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This thesis consists of three scientific papers dealing with invariants of Legendrian and Lagrangian submanifolds. Besides the scientific papers, the thesis contains an introduction to contact and symplectic geometry, and a brief outline of Symplectic field theory with focus on Legendrian contact homology. In Paper I we give an orientation scheme for moduli spaces of rigid flow trees in Legendrian contact homology. The flow trees can be seen as the adiabatic limit of sequences of punctured pseudo-holomorphic disks with boundary on the Lagrangian projection of the Legendrian. So to equip the trees with orientations corresponds to orienting the determinant line bundle of the dbar-operator over the space of Lagrangian boundary conditions on the punctured disk. We define an  orientation of this line bundle and prove that it is well-defined in the limit. We also prove that the chosen orientation scheme gives rise to a combinatorial algorithm for computing the orientation of the trees, and we give an explicit description of this algorithm. In Paper II we study exact Lagrangian cobordisms with cylindrical Legendrian ends, induced by Legendrian isotopies. We prove that the combinatorially defined DGA-morphisms used to prove invariance of Legendrian contact homology for Legendrian knots over the integers can be derived analytically.  This is proved using the orientation scheme from Paper I together with a count of abstractly perturbed flow trees  of the Lagrangian cobordisms. In Paper III we prove a flexibility result for closed, immersed Lagrangian submanifolds in the standard symplectic plane.

Es sei A_2 der toroidal kompaktifizierte Modulraum prinzipal polarisierter komplexer abelscher Flächen, und M_k(Sp_4(Z)) das Geradenbündel Siegel'scher Modulformen von Gewicht k auf A_2, versehen mit der Petersson-Metrik. Betrachtet man A_2 als komplexe Faser einer arithmetischen Varietät über Spec(Z), und M_k(Sp_4(Z)) als das von einem Geradenbündel auf dieser arithmetischen Varietät induzierte Geradenbündel, so kann man die Frage nach dem arithmetischen Grad dieses Geradenbündels stellen. Wir stellen nachfolgend den Grad als Ausdruck in speziellen Werten der logarithmischen Ableitung der Riemann'schen Zeta-Funktion dar. Der arithmetische Grad setzt sich aus einem Beitrag vom Schnitt über den endlichen Fasern und einem Integral von Green'schen Formen über die komplexe Faser zusammen. Die Berechnung des von der komplexen Faser A_2 induzierten Anteils am arithmetischen Grad erfolgt durch eine spezifische Wahl von Schnitten von M_k(Sp_4(Z)), deren Eigenschaften bekannt oder durch ihre Darstellung als Polynome in Theta-Funktionen ableitbar sind. Mittels eines induktiven Arguments werden wir das Integral über das Stern-Produkt der zugehörigen Green'schen Formen auf eine Summe von Integralen über spezielle Zykel zurückführen, die beim sukzessiven Schneiden der zu den Schnitten gehörigen Divisoren auftauchen. Bei diesem Prozess entstehen Randterme in Form von Integralen um den toroidalen Rand. Wir werden zeigen, dass diese verschwinden, indem wir Minkowski-Theorie anwenden und eine bestimmte Wahl der Teilung der Eins treffen, die in der arithmetischen Schnitttheorie für logarithmisch singuläre Metriken auftaucht. Die Integrale über die speziellen Zykel berechnen wir durch Zurückführen auf ein Resultat von Kudla sowie auf eine modulare Version der Jensen-Formel. / Let A_2 be the toroidally compactified moduli stack of principally polarized complex abelian surfaces, and let M_k(Sp_4(Z)) be the line bundle of Siegel modular forms of weight k on A_2, equipped with the Petersson metric. Viewing A_2 as the complex fibre of an arithmetic variety over Spec(Z), and M_k(Sp_4(Z)) as the complex line bundle induced by a line bundle on this arithmetic variety, we can ask for the arithmetic degree of this line bundle. We will state a formula for the arithmetic degree in terms of special values of the logarithmic derivative of the Riemann zeta-function. The arithmetic degree consists of a contribution from intersection over Spec(Z), and from an integral of Green forms over the complex fibre. The computation of the summand of the arithmetic degree coming from the complex fibre A_2 will be approached by making a specific choice of sections of M_k(Sp_4(Z)), whose behaviour is well-known or can be worked out by their representation via theta-functions. With an induction argument, we will trace back the integral over the star-product of the corresponding Green forms to a sum of integrals over particular cycles on A_2 coming from the successive intersection of the divisors of these sections, as well as some boundary terms in the form of integrals around the toroidal boundary. We will prove that the boundary terms vanish, using Minkowski theory and a specific choice of the partition of unity that appears in arithmetic intersection theory for logarithmically singular metrics. The integrals over the special cycles will be traced back to results of Kudla and an application of a modular version of Jensen's formula.

