Дисертації з теми "Curvature properties"

Cells are dynamic systems that generate and respond to forces through the complex interplay between biochemical and mechanical regulations. Since cellular processes often happen at the molecular level and are challenging to be observed under in vivo conditions due to limitations in optical microscopy, multiple analysis tools have been developed to gain insight into those processes. One of the ways to characterize these mechanical properties is by measuring their persistence length, the average length over which filaments stay straight. There are several approaches in the literature for measuring the persistence length of the filaments, including Fourier analysis of images obtained using fluorescence microscopy. Here, we show how curvature can be used to quantify local deformations of cell shape and cellular components. We develop a novel technique, called curvature analysis, to measure the stiffness of bio-filaments from fluorescent images. We test our predictions with Monte-Carlo generated filaments. We also apply our approach to microtubules and actin filaments obtained from in vitro gliding assay experiments with high densities of non-functional motors. The presented curvature analysis is significantly more accurate compared to existing approaches for small data sets. To study the effect of motors on filament deformations and velocities observed in gliding assays with functional and non-functional motors, we developed Langevin dynamics simulations of on glass and lipid surfaces. We found that generally the gliding velocity increases with an increase in motor density and a decrease in diffusion coefficient, and that motor density and diffusion coefficient have no clear effect on filament curvatures, except at a very low diffusion coefficients. Finally, we provide an ImageJ plugin to make curvature and persistence length measurements more accessible to everyone.

The two main problems we study are the \emph{Cheeger problem} and the \emph{Prescribed Mean Curvature problem}. The former consists in finding the subsets $E$ of a given ambient set $\Omega$ that realize the Cheeger constant, i.e. such that \[ \frac{P(E)}{|E|} = \inf \left \{ \frac{P(A)}{|A|} \right\} = h_1(\Om)\,, \] where the infimum is sought amongst all subsets of $\Om$ with positive volume; the latter is the non-linear partial differential equation given by \[ \div(Tu) = \div\left( \frac{\grad u}{\sqrt{1+|\grad u|^2}} \right) = H\,, \] which consists in finding functions $u$ whose graph has mean curvature $H$. At a first sight these two problems do not seem to be related but in the special case of a positive, constant prescribed mean curvature $H$ on $\Omega$, a necessary and sufficient condition to existence of solutions and uniqueness up to translations is that $H$ equals the Cheeger constant of $\Omega$ and $\Omega$ is a minimal Cheeger set. On one hand, we study a generalization of the Cheeger problem considering volumes with positive, non-vanishing $L^\infty$ weights and perimeters weighted through a function $g(x,\nu_\Omega (x))$ depending both on the point $x \in \de \Omega$ and the outer normal to $\Om$ at $x$. Then, we prove that any connected minimizer admits a Poincar\'e trace inequality, as well as the standard Sobolev embeddings. On the other hand, in the case of the standard Cheeger problem in dimension $2$ we show that, for simply connected sets $\Om$ that satisfy a ``no-bottleneck'' condition, the maximal Cheeger set $E$ equals the union of all balls contained in $\Om$ whose radius is $r=h_1^{-1}(\Om)$. Moreover, the inner Cheeger formula $|[\Om]^r|=\pi r^2$ holds, where $[\Om]^r$ denotes the set of points of $\Om$ at distance greater or equal than $r$ from $\de \Omega$. This result generalizes a property so far proved only for convex sets and planar strips. Concerning the Prescribed Mean Curvature problem, we show existence and uniqueness of solutions of the PMC equation only assuming that $\Omega$ is a \emph{weakly regular} open set, i.e., when $\Omega$ satisfies a Poincar\'e trace inequality and its perimeter agrees with the $(n-1)$-dimensional Hausdorff measure of the topological boundary. Under these assumptions, we show that uniqueness up to vertical translations is equivalent to several other properties. Namely, that the domain is maximal, i.e. no solutions for the same prescribed datum $H$ can exist in any set $\widetilde \Omega$ strictly containing $\Om$; that $\Om$ is critical, i.e. among all its subsets, it is the only one for which the inequality $|\int_A H| \le P(A)$ becomes an equality; that there exists a solution which solves the capillarity problem in a tube of cross-section $\Om$ with vertical contact angle, i.e. that it satisfies a tangential boundary condition in an integral sense or in a ``weak trace'' sense. Moreover, whenever the perimeter of $\Om$ agrees with the inner Minkowski content of $\Om$, this tangential ``weak trace'' condition assumes the stronger form $Tu(x) \to \nu_\Om (z)$ in a measure-theoretic sense, as $x\in \Omega$ approaches a point $z$ in the ``super-reduced boundary''. Finally, when the prescribed datum $H$ is positive and non-vanishing, we observe again the link between the Cheeger problem and the Prescribed Mean Curvature problem, as being critical corresponds to $\Omega$ being a minimal Cheeger set with Cheeger constant $1$, for the Cheeger problem with the standard perimeter and volume weighted through $H$.
I due principali problemi che studiamo sono il \emph{problema di Cheeger} ed il \emph{problema di curvatura media prescritta}. Il primo consiste nel trovare i sottoinsiemi $E$ di un certo insieme ambiente $\Om$ che realizzano la costante di Cheeger, ovvero tali che \[ \frac{P(E)}{|E|} = \inf \left \{ \frac{P(A)}{|A|} \right\} = h_1(\Om)\,, \] dove l'estremo inferiore \`e fra tutti i sottoinsiemi di $\Omega$ con volume positivo; il secondo problema \`e l'equazione alle derivate parziali non lineare data da \[ \div(Tu) = \div \left ( \frac{\grad u}{\sqrt{1+|\grad u|^2}} \right) = H\,, \] che consiste nel trovare delle funzioni $u$ il cui grafico abbia curvatura media $H$. A prima vista questi due problemi sembrano indipendenti, ma nel caso speciale di una curvatura media prescritta $H$ costante e positiva in $\Omega$, una condizione necessaria e sufficiente all'esistenza di soluzioni e all'unicit\`a a meno di traslazioni, \`e che $H$ sia uguale della costante di Cheeger e che $\Omega$ sia un insieme di Cheeger minimale. Da un lato, studiamo una generalizzazione del problema di Cheeger considerando dei volumi con pesi $L^\infty$ e dei perimetri pesati tramite funzioni $g(x, \nu_\Om (x))$ che dipendono sia dal punto $x\in \de \Omega$ sia dalla normale esterna ad $\Om$ nel punto $x$. Mostriamo che gli insiemi minimi connessi ammettono una disuguaglianza di traccia di Poincar\'e e le classiche immersioni di Sobolev. Dall'altro lato, nel caso del problema di Cheeger classico in $2$ dimensioni, mostriamo che, per insiemi $\Om$ semplicemente connessi che non presentano ``colli di bottiglia'', l'insieme di Cheeger massimale $E$ \`e l'unione di tutte le palle contenute in $\Omega$ di raggio $r= h_1^{-1}(\Om)$. Inoltre, vale la inner Cheeger formula $|[\Om]^r = \pi r^2$, dove $[\Om]^r$ indica l'insieme dei punti di $\Om$ che sono a una distanza maggiore o uguale ad $r$ da $\de \Om$. Questo risultato generalizza una propriet\`a finora dimostrata solo per insieme convessi e strisce. Riguardo al problema di curvatura media prescritta, mostriamo esistenza ed unicit\`a di soluzioni per l'equazione soltanto richiedendo che l insieme $\Om$ sia un aperto ``debolmente regolare'', ovvero che soddisfi una disuguaglianza di traccia di Poincar\'e e che il suo perimetro coincida con la misura di Hausdorff $(n-1)$-dimensionale del suo bordo topologico. Sotto tali ipotesi, dimostriamo che l'unicit\`a, a meno di traslazioni, \`e equivalente a diverse altre propriet\`a. In particolare, alla massimalit\`a del dominio, ovvero non esistono soluzioni per la stessa curvatura prescritta $H$ in nessun insieme $\widetilde \Omega$ che contiene strettamente $\Om$; alla criticalit\`a di $\Omega$, ovvero che $\Om$, fra tutti i suoi sottoinsiemi \`e l'unico per cui la disuguaglianza $|\int_A H| \le P(A)$ diventa un'uguaglianza; all'esistenza di una soluzione che risolve il problema di capillarit\`a in un cilindro di sezione $\Om$ con angolo di contatto verticale, ovvero con una condizione al bordo tangenziale, assunta in un senso integrale o di ``traccia debole''. Inoltre, questa condizione al bordo di ``traccia debole'', quando il perimetro di $\Om$ coincide con il contenuto interno di Minkoswki di $\Om$, assume la forma pi\`u forte $Tu(x) \to \nu_\Om (z)$ in misura, per $x\in \Omega$ che tendono a un punto $z$ nella frontiera ``super-ridotta''. Infine, quando la curvatura prescritta $H$ \`e positiva e non identicamente nulla, si osserva di nuovo il legame fra il problema di Cheeger e di curvatura media prescritta, in quanto la criticalit\`a di $\Om$ \`e equivalente a dire che la costante di Cheeger pesata tramite $H$ e con perimetro classico \`e $1$ e che $\Om$ \`e un insieme minimale di Cheeger.

