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Thesis--Halle-Wittenberg. / Vita. Includes bibliographical references (p. [76]).

Ce travail revisite la problématique des transitions de phases cristallines induites thermiquement et mécaniquement dans les polymères semi-cristallins à liaisons fortes. Ce point revêt une importance primordiale dans des matériaux où l'anisotropie de liaisons intermoléculaires (van der Waals vs hydrogène) conduit à l'existence de phases cristallines présentant une structure en feuillets des liaisons hydrogène. L'originalité principale réside dans le recours à l'expérimentation in situ pour le suivi de l'évolution structurale de ces matériaux polymorphes par diffraction et diffusion des rayons X sous rayonnement synchrotron. L'étude concerne les polyamides 11 et 6 et une attention particulière est portée à l'influence de ces transitions sur le comportement mécanique sous sollicitations uniaxiale et biaxiale. La caractérisation structurale confirme l'existence d'une transition de phase, la transition de Brill, vers une phase HT de symétrie hexagonale dans le cas de certaines structures cristallines (Alpha' et Delta' du PA11, Alpha défectueuse et Beta du PA6). Les formes stables (Alpha' du PA11 et Alpha du PA6) se reforment au refroidissement. Sous sollicitation uniaxiale, les polyamides se révèlent ductiles, quelle que soit la forme cristalline; une transformation ordre vers désordre intervient à T<TBrill et favorise l'apparition des mésophases (Delta’ du PA11 et Beta du PA6), tandis que la phase HT est stable mécaniquement. En étirage biaxial les phases présentant une organisation en feuillets des liaisons H sont fragiles, contrairement aux phases désordonnées et HT. Ceci souligne la nécessité de maîtriser l'évolution structurale dans la stratégie de mise en œuvre industrielle par biétirage à l'état solide. / This work revisits the problem of thermally and mechanically-induced crystal phase transitions in semi-crystalline polymers bearing H bonds. This point is of prime importance in materials where anisotropic intermolecular interactions (van der Waals vs H-bonding) gives rise to the existence of crystal phases with sheet-like H-bonded structures. The main originality of the present study lies in the use of in situ characterization of these polymorphic materials by wide angle and small angle X Ray scattering from a synchrotron source. Materials under concern are polyamides 11 and 6, and specific attention is paid to the role of these transitions on the mechanical behavior under uniaxial and biaxial drawing. The structural characterization confirms the existence of a phase transition, the Brill transition, towards a HT phase with hexagonal symmetry for some specific crystal structures (Alpha' and Delta' in PA11, Alpha defective and Beta in PA6). The most stable forms (Alpha' in PA11 and Alpha in PA6) rebuild upon cooling. Under uniaxial drawing, polyamides exhibit ductility, whatever the original crystal form is; an order towards disorder transition occurs for T<TBrill, which favors mesophase development (Delta’ in PA11 and Beta in PA6), while above TBrill the HT phase is mechanically stable. Upon biaxial stretching, phases with H-bonded sheet-like organization are brittle, contrary to mesomorphic and HT phases. These findings underline the need to monitor the structural evolution in order to achieve proper solid-state biaxial stretching in industrial processing.

[pt] Esta dissertação tem como propósito apresentar as fotografias de Alice Brill e sua relação com a trajetória pessoal da fotógrafa. O ponto de encontro entre as fotografias que ela produz e sua vida é o exílio, que transforma sua compreensão sobre o mundo a sua volta. Alice Brill nasceu na Alemanha em 1920 e residiu em Hamburgo até 1934, quando foi obrigada a deixar o país por causa de sua origem judaica. Neste período de exílio, ela percorreu um longo caminho até seu destino final, o Brasil. Está trajetória transformou o olhar de Brill e sua adaptação na cidade de São Paulo foi auxiliada pela sua arte. Dessa forma a artista expressou as dissonâncias que estava vivendo. Dentre sua vasta obra está a fotografia, que ela construiu ao longo da década de 50, apresentando um olhar distinto sobre as escolhas dos temas fotografados. Dentre os conjuntos que Brill construiu, as fotografias do hospital do juquery feitas em 1950 são importantes por diversos aspectos, pelo valor documental e artístico. / [en] The purpose of this dissertation is to present Alice Brill s photographs as well as their relationship with her personal life. The meeting point between her photographs and personal life is exile, which changes her understanding of the world. Alice Brill was born in Germany in 1920 and she has lived in Hamburg until 1934, when she was forced to leave her country due to her Jewish background. While in exile, she has traveled a long journey until her final destination, Brazil. These life experiences transformed Brill s gaze and her settlement in the city of São Paulo was facilitated by her art. In this way the artist expressed the dissonances she was experiencing. Among her vast work is photography, which she has built throughout the 1950s, presenting a distinct look to the subjects of her photography. Among the sets that Brill built, the photographs of the Juquery Hospital made in 1950 are important for several aspects, especially for their documentary and artistic value.