We introduce slow-roll inflation in string theory on both a conceptual level and a detailed one. In order to do this we first briefly review important concepts of inflation and string theory. We then reconstruct models of string inflation in the so-called Racetrack scenario for two different cases where the difference being the number of Kähler moduli used as inflaton. Furthermore, we briefly relate our results to the more recent discussion on whether AdS/dS solutions actually exist in string theory. In this instance our results seem to indicate that uplifting is a crucial component to obtain AdS/dS solutions.

O presente trabalho discute comparativamente o comportamento mecânico de solos lateríticos e não lateríticos para uso em pavimentação. Para tanto foram ensaiados 3 pares de solos, sendo cada par constituído por solos de curvas granulométricas semelhantes, mesma classificação HRB e comportamentos distintos quanto à laterização. Foram realizados ensaios triaxiais convencionais do tipo CD saturado e não saturado sem controle de sucção e ensaios de compressão simples. A partir dos resultados dos ensaios foram modeladas as deformações elásticas em função das tensões de confinamento e determinadas as envoltórias de ruptura de Mohr-Coulomb. Concluiu-se que a maior resistência dos solos lateríticos está representada na componente coesão da envoltória de Mohr-Coulomb e que esta é mobilizada praticamente ao máximo desde o início em um ensaio triaxial. A diferença de resistência entre os ensaios saturados e não saturados também se mostrou na coesão, com a soma nesta da componente coesão aparente, fruto da sucção. O ângulo de atrito mostrou-se constante para as duas gêneses, tanto para a condição saturada como para a condição não saturada. Os solos lateríticos apresentam rigidez maior que os não lateríticos, tanto na condição saturada como na condição não saturada. Para os níveis de tensão de confinamento utilizados, a rigidez dos solos, de ambas as gêneses, na condição saturada, diminui com o aumento da tensão confinante. Também se observou que a ação da sucção existente nos ensaios não saturados proporciona, para ambas as gêneses, uma mudança da sensibilidade da rigidez ao aumento da tensão confinante. / The present paper discusses the mechanical behavior of lateritic and no-lateritic soils for use in pavement. To attain that goal, 3 pair soils were rehearsed, being each pair constituted by soils of similar granulometric curves, same HRB classification and different genesis. The experimental program was constituted of static triaxial compression test of the type saturated CD and of the type unsaturated without suction control and unconfined compression strength test. With the results of the tests, the elastic strains were modeled in function of the confinement stresses and the rupture paths of Mohr-Coulomb were determined. The analysis that the shear strength of the lateritic soils is greater than no-lateritic soil because of the cohesion. Since the begin it, the cohesion is mobilized practically to the maximum for both soils. The difference of shear strength between the saturated and unsaturated tests it is also cohesion, with the sum in that component of the cohesion apparent produced for suction. The angle of internal friction is constant for the two genesis as much for the saturated test as for the unsaturated test. The lateritic soils present greater stiffness than the no-lateritic soils, as much for saturated test as for unsaturated test. For the levels of confinement stresses used, in the saturated condition the stiffness of the soils decreases with the increase of the confinement stresses of both genesis. In addition, it was observed that the suction existent in the unsaturated testing produce a change of the sensibility of the soils stiffness to the increase of the confinement stress for both genesis.