Contorted polycyclic aromatic hydrocarbons have found increasing utility in the application of molecular electronics due to the surpamolecular properties that result from these non-planar structures. The [n]circulene series of molecules are particularly attractive members of the contorted aromatic family due to the unique structural implications that result from their changing value of n. For example, when n ≤ 5, the structures adopt a bowl-like shape; when n = 6, a planar structure is observed; and when 7 ≤ n ≤ 16, the compounds assume a saddle-like shape. Very few molecules exhibit the structural contortions that these contorted aromatics do – primarily because aromatic molecules desire to adopt highly planar conformations. Following the model of aromaticity developed by Erich Clar, we set our sights on the synthesis of tetrabenzo[8]circulene, the stabilized form of [8]circulene established through the addition of four fused benzenoid rings around the periphery of the molecule. The initial approach towards this structure employs a Diels-Alder [4 + 2] cycloaddition reaction and a palladium catalyzed arylation reaction as the key transformation steps. The results of these studies were promising, establishing the structural characterization of this new molecule and providing access to functionalized derivatives of the saddle-shaped structure. However, access towards these functionalized derivatives proved limiting, compelling us to investigate alternative synthetic methodologies. In the course of our studies, we established a new methodology towards 2,5-diarylthiophene-1-oxides, a key precursor to the Diels-Alder cycloaddition reaction. These reactive dienes are prepared from readily available arylacetylene precursors via zirconacyclopentadiene intermediates. The isolated yields of the desired thiophene-1-oxides are comparable to those obtained from previously established oxidation strategies while avoiding the formation of over-oxidation products. Of significant importance to scope of our work, this newly established methodology offers broader versatility providing products outfitted with electron-donating or electron-withdrawing groups. These new methodologies provided access to functionalized derivatives of the saddle-shaped molecule tetrabenzo[8]circulene in improved yield when coupled with a revised Diels-Alder/oxidative cyclodehydrogenation approach. This methodology affords products containing both electron-rich and electron-poor functional groups in a more efficient manner. The optoelectronic effects that result from the introduction of this functionality and investigations into the development of larger contorted aromatic systems are also discussed.

L’objectif de la thèse est de présenter de nouveaux résultats d’analyse sur les espaces métriques mesurés. Nous étendons d’abord à une certaine classe d’espaces avec doublement et Poincaré des inégalités de Sobolev pondérées introduites par V. Minerbe en 2009 dans le cadre des variétés riemanniennes à courbure de Ricci positives. Dans le contexte des espaces RCD(0,N), nous en déduisons une inégalité de Nash pondérée et un contrôle uniforme du noyau de la chaleur pondéré associé. Puis nous démontrons la loi de Weyl sur les espaces RCD(K,N) compactes à l’aide d’un théorème de convergence ponctuelle des noyaux de la chaleur associés à une suite mGH-convergente d’espaces RCD(K,N). Enfin nous abordons dans le contexte RCD(K,N) un théorème de Bérard, Besson et Gallot fournissant, à l’aide du noyau de la chaleur, une famille de plongements asymptotiquement isométriques d’une variété riemannienne fermée dans l’espace de ses fonctions de carré intégrable. Nous introduisons notamment les notions de métrique RCD, de métrique pull-back, et de convergence faible/forte de métriques RCD sur un espace RCD(K,N) compacte, et nous prouvons un résultat de convergence analogue à celui de Bérard, Besson et Gallot
The aim of this thesis is to present new results in the analysis of metric measure spaces. We first extend to a certain class of spaces with doubling and Poincaré some weighted Sobolev inequalities introduced by V. Minerbe in 2009 in the context of Riemannian manifolds with non-negative Ricci curvature. In the context of RCD(0,N) spaces, we deduce a weighted Nash inequality and a uniform control of the associated weighted heat kernel. Then we prove Weyl’s law for compact RCD(K,N) spaces thanks to a pointwise convergence theorem for the heat kernels associated with a mGH-convergent sequence of RCD(K,N) spaces. Finally we address in the RCD(K,N) context a theorem from Bérard, Besson and Gallot which provides, by means of the heat kernel, an asymptotically isometric family of embeddings for a closed Riemannian manifold into its space of square integrable functions. We notably introduce the notions of RCD metrics, pull-back metrics, weak/strong convergence of RCD metrics, and we prove a convergence theorem analog to the one of Bérard, Besson and Gallot

[from the introduction]: The aim of this thesis is to study metric measure spaces with a synthetic notion of Ricci curvature bounded below. We study them from the point of view of Sobolev/Nash type functional inequalities in the non-compact case, and from the point of view of spectral analysis in the compact case. The heat kernel links the two cases: in the first one, the goal is to get new estimates on the heat kernel of some associated weighted structure; in the second one, the heat kernel is the basic tool to establish our results. The topic of synthetic Ricci curvature bounds has known a constant development over the past few years. In this introduction, we shall give some historical account on this theory, before explaining in few words the content of this work. The letter K will refer to an arbitrary real number and N will refer to any finite number greater or equal than 1.