Polymer clay nanocomposites of polyamides and biodegradable polymers with three kinds of organomodified clays were prepared by different techniques (in situ polymerization, solution casting, and melt mixing). The polymers used in this research were nylons 56, 65 and 47 and the biodegradable polymers: poly (glycolic acid-alt-6-hydrohexanoic acid) and poly(glycolic acid-alt-6-aminohexanoic acid). The development of biodegradable nanocomposites with improved or modified material properties is an interesting topic since these new materials are expected to replace already existing biodegradable and non-biodegradable commodity plastics in some specific applications.This project aims to study the influence of clay particles incorporated in a polymer matrix on the crystallization processes, the study of the in situ polymerization kinetics of mixtures of clays and monomers of biodegradable polymers, as well as the influence of nanoparticles on the thermal behavior and morphologic parameters. Even-odd, and odd-even polyamides were chosen to study the Brill transition and to prepare nanocomposites with organomodified clays. These polyamides have a peculiar structure where hydrogen bonds are established along two different directions. X-ray diffraction as well as SAXS-WAXD synchrotron experiments were employed to study the structural changes induced by temperature, during heating and cooling. Different organomodified clays were used to prepare nanocomposites, which final structure was found to be dependent on the preparation method. Nanocomposites derived from biodegradable polymers were characterized by means of X-ray diffraction and transmission electron microscopy. Morphological studies showed that the extent of clay dispersion depended on the clay type and on the preparation technique. Hence, exfoliated and intercalated nanocomposites could be obtained. The final nanocomposite structure was found to have a great influence on both cold and hot crystallization processes. Hence, the crystallization rate increased and decreased with respect to the neat polymer when intercalated and exfoliated structures were respectively obtained. The kinetics of the polymerization process was also studied by means of FTIR and SAXS-WAXD. The results indicate that the presence of the organomodified clay had a remarkable effect on the kinetic parameters.

Seit W. Diffie und M. Hellman im Jahr 1976 ihren Ansatz für einen sicheren kryptographischen Schlüsselaustausch vorgestellten, ist der sogenannte Diskrete Logarithmus zu einem zentrales Thema der Kryptoanalyse geworden. Dieser stellt eine Erweiterung des bekannten Logarithmus auf beliebige endliche Gruppen dar. In der vorliegenden Dissertation werden zwei von C. Diem eingeführte Algorithmen untersucht, mit deren Hilfe der diskrete Logarithmus in der Picardgruppe glatter, nichthyperelliptischer Kurven vom Geschlecht g > 3 bzw. g > 4 über endlichen Körpern berechnet werden kann. Beide Ansätze basieren auf der sogenannten Indexkalkül-Methode und benutzen zur Erzeugung der dafür benötigten Relationen spezielle Linearsysteme, welche durch Schneiden von ebenen Modellen der Kurve mit Geraden erzeugt werden. Um Aussagen zur Laufzeit der Algorithmen tätigen zu können, werden verschiedene Sätze über die Geometrie von Kurven bewiesen. Als zentrale Aussage wird zum einem gezeigt, dass ebene Modelle niedrigen Grades effizient berechnet werden können. Zum anderen wird bewiesen, dass sich bei genügend großem