O vidro com composição 2Na2O1CaO3SiO2, sofre nucleação cristalina homogênea em temperaturas entre 450 e 560oC. Os núcleos, essencialmente esféricos, supostamente tem a mesma composição da matriz vítrea. Em amostras amorfas, parcialmente cristalizadas e policristalinas foram feitas medidas de densidade, difratometria de raios-X, analise térmica por calorimetria exploratória de varredura (DSC), medidas ultrasônicas pelo método do pulso-eco, espectroscopias de absorção ótica, infravermelha e Raman. A densidade do vidro é de 2,66 g/cm3 e para amostra policristalina a densidade aumenta para 2,76 g/cm3. O aumento da densidade com o grau de cristalinidade é a causa do aumento das velocidades de propagação de ondas elásticas longitudinal e transversal, e do aumento do numero e da intensidade dos picos nos difratogramas de raios-X. Das medidas de DSC determinamos que a temperatura de transição vítrea ocorre em torno de 40 °C, e calculamos uma entalpia de ativação para a transição vítrea de 78 kcal/mol. Espectros de absorção ótica de amostras com Cr3+ apresentaram o efeito de anti-ressonância Fano, e pequeno deslocamento da banda 4T2 , para energias maiores com o aumento do grau de cristalinidade e em temperaturas baixas (~ 20 K). A partir dos níveis isoenergéticos 2E e 2T1 calculamos o parâmetro de Racah B = 690 cm-1 e a intensidade do campo ligante ? = 10 Dq = 14 840 cm-1. Junto com Cr3+ ocorre o Cr6+ na forma do íon cromato, CrO42-, cujas bandas de absorção estão próximas do ultravioleta, e é responsável pelo efeito Raman pré-ressonante observado. O espectro Raman do vidro é constituído de bandas assimétricas acima de 550 cm-1, e foram decompostas em seis bandas gaussianas. As bandas de maior freqüência foram tentativamente atribuídas à vibrações de tetraedros de sílica com 1 a 4 oxigênios não-ponteantes. Dos espectros Raman reduzidos concluímos que o pico de boson é devido à vibrações dos fônons térmicos o a freqüência da radiação espalhada. Algumas características dos espectros de absorção de amostras com Cr3+ e dos resultados de medidas ultrasônicas foram atribuídas à possível ocorrência de microtensão ou microfissuras na região da interface núcleo-vidro. / Glass with composition 2Na2O1CaO3SiO2, undergoes homogeneous crystal nucleation between 450 and 56OoC. The nuclei are essentially spherical and presumable have the same composition as the glass matrix. Measuriments of density, X-ray diffraction, thermal analysis by differential scanning calorimetry (DSC), ultrasonics by pulse-echo method, optical absorption, infrared and Raman spectroscopy were performed in amorphous, partially crystallized and polycrystalline samples. The density of the glass is 2,66 g/cm3 and 2,76 g/cm3 that of the polycrystalline sample. The increase in density with the degree of crystallinity is the cause of the increasing propagation velocities of longitudinal and transversal elastic waves, and of the increasing peak number and intensities in the X-ray diffractograms. From DSC measurements we determine that the glass transition temperature is about 470o C, and the activation enthalpy for the glass transition was calculated to be 78 kcal/mol. Absorption spectra of Cr3+ containing samples shows the anti-resonance Fano effect, and small displacement of the 4T2 band to higher energies with increasing degree of crystallinity and at lower temperatures (~20 K). From the isoenergetic levels 2E and 2T1 we calculate the Racah parameter B = 690 cm-1 and the ligand field intensity ? = 10 Dq = 14 840 cm-1. Together with Cr3+ occurs Cr6+ as cromate ion, CrO4-2 with absorption bands are near the ultraviolet, and is responsible for the observed pre-resonant Raman effect. The Raman spectrum of the glass is composed of asimetric bands in frequencies above 550 cm-1, which we decompose in six Gaussian shaped bands. The four bands of higher frequencies were tentativily assigned to stretching vibration bond Si-O of silica tetraedra with 1 to 4 non-bridging oxigens. From reduced Raman spectra we concluded that the boson peak is due to thermal phonon vibrations and to the scattered radiation frequency. Some features of absorption spectra of Cr3+ containing glasses and of ultrasonic measurements were assigned to the possible occurence of microtensions or microcracks in the nucleous-glass interf ace region.