Le manuscrit est constitué de deux parties indépendantes.Propriétés des Solutions de Viscosité des Equations Integro-Différentielles.Nous considérons des équations intégro-différentielles elliptiques et paraboliques non-linéaires (EID), où les termes non-locaux sont associés à des processus de Lévy. Ce travail est motivé par l'étude du Comportement en temps long des solutions de viscosité des EID, dans le cas périodique. Le résultat classique nous dit que la solution u(¢, t ) du problème de Dirichlet pour EID se comporte comme ?t Åv(x)Åo(1) quand t !1, où v est la solution du problème ergodique stationaire qui correspond à une unique constante ergodique ?.En général, l'étude du comportement asymptotique est basé sur deux arguments: la régularité de solutions et le principe de maximumfort.Dans un premier temps, nous étudions le Principe de Maximum Fort pour les solutions de viscosité semicontinues des équations intégro-différentielles non-linéaires. Nous l'utilisons ensuite pour déduire un résultat de comparaison fort entre sous et sur-solutions des équations intégro-différentielles, qui va assurer l'unicité des solutions du problème ergodique à une constante additive près. De plus, pour des équationssuper-quadratiques le principe de maximum fort et en conséquence le comportement en temps grand exige la régularité Lipschitzienne.Dans une deuxième partie, nous établissons de nouvelles estimations Hölderiennes et Lipschitziennes pour les solutions de viscosité d'une large classe d'équations intégro-différentielles non-linéaires, par la méthode classique de Ishii-Lions. Les résultats de régularité aident de plus à la résolution du problème ergodique et sont utilisés pour fournir existence des solutions périodiques des EID.Nos résultats s'appliquent à une nouvelle classe d'équations non-locales que nous appelons équations intégro-différentielles mixtes. Ces équations sont particulièrement intéressantes, car elles sont dégénérées à la fois dans le terme local et non-local, mais leur comportement global est conduit par l'interaction locale - non-locale, par exemple la diffusion fractionnaire peut donner l'ellipticité dans une direction et la diffusion classique dans la direction orthogonale.Visualisation et Restauration d'Images par Mouvements de CourbureLe rôle de la courbure dans la perception visuelle remonte à 1954, et on le doit à Attneave. Des arguments neurologiques expliquent que le cerveau humain ne pourrait pas possiblement utiliser toutes les informations fournies par des états de simulation. Mais en réalité on enregistre des régions où la couleur change brusquement (des contours) et en outre les angles et les extremas de courbure. Pourtant, un calcul direct de courbures sur une image est impossible. Nous montrons comment les courbures peuvent être précisément évaluées, à résolution sous-pixelique par un calcul sur les lignes de niveau après leur lissage indépendant.Pour cela, nous construisons un algorithme que nous appelons Level Lines (Affine) Shortening, simulant une évolution sous-pixelique d'une image par mouvement de courbure moyenne ou affine. Aussi bien dans le cadre analytique que numérique, LLS (respectivement LLAS) extrait toutes les lignes de niveau d'une image, lisse indépendamment et simultanément toutes ces lignes de niveau par Curve Shortening(CS) (respectivement Affine Shortening (AS)) et reconstruit une nouvelle image. Nousmontrons que LL(A)S calcule explicitement une solution de viscosité pour le le Mouvement de Courbure Moyenne (respectivement Mouvement par Courbure Affine), ce qui donne une équivalence avec le mouvement géométrique.Basé sur le raccourcissement de lignes de niveau simultané, nous fournissons un outil de visualisation précis des courbures d'une image, que nous appelons un Microscope de Courbure d'Image. En tant que application, nous donnons quelques exemples explicatifs de visualisation et restauration d'image : du bruit, des artefacts JPEG, de l'aliasing seront atténués par un mouvement de courbure sous-pixelique

The main objective of this thesis is to obtain critical insight on the role of crystalline incompatibilities in strain and curvature, induced in presence of line defects i.e. dislocations and disclinations, on the energy and geometry of specific features of the local microstructure, and on the bulk mechanical response of nanocrystalline/ultra-fine grained materials. To that end, studies are performed at the (1) inter-atomic and fine scale, and (2) at the mesoscale. The modelling approach is based on the field dislocation and disclination mechanics theory of continuously representated dislocations and disclinations. New, thermodynamically rigorous, multi-scale elastic constitutive laws based on the couple stress theory are developed to capture the effect of strain and curvature incompatibilities on the Cauchy and couple stresses. A new meso-scale elasto-viscoplastic constitutive model of defect incompatibilities based on a fast Fourier transform technique is developed. The desired scale transitioning is achieved via novel phenomenological defect density transport equations and the newly developed elastic constitutive laws. At the fine scale, the model is applied to study energetic interactions between strain and curvature incompatibilities associated with grain boundaries and their influence on triple line energies. Results reveal that incompatible lattice strains have the most significant contribution to the energy. Incompatible lattice curvatures have negligible energetic contributions but are necessary to characterize the geometry of grain boundaries. Finally, both incompatible lattice strains and curvatures are necessary to capture the structure sensitive mechanical behavior of grain boundaries. At the mesoscale, deformation of nanocrystalline aggregates characterized by residual curvatures is studied to identify the impact of the latter's presence on the local and bulk mechanical response of the aggregate. Relaxation of local stresses generated from residual curvatures reproduces the effect of GB dislocation emission. Uniaxial tensile loading of nanocrystalline microstructures containing residual curvatures reveals a softening in the yield stress which could explain the breakdown in Hall-Petch law in the nanocrystalline regime. Next, the possibility of characterizing incompatibilities using X-ray or neutron diffraction techniques is tested. Results reveal that only strains and their gradients contribute to the broadening of diffraction peaks; curvatures and their gradients have no contribution. This study leads to the development of a new multi-scale averaged strain based Fourier technique for generating virtual diffraction peaks.