Grundkörper die Anzahl der vollständig über dem Grundkörper zerfallenden Geraden wie heuristisch erwartet verhällt. Für beide Aussagen werden dabei Familien von Kurven betrachtet und diese gelten daher uniform für alle glatten, nichthyperelliptischen Kurven eines festen Geschlechts. Die genannten Resultate führen schlussendlich zu dem Beweis einer erwarteten Laufzeit von O(q^(2-2/(g-1))) für den ersten der beiden Algorithmen, wobei q die Anzahl der Elemente im Grundkörper darstellt. Der zweite Algoritmus verbessert dies auf eine heuristische Laufzeit in O(q^(2-2/(g-2))), imdem er Divisoren von höherem Spezialiätsgrad erzeugt. Es wird bewiesen, dass dieser Ansatz für einen uniform gegen 1 konvergierenden Anteil an glatten, nichthyperelliptischen Kurven eines festen Geschlechts über Grundkörpern großer Charakteristik eine große Anzahl an Relationen erzeugt. Wiederum werden zum Beweis der zugrundeliegenden geometrischen Aussagen Familien von Kurven betrachtet, um so die Uniformität zu gewährleisten. Beide Algorithmen wurden zudem implementiert. Zum Abschluss der Arbeit werden die Ergebnisse der entsprechenden Experimente vorgestellt und eingeordnet.

Neste trabalho aplicamos métodos espectrais para a determinação da configuração inicial de três espaços-tempos contendo buracos negros. Para isto apresentamos primeiro a foliação do espaço-tempo em hipersuperfícies tridimensionais espaciais parametrizadas pela função temporal t. Este processo é chamado de decomposição 3+1 [2] [5]. O resultado deste processo são dois conjuntos de equações classificadas em equações de vínculo e evolução [4]. As equações de vínculo podem ser divididas em vínculos Hamiltoniano e dos momentos. Para a obtenção dos dados iniciais dos problemas estudados aqui, apenas a equação de vínculo Hamiltoniano será resolvida numericamente, pois as equações de vínculo dos momentos possuem solução analítica nestes casos. Uma pequena descrição dos métodos espectrais é apresentada, destacando-se os método de Galerkin, método pseudoespectral ou de colocação e método de Tau, que são empregados na resolução das equações de vínculo Hamiltoniano dos problemas estudados. Verificamos que os resultados obtidos neste trabalho superam aqueles produzidos por Kidder e Finn [15], devido a uma escolha diferente das funções de base, que aqui satisfazem uma das condições de contorno. / In this work we apply spectral methods for determining the initial configuration of three spacetimes containing black holes. For this we present first the foliation of spacetime into three-dimensional spacelike hypersurfaces parameterized by the time function t. This process is called 3 + 1 decomposition [2] [5]. The result of this process are two sets of equations classified into constraint and evolution equations [4]. The constraint equations can be divided into Hamiltonian and momentum constraints.To obtain the initial data of the problems studied here, only the Hamiltonian constraint is solved numerically, since the momentum constraint of these cases have analytical solution. A short description of spectral methods is presented, highlighting Galerkin method, pseudospectral or collocation method and Tau method, which are employed in solving the constraint equations Hamiltonian of the problems studied. We found that the results obtained in this work outperform those produced by Kidder and Finn [15], due to a different choice of basis functions, which meet here one of the boundary conditions.