Diese Dissertation hat zwei Teile. Im ersten Teil untersuchen wir die Modulräume von Kurven mit multiplen Spinstrukturen. Wir stellen eine neue Kompaktifizierung dieser Räume mit geometrisch sinnvollem Grenzverhalten vor. Die irreduziblen Komponenten dieser Räume werden vollstandig klassifiziert. Die Ergebnisse aus diesem ersten Teil der Dissertation sind fundamental für die Degenerationstechniken im zweiten Teil. Im zweiten Teil untersuchen wir eine Reihe von Problemen, die von der klassischen Geometrie inspiriert werden. Unser Hauptaugenmerk liegt hierbei auf dem Fall von zwei Hyperebenen, die eine kanonische Kurve in jedem Schnittpunkt tangential berühren. Wir fragen, ob eingemensamer Tangentialpunk existieren kann. Unsere Analyse zeigt, dass so ein gemeinsamer Punkt nur in Kodimension 1 im Modulraum existieren kann. Wir berechen dann weiter die Klasse dieses Divisors. Insbesonders zeigen wir, dass diese Klasse eine hinreichend kleine Steigung hat, sodass die kanonischen Klassen von Modulräumen von Kurven mit zwei ungeraden Spinstrukturen gross ist, wenn der Genus grösser ist als neun. Falls die zugehörigen groben Modulräume gutartige Singularitäten haben, dann haben sie in diesem Intervall maximale Kodaria Dimension. / This thesis has two parts. In Part I we consider the moduli spaces of curves with multiple spin structures and provide a compactification using geometrically meaningful limiting objects. We later give a complete classification of the irreducible components of these spaces. The moduli spaces built in this part provide the basis for the degeneration techniques required in the second part. In the second part we consider a series of problems inspired by projective geometry. Given two hyperplanes tangential to a canonical curve at every point of intersection, we ask if there can be a common point of tangency. We show that such a common point can appear only in codimension 1 in moduli and proceed to compute the class of this divisor. We then study the general properties of curves in this divisor. Our divisor class has small enough slope to imply that the canonical class of the moduli space of curves with two odd spin structures is big when the genus is greater than 9. If the corresponding coarse moduli spaces have mild enough singularities, then they have maximal Kodaira dimension in this range.

Diese Dissertation beschäftigt sich mit asymptotischen Syzygien und Gleichungen Abelscher Varietäten, sowie mit deren Anwendung auf zyklische Überdeckungen von Kurven von Geschlecht zwei. Was asymptotischen Syzygien angeht, zeigen wir für beliebige Geradenbündel auf projektiven Schemata: Wenn die asymptotischen Syzygien von Grad p eines Geradenbündels verschwinden, dann ist das Geradenbündel p-sehr ampel. Darüber hinaus verwenden wir die Bridgeland-King-Reid-Haiman Korrespondenz, um zu zeigen, dass dieses Ergebnis auch umgekehrt wahr ist, wenn es um eine glatte Fläche und kleine p geht. Dies dehnt Ergebnisse von Ein-Lazarsfeld und Ein-Lazarsfeld-Yang aus. Wir verwenden unsere Ergebnisse, um zu untersuchen, wie Syzygien verwendet werden können, um den Grad der Irrationalität einer Varietät zu begrenzen. Ferner, beweisen wir eine Vermutung von Gross and Popescu über Abelsche Flächen, deren Ideal durch Quadriken und Kubiken erzeugt wird. Außerdem verwenden wir die projektive Normalität einer Abelschen Fläche, um die Prym Abbildung, die mit zyklischen Überdeckungen von Geschlecht zwei Kurven assoziert ist, zu untersuchen. Wir zeigen, dass das Differential der Abbildung generisch injektiv ist, wenn der Grad der Überdeckung mindestens sieben ist. Wir dehnen damit Ergebnisse von Lange und Ortega aus. Abschließend zeigen wir, dass das Differential genau für bielliptische Überdeckungen nicht injectiv ist. / In this thesis we study asymptotic syzygies of algebraic varieties and equations of abelian surfaces, with applications to cyclic covers of genus two curves. First, we show that vanishing of asymptotic p-th syzygies implies p-very ampleness for line bundles on arbitrary projective schemes. For smooth surfaces we prove that the converse holds, when p is small, by studying the Bridgeland-King-Reid-Haiman correspondence for the Hilbert scheme of points. This extends previous results of Ein-Lazarsfeld and Ein-Lazarsfeld-Yang. As an application of our results, we show how to use syzygies to bound the irrationality of a variety. Furthermore, we confirm a conjecture of Gross and Popescu about abelian surfaces whose ideal is generated by quadrics and cubics. In addition, we use projective normality of abelian surfaces to study the Prym map associated to cyclic covers of genus two curves. We show that the differential of the map is generically injective as soon as the degree of the cover is at least seven, extending a previous result of Lange and Ortega. Moreover, we show that the differentials fails to be injective precisely at bielliptic covers.