Dans l'objectif d'améliorer et d'automatiser la chaîne de reproductiond'objet qui va de l'acquisition à l'impression 3D. Nous avons cherché à caractériserde la saillance sur les objets 3D modélisés par la structure d'un maillage 3D.Pour cela, nous avons fait un état de l'art des méthodes d'estimation des proprié-tés différentielles, à savoir la normale et la courbure, sur des surfaces discrètes sousla forme de maillage 3D. Pour comparer le comportement des différentes méthodes,nous avons repris un ensemble de critères de comparaison classique dans le domaine,qui sont : la précision, la convergence et la robustesse par rapport aux variations duvoisinage. Pour cela, nous avons établi un protocole de tests mettant en avant cesqualités. De cette première comparaison, il est ressorti que l'ensemble des méthodesexistantes présentent des défauts selon ces différents critères. Afin d'avoir une estimationdes propriétés différentielles plus fiable et précise nous avons élaboré deuxnouveaux estimateurs
With the aim to improve and automate the object reproduction chainfrom acquisition to 3D printing .We sought to characterize the salience on 3D objectsmodeled by a 3D mesh structure. For this, we have a state of the art of estimatingdifferential properties methods, namely normal and curvature on discrete surfaces inthe form of 3D mesh. To compare the behavior of different methods, we took a set ofclassic benchmarks in the domain, which are : accuracy, convergence and robustnesswith respect to variations of the neighbourhood. For this, we have established atest protocol emphasizing these qualities. From this first comparision, it was foundthat all the existing methods have shortcomings as these criteria. In order to havean estimation of the differential properties more reliable and accurate we developedtwo new estimators

In this thesis we study several properties of finitely presented groups, through the unifying paradigm of encoding sought-after group properties into presentations and detecting group properties from presentations, in the context of Geometric Group Theory. A group law is said to be detectable in power subgroups if, for all coprime m and n, a group G satisfies the law if and only if the power subgroups G(^m) and G(ⁿ) both satisfy the law. We prove that for all positive integers c, nilpotency of class at most c is detectable in power subgroups, as is the k-Engel law for k at most 4. In contrast, detectability in power subgroups fails for solvability of given derived length: we construct a finite group W such that W(²) and W(³) are metabelian but W has derived length 3. We analyse the complexity of the detectability of commutativity in power subgroups, in terms of finite presentations that encode a proof of the result. We construct a census of two-generator one-relator groups of relator length at most 9, with complete determination of isomorphism type, and verify a conjecture regarding conditions under which such groups are automatic. Furthermore, we introduce a family of one-relator groups and classify which of them act properly cocompactly on complete CAT(0) spaces; the non-CAT(0) examples are counterexamples to a variation on the aforementioned conjecture. For a subclass, we establish automaticity, which is needed for the census. The deficiency of a group is the maximum over all presentations for that group of the number of generators minus the number of relators. Every finite group has non-positive deficiency. For every prime p we construct finite p-groups of arbitrary negative deficiency, and thereby complete Kotschick's proposed classification of the integers which are deficiencies of Kähler groups. We explore variations and embellishments of our basic construction, which require subtle Schur multiplier computations, and we investigate the conditions on inputs to the construction that are necessary for success. A well-known question asks whether any two non-isometric finite volume hyperbolic 3-manifolds are distinguished from each other by the finite quotients of their fundamental groups. At present, this has been proved only when one of the manifolds is a once-punctured torus bundle over the circle. We give substantial computational evidence in support of a positive answer, by showing that no two manifolds in the SnapPea census of 72 942 finite volume hyperbolic 3-manifolds have the same finite quotients. We determine examples of sizeable graphs, as required to construct finitely presented non-hyperbolic subgroups of hyperbolic groups, which have the fewest vertices possible modulo mild topological assumptions.

Les membranes des cellules sont composées d’une bicouche lipidique et de protéines transmembranaires qui sont responsables de la plupart des fonctions membranaires. Les membranes peuvent exercer une contrainte mécanique capable d’altérer la forme de la protéine et donc sa fonction. Réciproquement, une inclusion dans la membrane peut lui imposer une tension ou une courbure. Cette interaction peut s’avérer cruciale pour des protéines qui subissent un changement de conformation. Nous étudions BmrA, un transporteur ABC bactérien issu de B.subtillis. Les transporteurs ABC (ATP Binding Cassette) sont une des plus grande familles de protéines membranaires. Le transporteur humain P-glycoprotéine (P-gp) exporte des agents anti-cancéreux à l’extérieur de la cellule et crée ainsi un phénotype de résistance aux médicaments. BmrA est un homologue de P-gp et subit un large changement de conformation entre une forme dite « ouverte » et une « fermée ». L’objectif est d’étudier l’interaction entre le cycle conformationnel de BmrA et la courbure membranaire à l’échelle de la molécule unique. Les différentes conformations sont discriminées grâce à la méthode FRET en microscopie TIRF : une faible (resp. haute) efficacité de FRET correspond à la conformation ouverte (resp. fermée). BmrA est purifiée, marquée avec des sondes fluorescentes compatibles avec la méthode FRET et incorporée dans des petits liposomes. Trois tailles de liposomes sont étudiées pour faire varier la courbure membranaire avec des diamètres de 140, 60 et 40nm. Nous avons observé un comportement différent pour la protéine dans les liposomes de 40nm, indiquant un effet de la courbure membranaire sur les conformations de BmrA
Cell membranes are composed of a lipid bilayer, crowded with transmembrane proteins that mediate nearly all of the membrane functions, such as detoxification and communication. There is a tight interaction between lipids and transmembrane proteins. Membrane can apply mechanical stress and impact transmembrane proteins shape and function. Reciprocally, the inclusion of a transmembrane protein can bend or stretch the membrane. In particular, this interplay might play a crucial role for proteins that change conformation to mediate cargoes transport. We study BmrA, a bacterial ABC exporter from B.subtillis. ABC (ATP Binding Cassette) transporters represent one of the largest families of membrane proteins. Some ABC exporters lead to a phenotype of multi-drug resistance, such as human P-glycoprotein (P-gp) which transports anti-cancer agents out the cell. BmrA shares high homology with P-gp and is expected to undergo a large conformational change between “open” and “closed” conformations. The objective is to characterize the interplay between the conformation cycle of BmrA and membrane curvature, at the single molecule level. BmrA is purified in detergent, labelled with dyes suitable for FRET experiments, and incorporated in small liposomes. Conformations of BmrA are probed by single-molecule FRET in TIRF microscopy: a low (resp. high) FRET efficiency corresponds to a protein in open (resp. closed) conformation. Three different liposome sizes are used in order to vary the membrane curvature: diameter 140, 60 and 40nm. We have found a different protein behavior in 40nm liposomes as compared to larger ones, indicating an effect of the membrane curvature on BmrA conformations

