich von 0.6 bis 1.1 nm, wenn NaCl als Elektrolyt mit einer Konzentration von 0,5 mol/l eingesetzt wird. Die Breite der Strukturen beträgt im Mittel 230 µm. Der Prozess wurde erweitert, um Nanomechanische Cantilever Sensoren (NCS) zu beschichten. Auf einem Array bestehend aus acht Cantilevern wurden je zwei Cantilever mit fünf Doppelschichten PAH/ PSS und je zwei Cantilever mit zehn Doppelschichten PAH/ PSS schnell und reproduzierbar beschichtet. Die Massenänderung für die individuellen Cantilever war 0,55 ng für fünf Doppelschichten und 1,08 ng für zehn Doppelschichten. Der daraus resultierende Sensor wurde einer Umgebung mit definierter Luftfeuchtigkeit ausgesetzt. Die Cantilever verbiegen sich durch die Ausdehnung der Beschichtung, da Wasser in das Polymer diffundiert. Eine maximale Verbiegung von 442 nm bei 80% Luftfeuchtigkeit wurde für die mit zehn Doppelschichten beschichteten Cantilever gefunden. Dies entspricht einer Wasseraufnahme von 35%. Zusätzlich konnte aus den Verbiegungsdaten geschlossen werden, dass die Elastizität der Polyelektrolytmultischichten zunimmt, wenn das Polymer gequollen ist. Das thermische Verhalten in Wasser wurde im nächsten Teil an nanomechanischen Cantilever Sensoren, die mit Poly(N-isopropylacrylamid)bürsten (PNIPAM) und plasmapolymerisiertem N,N-Diethylacrylamid beschichtet waren, untersucht. Die Verbiegung des Cantilevers zeigte zwei Bereiche: Bei Temperaturen kleiner der niedrigsten kritischen Temperatur (LCST) ist die Verbiegung durch die Dehydration der Polymerschicht dominiert und bei Temperaturen größer der niedrigsten kritischen Temperatur (LCST) reagiert der Cantilever Sensor überwiegend auf Relaxationsprozesse innerhalb der kollabierten Polymerschicht. Es wurde gefunden, dass das Minimum in der differentiellen Verbiegung mit der niedrigsten kritischen Temperatur von 32°C und 44°C der ausgewählten Polymeren übereinstimmt. Im letzten Teil der Arbeit wurden µ-Reflektivitäts- und µ-GISAXS Experimente eingeführt als neue Methoden, um mikrostrukturierte Proben wie NCS oder PEM Linien mit Röntgenstreuung zu untersuchen. Die Dicke von jedem individuell mit PMMA Bürsten beschichtetem NCS ist im Bereich von 32,9 bis 35,2 nm, was mit Hilfe von µ-Reflektivitätsmessungen bestimmt wurde. Dieses Ergebnis kann mit abbildender Ellipsometrie als komplementäre Methode mit einer maximalen Abweichung von 7% bestätigt werden. Als zweites Beispiel wurde eine gedruckte Polyelektrolytmultischicht aus PAH/PSS untersucht. Die Herstellungsprozedur wurde so modifiziert, dass Goldnanopartikel in die Schichtstruktur eingebracht wurden. Durch Auswertung eines µ-GISAXS Experiments konnte der Einbau der Partikel identifiziert werden. Durch eine Anpassung mit einem Unified Fit Modell wurde herausgefunden, dass die Partikel nicht agglomeriert sind und von einer Polymermatrix umgeben sind.

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Poly(lactide): from hyperbranched copolyesters to new block copolymers with functional methacrylates

The prologue of this thesis (Chapter 1.0) gives a general overview on lactone based poly(ester) chemistry with a focus on advanced synthetic strategies for ring-opening polymerization, including the emerging field of organo catalysis. This section is followed by a presentation of the state-of the art regarding the two central fields of the thesis: (i) polyfunctional and branched poly(ester)s in Chapter 1.1 as well as (ii) the development of new poly(ester) based block copolymers with functional methacrylates (Chapter 1.2). Chapter 2 deals with the synthesis of new, non-linear poly(ester) structures. In Chapter 2.1, the synthesis of poly(lactide)-based multiarm stars, prepared via a grafting-from method, is described. The hyperbranched poly(ether)-poly(ol) poly(glycerol) is employed as a hydrophilic core molecule. The resulting star block copolymers exhibit potential as phase transfer agents and can stabilize hydrophilic dyes in a hydrophobic environment. In Chapter 2.2, this approach is expanded to poly(glycolide) multiarm star polymers. The problem of the poor solubility of linear poly(glycolide)s in common organic solvents combined with an improvement of the thermal properties has been approached by the reduction of the total chain length. In Chapter 2.3, the first successful synthesis of hyperbranched poly(lactide)s is presented. The ring-opening, multibranching copolymerization of lactide with the “inimer” 5HDON (a hydroxyl-functional lactone monomer) was carefully examined. Besides a precise molecular characterization involving the determination of the degree of branching, we were able to put forward a reaction model for the formation of branching during polymerization. Several innovative approaches to amphiphilic poly(ester)/poly(methacrylate)-based block copolymers are presented in the third part of the thesis (Chapter 3). Block copolymer build-up especially relies on the combination of ring-opening and living radical polymerization. Atom transfer radical polymerization has been successfully combined with lactide ring-opening, using a “double headed” initiator. This strategy allowed for the realization of poly(lactide)-block-poly(2-hydroxyethyl methacrylate) copolymers, which represent promising materials for tissue engineering scaffolds with anti-fouling properties (Chapter 3.1). The two-step/one-pot approach forgoes the use of protecting groups for HEMA by a careful selection of the reaction conditions. A series of potentially biocompatible and partially biodegradable homo- and block copolymers is described in Chapter 3.2. In order to create a block copolymer with a comparably strong hydrophilic character, a new acetal-protected glycerol monomethacrylate monomer (cis-1,3- benzylidene glycerol methacrylate/BGMA) was designed. The hydrophobic poly(BGMA) could be readily transformed into the hydrophilic and water-soluble poly(iso-glycerol methacrylate) (PIGMA) by mild acidic hydrolysis. Block copolymers of PIGMA and poly(lactide) exhibited interesting spherical aggregates in aqueous environment which could be significantly influenced by variation of the poly(lactide)s stereo-structure. In Chapter 3.3, pH-sensitive poly(ethylene glycol)-b-PBGMA copolymers are described. At slightly acidic pH values (pH 4/37°C), they decompose due to a polarity change of the BGMA block caused by progressing acetal cleavage. This stimuli-responsive behavior renders the system highly attractive for the targeted delivery of anti-cancer drugs. In Chapter 3.4, which was realized in cooperation, the concept of biocompatible, amphiphilic poly(lactide) based polymer drug conjugates, was pursued. This was accomplished in the form of fluorescently labeled poly(HPMA)-b-poly(lactide) copolymers. Fluorescence correlation spectroscopy (FCS) of partially biodegradable block copolymer aggregates exhibited fast cellular uptake by human cervix adenocarcinoma cells without showing toxic effects in the examined concentration range (Chapter 4.1). The current state of further projects which will be pursued in future studies is addressed in Chapter 4. This covers the synthesis of biocompatible star block copolymers (Chapter 4.2) and the development of new methacrylate monomers for biomedical applications (Chapters 4.3 and 4.4). Finally, the further investigation of hydroxyl-functional lactones and carbonates which are promising candidates for the synthesis of new hydrophilic linear or hyperbranched biopolymers, is addressed in Chapter 4.5.