In dieser Arbeit behandeln wir die birationale Geometrie verschiedener Modulräume; die Modulräume von Kurven mit einem k-Differential mit vorgeschierbenen Nullen, besser bekannt als Strata von Differenzialen, Moduln von K3 Flächen mit markierten Punkten und Moduln von Kurven. Für bestimmte Geschlechter nennen wir Abschätzungen der Kodaira-Dimension, konstruieren unirationale Parametrisierungen, rationale deckende Kurven und unterschiedliche birationale Modelle. In Kapitel 1 führen wir die zu untersuchenden Objekte ein und geben einen kurzen Überblick ihrer wichtigsten Eigenschaften und offenen Problemen. In Kapitel 2 konstruieren wir einen Hilfsmodulraum, der als Brücke zwischen bestimmten finiten Quotienten von Mgn für kleines g und den Moduln der polarisierten K3 Flächen vom Geschlecht 11 dient. Wir entwickeln die Deformationstheorie, die nötig ist, um die Eigenschaften und die oben genannten Modulräume zu erforschen. In Kapitel 3 bedienen wir uns dieser Werkzeuge, um birationale Modelle für Moduln polarisierter K3 Flächen vom Geschlecht 11 mit markierten Punkten zu konstruieren. Diese nutzen wir, um Resultate über die Kodaira-Dimension herzuleiten. Wir beweisen, dass der Modulraum von polarisierten K3 Flächen vom Geschlecht 11 mit n markierten Punkten unirational ist, falls n<=6, und uniruled, falls n<=7. Wir beweisen auch, dass die Kodaira-Dimension von Modulraum von polarisierten K3 Flächen vom Geschlecht 11 mit n markierten Punkten nicht-negativ ist für n>= 9. Im letzten Kapitel gehen wir noch auf die fehlenden Fälle der Kodaira-Klassifizierung von Mgnbar ein. Schliesslich behandeln wir in Kapitel 4 die birationale Geometrie mit Blick auf die Strata von holomorphen und quadratischen Differentialen. Wir zeigen, dass die Strata holomorpher und quadratischer Differentiale von niedrigem Geschlecht uniruled sind, indem wir rationale Kurven mit pencils auf K3 und del Pezzo Flächen konstruieren. Durch das Beschränken des Geschlechts 3<= g<=6 bilden wir projektive Bündel über rationale Varietäten, die die holomorphe Strata mit maximaler Länge g-1 dominieren. Also zeigen wir auch, dass diese Strata unirational sind. / In this thesis we investigate the birational geometry of various moduli spaces; moduli spaces of curves together with a k-differential of prescribed vanishing, best known as strata of differentials, moduli spaces of K3 surfaces with marked points, and moduli spaces of curves. For particular genera, we give estimates for the Kodaira dimension, construct unirational parameterizations, rational covering curves, and different birational models. In Chapter 1 we introduce the objects of study and give a broad brush stroke about their most important known features and open problems. In Chapter 2 we construct an auxiliary moduli space that serves as a bridge between certain finite quotients of Mgn for small g and the moduli space of polarized K3 surfaces of genus eleven. We develop the deformation theory necessary to study properties of the mentioned moduli space. In Chapter 3 we use this machinery to construct birational models for the moduli spaces of polarized K3 surfaces of genus eleven with marked points and we use this to conclude results about the Kodaira dimension. We prove that the moduli space of polarized K3 surfaces of genus eleven with n marked points is unirational when n<= 6 and uniruled when n<=7. We also prove that the moduli space of polarized K3 surfaces of genus eleven with n marked points has non-negative Kodaira dimension for n>= 9. In the final section, we make a connection with some of the missing cases in the Kodaira classification of Mgnbar. Finally, in Chapter 4 we address the question concerning the birational geometry of strata of holomorphic and quadratic differentials. We show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on K3 and del Pezzo surfaces respectively. Restricting to genus 3<= g<=6 we construct projective bundles over rational varieties that dominate the holomorphic strata with length at most g-1, hence showing in addition, these strata are unirational.