La premiere partie de cette these est consacree a l'etude theorique des proprietes elastiques de reseaux de passages connectant des bicouches phospholipidiques. Elle a ete motivee par des observations experimentales faites par michalet et al. Le calcul que nous proposons prend en compte la conservation du volume du systeme. Il nous a permis de montrer que ces reseaux sont destabilises par les deformations de cisaillement, qui sont energetiquement plus favorables que les deformations de compression. La contrainte de volume permet aussi de determiner la densite de passages dans ces systemes. Enfin, la generalisation aux systemes multilamellaires de la notion de courbure constante introduite par michalet et al, met en evidence un comportement collectif remarquable des passages. La seconde partie concerne l'etude des interactions entre un peptide (la penetratine) et les phospholipides de la membrane cellulaire. Celle-ci est modelisee par une bicouche deposee sur un substrat solide par la methode de langmuir-blodgett. L'essentiel du travail expose dans cette these a consiste a developper un protocole experimental permettant de caracteriser ces bicouches par reflectivite de neutrons. Il a ainsi ete possible d'observer pour la premiere fois des quadricouches controlees de dspc. Enfin, les premiers resultats que nous avons obtenus sur l'etude de l'influence de la penetratine, montrent une influence importante du peptide sur la bicouche. La derniere partie de ce travail s'interesse aux proprietes elastiques d'un fil ferme spontanement courbe. Elle s'inscrit dans le cadre de la theorie classique de l'elasticite, et fait intervenir un couplage local entre la courbure et la torsion qui permet d'expliquer l'existence d'un etat metastable observable sur une rondelle de caoutchouc. Une application a l'adn est envisagee.

Chemistry
Ph.D.
This work is devoted to understanding the formation of supported lipid bilayers (SLBs) on curved surfaces as a function of lipid properties such as headgroup charge/charge density and alkyl chain length, and nanoparticle properties such as size and surface characteristics. In particular, the formation of SLBs on curved surfaces was studied by varying the size of the underlying substrate SiO2 nanoparticles with size range from 5-100 nm. Curvature-dependent shift in the phase transition behavior of these supported lipid bilayers was observed for the first time. We found that the phase transition temperature, Tm of the SLBs first decreased with decreasing the size of the underlying support, reached a minimum, and then increased when the size of the particles became comparable with the dimensions of the lipid bilayer thickness; the Tm was above that of the multilamellar vesicles (MLVs) of the same lipids. The increase in Tm indicated a stiffening of the supported bilayer, which was confirmed by Raman spectroscopic data. Moreover, Raman data showed better lipid packing and increased lateral order and trans conformation for the SLBs with increasing the curvature of the underlying support and decrease of the gauche kinks for the terminal methyl groups at the center of the bilayer. These results were consistent with a model in which the high free volume and increased outer headgroup spacing of lipids on highly curved surfaces induced interdigitation in the supported lipids. These results also support the symmetric lipid exchange studies of the SLBs as a function of the curvature, which was found to be slower on surfaces with higher curvature. Further, the effect of surface properties on the formation of SLBs was studied by changing the silanol density on the surface of SiO2 via thermal/chemical treatment and monitoring fusion of zwitterionic lipids onto silica (SiO2) nanoparticles. Our findings showed that the formation of SLBs was faster on the surfaces with lower silanol density and concomitantly less bound water compared to surfaces with higher silanol density and more bound water. Since the two SiO2 nanoparticles were similar in other respects, in particular their size and charge (ionization), as determined by zeta potential measurements, differences in electrostatic interactions between the neutral DMPC and SiO2 could not account for the difference. Therefore the slower rate of SLB formation of DMPC onto SiO2 nanoparticles with higher silanol densities and more bound water was attributed to greater hydration repulsion of the more hydrated nanoparticles. Lastly, we have investigated the effect and modulation of the surface charge of vesicles on the formation of SLBs by using different ratios of zwitterionic and cationic DMPC/DMTAP lipids. Through these studies we discovered a procedure by which assemblies of supported lipid bilayer nanoparticles, composed of DMPC/DMTAP (50/50) lipids on SiO2, can be collected and released from bilayer sacks as a function of the phase transition of these lipids. The lipids in these sacks and SLBs could be exchanged by lipids with lower Tm via lipid transfer.
Temple University--Theses

This thesis is devoted to the optical properties of low-dimensional structures based on such two-dimensional materials as graphene, silicene and phosphorene. We investigate optical properties of a variety of quasi-one dimensional and quasi-zero-dimensional structures, which are promising for future optoelectronics. Primarily we focus on their low-energy optical properties and how these properties are influenced by the structures’ geometry, external fields, intrinsic strain and edge disorder. As a consequence of this endeavor, we find several interesting effects such as correlation between the optical properties of tubes and ribbons whose periodic and ‘hard wall’ boundary conditions are matched and a universal value of matrix element in narrow-gap tubes and ribbons characterizing probability of transitions across the band gap opened up by intrinsic strain originating from the tube’s surface curvature or ribbon’s edge relaxation. The analytical study of the gapped 2D Dirac materials such as silicene and germanene, which have some similarity to the aforementioned quasi-one-dimensional systems in terms of physical description, reveals a valley- and polarization-dependent selection rules. It was also found that absorption coefficient should change in gapped materials with increasing frequency and become a half of its value for gap edge transitions when the spectrum is linear. Our analysis of the electronic properties of flat clusters of silicene and phosphorene relates the emergence and the number of the peculiar edge states localized at zero energy, so-called zero-energy states, which are know to be of topological origin, to the cluster’s structural characteristics such as shape and size. This allows to predict the presence and the number of such states avoiding complicated topological arguments and provides a recipes for design of metallic and dielectric clusters. We show that zero-energy states are optically active and can be efficiently manipulated by external electric field. However, the edge disorder is important to take into account. We present a new fractal-based methodology to study the effects of the edge disorder which can be applied also to modeling of composite materials. These finding should be useful in design of optoelectronic devices such as tunable emitters and detectors in a wide region of electromagnetic spectrum ranging form the mid-infrared and THz to the optical frequencies.