Neste trabalho aplicamos métodos espectrais para a determinação da configuração inicial de três espaços-tempos contendo buracos negros. Para isto apresentamos primeiro a foliação do espaço-tempo em hipersuperfícies tridimensionais espaciais parametrizadas pela função temporal t. Este processo é chamado de decomposição 3+1 [2] [5]. O resultado deste processo são dois conjuntos de equações classificadas em equações de vínculo e evolução [4]. As equações de vínculo podem ser divididas em vínculos Hamiltoniano e dos momentos. Para a obtenção dos dados iniciais dos problemas estudados aqui, apenas a equação de vínculo Hamiltoniano será resolvida numericamente, pois as equações de vínculo dos momentos possuem solução analítica nestes casos. Uma pequena descrição dos métodos espectrais é apresentada, destacando-se os método de Galerkin, método pseudoespectral ou de colocação e método de Tau, que são empregados na resolução das equações de vínculo Hamiltoniano dos problemas estudados. Verificamos que os resultados obtidos neste trabalho superam aqueles produzidos por Kidder e Finn [15], devido a uma escolha diferente das funções de base, que aqui satisfazem uma das condições de contorno. / In this work we apply spectral methods for determining the initial configuration of three spacetimes containing black holes. For this we present first the foliation of spacetime into three-dimensional spacelike hypersurfaces parameterized by the time function t. This process is called 3 + 1 decomposition [2] [5]. The result of this process are two sets of equations classified into constraint and evolution equations [4]. The constraint equations can be divided into Hamiltonian and momentum constraints.To obtain the initial data of the problems studied here, only the Hamiltonian constraint is solved numerically, since the momentum constraint of these cases have analytical solution. A short description of spectral methods is presented, highlighting Galerkin method, pseudospectral or collocation method and Tau method, which are employed in solving the constraint equations Hamiltonian of the problems studied. We found that the results obtained in this work outperform those produced by Kidder and Finn [15], due to a different choice of basis functions, which meet here one of the boundary conditions.

Diese Dissertation untersucht Brill-Noether-Theorie der algebraischen Kurven, unter besonderer Berücksichtigung von Kurven auf K3-Flächen und Del-Pezzo-Flächen. In Kapitel 2 studieren wir den Gieseker-Petri-Ort GP_g im Modulraum M_g der glatten irreduziblen Kurven vom Geschlecht g. Dieser Ort wird definiert durch Kurven mit einer Brill-Noether-Varietät G^r_d(C), die singulär ist oder deren Dimension größer als erwartet ist. Der Satz von Gieseker-Petri impliziert, dass GP_g mindestens Kodimension 1 hat, und es wurde vermutet, dass er von reiner Kodimension 1 ist. Wir beweisen diese Vermutung für Geschlecht höchstens 13. Dies wird dadurch ermöglicht, dass man für kleine Geschlechter die Dimension der irreduziblen Komponenten von GP_g mittels "ad hoc"-Beweisführungen untersuchen kann. Lazarsfelds Beweis des Gieseker-Petri-Theorems mittels Kurven auf allgemeninen K3-Flächen deutet darauf hin, dass die Brill-Noether-Theorie von K3-Schnitten wichtig ist, um den Gieseker-Petri-Ort besser zu verstehen. Linearscharen von Kurven, die auf K3-Flächen liegen, stehen in tiefgehender Beziehung zu sogenannten Lazarsfeld-Mukai-Vektorbündeln. In Kapitel 3 untersuchen wir die Stabilität der Lazarsfeld-Mukai-Vektorbündel vom Rang 3 auf einer K3-Fläche S, und wir zeigen, dass sie viele Informationen über Netze vom Typ g^2_d auf Kurven in S enthalten. Wenn d größ genug ist, erhalten wir eine obere Schranke für die Dimension der Varietät G^2_d(C). Wenn die Brill-Noether-Zahl negativ ist, beweisen wir, dass jedes g^2_d in einer von einem Geradenbündel induzierten Linearschar enthalten ist, wie von Donagi und Morrison vermutet wurde. Kapitel 4 befasst sich mit Syzygien einer gegebenen Kurve C, die auf einer Del-Pezzo-Fläche liegt. Wir insbesondere, dass C die Greens Vermutung erfüllt, die impliziert, dass die Existenz gewisser spezieller Linearscharen auf C von den Gleichungen ihrer kanonischen Einbettung abgelesen werden kann. / We investigate Brill-Noether theory of algebraic curves, with special emphasis on curves lying on $K3$ surfaces and Del Pezzo surfaces. In Chapter 2, we study the Gieseker-Petri