Progress in biomedicine requires the design of functional biomaterials, in particular, 3-dimensional (3D) scaffolds. Shear thinning, β-sheet based peptide hydrogels have attracted wide interest due to their potential use in tissue engineering and biomedical applications as 3D functional scaffolds. The emergence of carbon nanomaterials has also opened the door for the construction of increasingly functional hybrid hydrogels built from nanofibres and graphene-based materials using non-covalent physical interactions. The relationship between peptide molecular structure and the formed hydrogel is important for understanding the material response to shear. In particular, the physicochemical properties of peptide based biomaterials will affect the feasibility of injecting them during medical procedures. In the first part of this work, four peptides: FEFKFEFK (F8), FKFEFKFK (FK), KFEFKFEFK (KF8) and KFEFKFEFKK (KF8K) (F - phenylalanine, E - glutamic acid, K - lysine) were designed and used at identical charge to explore the effect of lysine rich β-sheet self-assembling sequences on the shear thinning behaviour and final properties of bulk hydrogels. By varying the peptide sequence design and concentration of the peptide, the tendency of the nanofibres formed to aggregate and the balance of nanofibre junction strength versus fibre cohesive strength could be explored. This allowed the existing theory of the shear thinning behaviour of this class of materials to be extended. The relationship between molecular structures of nanofibres forming the 3D network and the nano-filler is critical to understand in order to design tuneable and functional materials. In the next part of the work, three rationally designed β-sheet peptides, which form hydrogels: VEVKVEVK (V8), FEFKFEFK (F8) and FEFEFKFE (FE) (V - valine) and five graphene-based materials: graphene oxide (GO), reduced graphene oxide (rGO), three graphene-polymer hybrid flakes: GO with polydiallyldimethylammonium chloride (GO/PDADMAC), rGO with PDADMAC (rGO/PDADMAC) and rGO with polyvinylpyrrolidone (rGO/PVP) were used to form a selection of hybrid hydrogels. Graphene derivatives of the lateral flake sizes of 16.8 ± 10.1 µm were used. Various interactions between the graphene flakes and the peptides were observed that affected the overall mechanical properties of the hydrogels. Electrostatic interactions and pie-pie stacking, when phenylalanine residues are present, were shown to play a key role in determining the dispersion of graphene materials in the peptide hydrogels and stiffness of the hybrid materials. In particular, FE with reduced graphene oxide (rGO) and FE with rGO covered with polydiallyldimethylammonium chloride (PDADMAC) thin film formed double network-like hybrid hydrogels due to strong formation of peptide nanofibrillar bridges between adjacent rGO flakes. This corresponded to the 3- and 4-fold increase in the storage modulus (Gꞌ) of these hydrogels in comparison to controls. FE hydrogels with homogeneus dispersions of graphene oxide (GO) and reduced graphene oxide (rGO) are further shown to be suitable for 3D culture of human mesenchymal stem cells (hMSCs) with no cytotoxicity. These results focus attention on the importance of understanding interactions between the nano-filler and the nanofibrillar network in forming hybrid hydrogels with tuneable mechanical and biological properties, and demonstrates the possibility of using these materials as 3D cell culture scaffolds for biomedical purposes. Furthermore, graphene oxide (GO) itself is currently used in a number of processes of technological relevance such as wet spinning, injection moulding or inkjet printing to form graphene fibres, composites and printed conductors. Typically, such processes utilise well-aligned layered GO liquid crystal (LC) structures in aqueous dispersions. Flow and confinement encountered during processing affects the alignment and stability of this phase. In the final part of this work, the alignment of GOLCs of two lateral flake sizes (42.1 ± 29.4 µm and 15.5 ± 7.5 µm) were probed under a wide range of rotational shear flow conditions that overlap with the manufacturing processes defined by angular speeds from 0.08 to 8 rad.s-1 (and corresponding maximum shear rates from 0.1 s-1 to 100 s-1), in real-time, using shear induced polarized light imaging and small angle X-ray scattering, both coupled with an in-situ rheometer (Rheo-SIPLI and Rheo-SAXS, respectively). Under certain conditions, a unique pattern in Rheo-SIPLI: a Maltese cross combined with shear banding was observed. This phenomenon is unique to GO flakes of sufficiently large lateral size. The structure formed is attributed to a helical flow arising from a combination of shear flow and Taylor-vortex type flow, which is reinforced by a mathematical model. The orientations prescribed by this model are consistent with anomalous rheopecty oberved in Rheo-SIPLI and an anomolous scattering pattern in Rheo-SAXS. With the current trend towards producing ultra-large GO flakes, evidence that the flow behaviour changes from a Couette flow to a Taylor vortex flow was provided, which would lead to undesired, or alternatively, controllable alignment of GO flakes for a variety of applications, including aligned structures for biomedical purposes.