Introduction: This in vitro study aimed to evaluate and compare the fatigue resistance of ProFile Vortex® (VX) and Vortex Blue® (VB) files in two different artificial double curvature canals (DC1 and DC2) and in an artificial single curvature canal (SC). The bending moment of VX and VB was assessed. Methods: The bending moment (g·cm) was used to measure flexibility of VX and VB (size 25/.04, length: 25mm) according to ISO 3630-1 specifications. Both files types were tested for cyclic fatigue failure inside canals containing: a single curvature (SC: 60⁰ curvature, 5 mm radius) and two canals with different double curvature (DC); [DC1: coronal curvature of 60⁰ and 5 mm radius, and apical curvature of 30⁰ and 2 mm radius; DC2: coronal curvature of 60⁰ and 5 mm radius, and apical curvature of 60⁰ and 2 mm radius]. The number of cycles to failure (NCF) was recorded and the fracture surface of all fragments was examined with a scanning electron microscope (SEM) to confirm cyclic fatigue failure and for qualitative analysis of pattern of fracture. Results: VX and VB followed slightly different trajectories in the identical canals, especially in double curvature canals. The mean bending moment value was significantly lower for VB than for VX (p < .001). NCF for the two files were significantly higher in the single curvature canal (SC) compared to the two double curvature canals (DC1 and DC2) (p < .001). Of the double curvature canals, the NCF was significant higher in DC1 than in DC2 for VB (p < .05) but not for VX (p > .05). In the SC group, VB had NCF superior to VX (p < .05). In DC1 and DC2 groups, NCF of VX and VB was not statistically different from each other (p > .05). Multiple crack origins were observed for the majority of files fractured in DC1 and DC2 canals. Conclusions: DC1 and DC2 canals demonstrated a more stressful and challenging anatomy than the SC canal for VX and VB. In double curvature canals, degree of curvature and radius, and the file’s flexibility may affect the mean NCF.
Dentistry, Faculty of
Graduate

Die vorliegende Arbeit verfolgt das Ziel, Cu(Ag)-Dünnschichten als potentiellen Werkstoff für Leiterbahnen in der Mikroelektronik zu untersuchen. Für die Beurteilung dieses Materialsystems wurden vier Schwerpunkte bezüglich der Schichtcharakterisierung definiert: Herstellung, Gefüge, thermomechanische Eigenschaften, Elektromigrationsresistenz. Grundlage sämtlicher Untersuchungen ist eine geeignete Probenpräparation. In Anlehnung an Technologien, die zur Zeit bei der Herstellung von reinen Cu-Leiterbahnen Anwendung finden, erfolgte die Beschichtung der Cu(Ag)-Schichten (Dicke bis 1 µm) galvanisch aus einem schwefelsauren Elektrolyten unter Additiveinsatz auf thermisch oxidierten Siliziumwafern. Hierbei war nicht nur die Abscheidung von ganzflächigen Dünnschichten, sondern auch die Beschichtung auf strukturierte Substrate von Interesse. Die erzeugten Schichtproben werden in ihren Gefügeeigenschaften, vergleichend zu reinen Kupferschichten, charakterisiert. Hierzu zählen Korngrößen und -orientierungen, thermisches Gefügeverhalten, Einbau, Verteilung und Segregation von Silber und Fremdstoffen sowie die elektrischen Eigenschaften. Von grundsätzlicher Bedeutung für das Elektromigrationsverhalten und damit für die Zuverlässigkeit und das Leistungsvermögen sind die thermomechanischen Eigenschaften. Diese werden an ausgedehnten Schichten mit der Substratkrümmungsmessung bis zu Temperaturen von 500°C beschrieben. Die Diskussion des mechanischen Schichtverhaltens umfasst sowohl thermische als auch temporale Charakteristika. Die Untersuchungen geben einen Einblick in die wirkenden Mechanismen des Stofftransports und des Spannungsabbaus. Den Abschluss der Arbeit stellen erste Experimente zum Elektromigrationsverhalten der Cu(Ag)-Dünnschichten dar. Den Kern dieser Analysen bilden Messungen an sog. Blech-Strukturen (Materialdriftexperimente). Hierbei werden geeignete Technologien für die mikrotechnologische Herstellung von derartigen Cu(Ag)-Strukturen vorgestellt. Anhand erster Messungen wird das Elektromigrationsverhalten von Cu(Ag)-Metallisierungen in seinen Grundcharakteristika beschrieben.

Die vorliegende Arbeit verfolgt das Ziel, Cu(Ag)-Dünnschichten als potentiellen Werkstoff für Leiterbahnen in der Mikroelektronik zu untersuchen. Für die Beurteilung dieses Materialsystems wurden vier Schwerpunkte bezüglich der Schichtcharakterisierung definiert: Herstellung, Gefüge, thermomechanische Eigenschaften, Elektromigrationsresistenz. Grundlage sämtlicher Untersuchungen ist eine geeignete Probenpräparation. In Anlehnung an Technologien, die zur Zeit bei der Herstellung von reinen Cu-Leiterbahnen Anwendung finden, erfolgte die Beschichtung der Cu(Ag)-Schichten (Dicke bis 1 µm) galvanisch aus einem schwefelsauren Elektrolyten unter Additiveinsatz auf thermisch oxidierten Siliziumwafern. Hierbei war nicht nur die Abscheidung von ganzflächigen Dünnschichten, sondern auch die Beschichtung auf strukturierte Substrate von Interesse. Die erzeugten Schichtproben werden in ihren Gefügeeigenschaften, vergleichend zu reinen Kupferschichten, charakterisiert. Hierzu zählen Korngrößen und -orientierungen, thermisches Gefügeverhalten, Einbau, Verteilung und Segregation von Silber und Fremdstoffen sowie die elektrischen Eigenschaften. Von grundsätzlicher Bedeutung für das Elektromigrationsverhalten und damit für die Zuverlässigkeit und das Leistungsvermögen sind die thermomechanischen Eigenschaften. Diese werden an ausgedehnten Schichten mit der Substratkrümmungsmessung bis zu Temperaturen von 500°C beschrieben. Die Diskussion des mechanischen Schichtverhaltens umfasst sowohl thermische als auch temporale Charakteristika. Die Untersuchungen geben einen Einblick in die wirkenden Mechanismen des Stofftransports und des Spannungsabbaus. Den Abschluss der Arbeit stellen erste Experimente zum Elektromigrationsverhalten der Cu(Ag)-Dünnschichten dar. Den Kern dieser Analysen bilden Messungen an sog. Blech-Strukturen (Materialdriftexperimente). Hierbei werden geeignete Technologien für die mikrotechnologische Herstellung von derartigen Cu(Ag)-Strukturen vorgestellt. Anhand erster Messungen wird das Elektromigrationsverhalten von Cu(Ag)-Metallisierungen in seinen Grundcharakteristika beschrieben.