locus GP_g inside the moduli space M_g of smooth, irreducible curves of genus g. This consists, by definition, of curves [C] in M_g such that for some r, d the Brill-Noether variety G^r_d(C), which parametrizes linear series of type g^r_d on C, either is singular or has some components exceeding the expected dimension. The Gieseker-Petri Theorem implies that GP_g has codimension at least 1 in M_g and it has been conjectured that it has pure codimension 1. We prove this conjecture up to genus 13; this is possible since, when the genus is low enough, one is able to determine the irreducible components of GP_g and to study their codimension by "ad hoc" arguments. Lazarsfeld''s proof of the Gieseker-Petri-Theorem by specialization to curves lying on general K3 surfaces suggests the importance of the Brill-Noether theory of K3-sections for a better understanding of the Gieseker-Petri locus. Linear series on curves lying on a K3 surface are deeply related to the so-called Lazarsfeld-Mukai bundles. In Chapter 3, we study the stability of rank-3 Lazarsfeld-Mukai bundles on a K3 surface S, and show it encodes much information about nets of type g^2_d on curves C contained in S. When d is large enough and C is general in its linear system, we obtain a dimensional statement for the variety G^2_d(C). If the Brill-Noether number is negative, we prove that any g^2_d is contained in a linear series which is induced from a line bundle on S, as conjectured by Donagi and Morrison. Chapter 4 concerns syzygies of any given curve C lying on a Del Pezzo surface S. In particular, we prove that C satisfies Green''s Conjecture, which implies that the existence of some special linear series on C can be read off the equations of its canonical embedding.

Diese Arbeit widmet sich der Untersuchung von zwei Problemen der abzählenden Geometrie im Zusammenhang mit linearen Systemen auf algebraischen Kurven. Das erste Problem besteht darin, die Frage der Gültigkeit der Jonquières-Formeln zu klären. Diese Formeln berechnen die Anzahl von Divisoren mit vorgeschriebener Multiplizität, genannt de Jonquières-Divisoren, die in einem linearen System auf einer glatten projektiven Kurve enthalten sind. Um dies zu tun, konstruieren wir den Raum der de Jonquières-Divisoren als einen Determinantenzyklus des symmetrischen Produkts der Kurve und beweisen, dass er für eine allgemeine Kurve die erwartete Dimension hat. Dabei beschreiben wir die Degenerationen der Jonquières-Divisoren zu den Knotenkurven sowohl mit linearen Systemen als auch mit kompaktifizierten Picard-Schemata. Das zweite Problem behandelt Zyklen von Untergeordneten-, oder allgemeiner, Sekanten-Divisoren zu einem gegebenen linearen System auf einer Kurve. Wir betrachten den Durchschnitt zweier solcher Zyklen, die Sekanten-Divisoren von zwei verschiedenen linearen Systemen auf der gleichen Kurve entsprechen, und untersuchen die Gültigkeit der enumerativen Formeln, die die Anzahl der Teiler im Durchschnitt zählen. Wir untersuchen einige interessante Fälle mit unerwarteten Transversalitätseigenschaften und etablieren eine allgemeine Methode, um zu überprüfen, wann dieser Durchschnitt leer ist. / This thesis is dedicated to the study of two enumerative geometry problems in the context of linear series on algebraic curves. The first problem is that of settling the issue of the validity of the de Jonquières formulas. These formulas compute the number of divisors with prescribed multiplicity, or de Jonquières divisors, contained in a linear series on a smooth projective curve. To do so, we construct the space of de Jonquières divisors as a determinantal cycle of the symmetric product of the curve and prove that, for a general curve with a general linear series, it is of expected dimension. In doing so, we describe the degenerations of de Jonquières divisors to nodal curves using both limit linear series and compactified Picard schemes. The second problem deals with cycles of subordinate or, more generally, secant divisors to a given linear series on a curve. We consider the intersection of two such cycles corresponding to secant divisors of two different linear series on the same curve and investigate the validity of the enumerative formulas counting the number of divisors in the intersection. We study some interesting cases, with unexpected transversality properties, and establish a general method to verify when this intersection is empty.