This Thesis is devoted to the study of two different aspects of electron behavior in two-dimensional materials, namely hydrodynamic electron transport and plasmon propagation. The Thesis is structured as follows. In Chapter 1 the main experimental facts that motivated our work on electron hydrodynamics and plasmonics are presented and critically discussed. Chapter 2 contains our main results on hydrodynamic electron transport. After deriving the basic equations of the electron hydrodynamics and discussing their limit of applicability, we use them to quantify the impact of two different transport coffcients, the shear and Hall viscosities of the electron liquid, on steady-state transport. Our results are used to propose experimental protocols that allow an experimental determination of these transport coeffcients. Chapter 3 deals with plasmon propagation through inhomogeneous media. We consider three dfferent geometries: an interface between two dfferent materials, a one dimensional perturbation, and a zero dimensional perturbation in an otherwise uniform electron system. We calculate scattering observables for plasmons in these geometries. For the interface geometry we also investigated the presence of plasmonic bound states localized near the interface, while for the second and third geometries we quantify the impact of non-local fects. Chapter 4 presents a theory of chiral plasmons in materials with a non-trivial Berry curvature in the electronic band structure. We firstly employ the results of Chapter 3 to obtain a semi-classical theory of Chiral Berry Plasmons (CBPs) at a generic interface between two materials having different Berry uxes across the Fermi surface. We then test the impact of different types of screened electron-electron interaction, and of a finite damping rate on the dispersion and lifetime of CBPs.

碩士
國立高雄第一科技大學
工學院
101
The application of the light guide rod (LGR) has become increasingly common, but its complex and changing modeling is bringing about the light emitting uniform phenomenon. The main reason is that the spread of light is straight, and a turning point will be affected by the reflection or refraction. This paper aims to investigate the curvature effect on the LGR optical properties. The real-coded genetic algorithm (RGA) and grey relational analysis (GRA) in conjunction with Excel VBA combined with Solidworks and Lighttools softwares are employed together to find the best parameters from the limit specifications or the random values. In this paper, the total power (TP) rather than average power, average difference (AD) and contrast ratio (CR) are combined into a single parameter. Moreover, the area of light pattern is not fixed to avoid the incorrect mesh data in the “dark zone”. Finally it is validated by comparing with the previous results that the proposed design method can quickly and efficiently complete the LGR design when considering curvature effect on optical properties by changing the scattered particles in the LGR.

The main aim of this thesis is to understand curvature properties of a given hermitian metric by restricting it to the leaves of a suitable singular Riemann surface foliation. We will specifically consider the complete Kahler metric example given by Grauert on (C^n)*, from which we can construct complete Kahler metric on the complement of any closed analytic subset of a Stein manifold. Note that for n ≥ 2, (C^n)* = C^n - {0} is a non-domain of holomorphy. So, this construction helps us to get a complete Kahler metric on the complement of singular set of a Riemann surface foliation. We will study this metric in some prototype models, i.e., we will calculate holomorphic sectional curvature of the Grauert metric (for n ≥ 2) on (i) (C^n)* and (ii) B^n - A, where A ⊂ B^n is a k-dimensional affine plane, where 0 ≤ k ≤ n-2, and make observations about how this curvature behaves near singular points and away from singular points. We will observe that this is a non-positively curved metric on C*. Next, we will use this construction to get a better understanding of this complete Kahler metric on the complement of a non-negative principal divisor D in a Stein manifold M. We will prove some facts about its holomorphic sectional curvature in this case. We will also prove that there is an intrinsic continuity property in its construction. More specifically, we will show that we can choose these metrics in a continuous fashion if the corresponding divisor vary continuously in an appropriate sense. The same regularity can be seen for the Gaussian curvature of the restricted metric on leaves of a foliation induced by a non-singular holomorphic vector field, as the corresponding non-negative principal divisor vary continuously. Finally, we will consider the leafwise Poincare metric of a singular Riemann surface lamination whose leaves are all hyperbolic and prove that this metric converges pointwise if the domain of definition of this lamination varies in an appropriate sense. This convergence is uniform on compacts under additional hypothesis on the domain of definition and regularity of leafwise Poincare metric of the lamination of limiting domain. We will also give an analogue of the Minda's Domain Bloch constant in the foliated case and show that a similar lower bound holds in this case also as in the case of hyperbolic Riemann surfaces.
Shyama Prasad Mukherjee Fellowship, Council of Scientific & Industrial Research (CSIR), India

碩士
國立成功大學
機械工程學系
107
For the first experiment, nine specimens are prepared on the basis of the L9(33) orthogonal array design to evaluate the optical and electrical properties, morphology, and the microstructure of a-IGZO/Ag/a-IGZO (IAI) triple-layer composite films deposited on curved glass substrates with different radius of curvature efficiently. The experiments are arranged for the changes in three controlling factors, namely the IGZO and Ag thicknesses, and substrate’s radius of curvature. Radius of curvature has the highest contribution for the RMS surface roughness (SRq) and the mean particle size (PS). The carrier mobility (CM) and carrier concentration (CC) are proportional to each, irrespective of the controlling factor change in this study. An increase in the radius of curvature can result in the increases of SRq and PS, and therefore brings in a surface scattering effect which can cause the reduction of CM as well as the rise of resistivity (R). In addition, a sufficiently large radius of curvature can elevate the transmittance at 550 nm and Haack’s figure of merit (FOM) effectively, but it can lower the reflectance of blue, green and red. Via the carrier injections, increasing the Ag thickness can elevate the carrier mobility and concentration significantly. The reflectance for blue, green, and red are also risen by increasing the Ag thickness. As a result of Burstein-Moss effect, carrier concentration and optical bandgap are elevated by increasing the IGZO thickness. Additionally, the reflectance of blue, green, and red are also risen. Appropriate choices in the IGZO and Ag thicknesses and the radius of curvature can obtain the transmittance 〉80 %, and elevate the FOM significantly. For the second set of experiments, AZO and AZO/Ag/AZO (AAA) specimens are prepared by varying O2 and N2 flow rates to investigate the gas effects on the microstructure, and the optical and electrical properties. The AZO specimens are found to have the decreases in grain size and SRq, and an increase in the compressive residual stress when N2 flow rate increases higher than 2.5 sccm. The addition of O2 can contribute to a similar tendency for grain size, SRq and residual stress; the grain size and SRq are always smaller, while residual stress is larger than that prepared with N2. The thickness of AZO is proportional to the grain size and SRq, whereas it is inversely proportional to the residual stress of AZO, they are valid for both AZO and AAA thin films. Specimen D with 60-nm AZO thickness possesses the strongest anti-reflection effect of the AAA structure, and therefore suppresses the reflection from the Ag interlayer significantly. P-type conductivity is achieved by introducing the N2 into AZO layers. The carrier mobility and carrier concentration are lowered by increasing the amount of O2 because the oxygen vacancies are reduced. The Burstein-Moss effect is observed for the n-type AAA thin films where a decrease in optical bandgap along with an increase in carrier concentration is found for the p-type AAA films. Specimen D possesses the highest FOM value and relative high T at 550 nm because the 60-nm AZO can contribute to the strongest anti-reflection effect.

Recently, different studies on Weyl semimetals have shown some great potential for applications in spintronics. Indeed, spin-chiral Weyl nodes are perfect sources or sinks of the Berry curvature, which give new transport properties due to their topological nature, such as the chiral anomaly, and a large anomalous Hall response. Moreover, type-II Weyl semimetals, such as WTe2, have a specific band structure with tilted Weyl cones and overlapping electron/hole bands that can result in a perfect charge compensation and an extremely large magnetoresistance (XMR) . Yet, in WTe2 , Weyl nodes are usually located about 50 meV above the Fermi energy, a situation that questions the observation of both a large positive XMR and a negative magnetoresistance attributed to the chiral anomaly in some studies. In this work, we investigate the magneto-transport properties of WTe2 nanos- tructures obtained by different methods (mechanical exfoliation, chemical vapor transport), considering both the real electronic band structure and scattering by dis- order. Although the XMR amplitude also depends on charge mobilities, it is shown that the subquadratic response is not strongly influenced by the degree of disorder. Taking carrier densities infered from quantum oscillations into account, a three-band model explains this behavior by a large difference in hole mobilities, as confirmed by numerical simulations. At low temperatures and for small magnetic fields, an isotropic negative magneto-resistance is observed and attributed to a topological property of the band structure far away from the Weyl nodes. This new mechanism, different from the chiral anomaly, allows us to reproduce the experimental results by numerical calculations based on the real band structure of WTe2.
In den vergangenen Jahren haben verschiedene Untersuchungen von Weyl Halb- metallen gezeigt, dass sich diese sehr gut als Spintronische Geräte eignen. In der Tat sind die Spin-chiralen Weyl Quasiteilchen perfekte Quellen und Abflüsse der Berrykrümmung, was auf Grund ihrer topologischen Natur neue Transporteigen- schaften hervorruft, wie beispielsweise die chirale Anomalie und einen großen, anomalen Hall Effekt. Außerdem haben Typ II Weyl Halbmetalle wie WTe2 eine spezifische Bandstruktur mit gekippten Weylkegeln und überlappenden Elektronen-/Lochbändern, die dazu führen können, dass die Ladungsträgerkompensation ideal wird und ein sehr starker Magnetowiderstand (XMR) entsteht. Dennoch befinden sich die Weylknoten in WTe2 ca. 50 meV über dem Ferminiveau, eine Beobachtung die sowohl den starken positiven Magnetowiderstand, als auch den negativen Mag- netowiderstand, der meist mit der chiralen Anomalie in Verbindung gebracht wird, in Frage stellt. In dieser Arbeit untersuchen wir die Magnetotransporteigenschaften von WTe2 Nanostrukturen, die durch verschiedene Wachstumsarten hergestellt werden (mech- anische Exfoliation, chemische Gasphasenabscheidung), um sowohl die reale Band- struktur, als auch Streuung an Störstellen in Betracht ziehen zu können. Es wird gezeigt, dass der extrem große Magnetowiderstand nicht direkt vom Grad der Un- ordnung abhängt und dass das typisch subquadratische Verhalten im Rahmen eines Multibandmodells, was über das Zweibandmodell hinaus geht, verstanden wer- den kann und sich auch mit numerischen Simulationen bestätigt lässt. Bei tiefen Temperaturen und für kleine Magnetfelder kann ein isotropisch negativer Magne- towiderstand beobachtet werden, der der topologischen Eigenschaft der Bandstruk- tur weit weg von den Weylknoten geschuldet ist. Dieser neue Mechanismus, der sich von der chiralen Anomalie unterscheidet, erlaubt es uns die experimentellen Ergebnisse mit numerischen Berechnungen, die auf der realen Bandstruktur basieren, zu reproduzieren.
Récemment, différentes études sur les semimétaux de Weyl ont montré leur large potentiel pour des applications en spintronique. En effet, les noeuds de Weyl avec leur chiralité de spin sont des sources ou puits parfaits de la courbure de Berry, ce qui peut conduire à de nouvelles propriétés de transport, dues à la nature topologique de la structure de bande, comme l’anomalie chirale et une large réponse liée à l’effet Hall anormal dit intrinsèque. De plus, les semimétaux de Weyl de type II, comme WTe2, ont une structure de bande particulière avec des cônes de Weyl inclinés et un chevauchement des bandes de trous et d’électrons qui résulte en une forte compensation de charge et une magnétorésistance extrêmement large (XMR) associée. Cependant, dans WTe2, les noeuds de Weyl se trouvent environ 50 meV au-dessus de l’énergie de Fermi, ce qui remet en cause la possibilité d’observer à la fois une XMR positive à fort champ et une magnétorésistance négative à champ faible due à l’anomalie chirale. Dans ce travail, nous étudions les propriétés de magnéto-transport de nanostructures WTe2 obtenues par différentes méthodes (exfoliation mécanique, transport en phase vapeur), avec des degrés de désordre microscopique différents, en considérant à la fois la structure de bande réelle du matériau et les processus de diffusion liés au désordre. Il est montré que la XMR présente un comportement subquadratique, qui peut être compris dans le cadre d’un modèle multi-bandes, au-delà de deux bandes, comme confirmé par des simulations numériques. A très basse température et faible champ magnétique, une magnétorésistance négative et isotrope est observée et attribuée à une propriété topologique de la structure de bandes loin des noeuds de Weyl. Ce nouveau mécanisme, différent de celui de l’anomalie chirale, nous permet de reproduire nos résultats expérimentaux par des simulations numériques basées sur la structure de bande réelle de WTe2.

The aim of this thesis is a comprehensive description of the properties of a nonlinear least squares estimator for a nonlinear regression model with normally distributed errors and thorough development of various methods for constructing confidence regions and confidence intervals for the parameters of the nonlinear model. Due to the fact that, unlike the case of linear models, there is no easy way to construct an exact confidence region for the parameters, most of these methods are only approximate. A short simulation study comparing observed coverage of various confidence regions and confidence intervals for models with different curvatures and sample sizes is also included. In case of negligible intrinsic curvature the use of likelihood-ratio confidence regions seems the most appropriate.

The discovery of topological quantum states of matter has required physicists to look beyond Landau’s theory of symmetry-breaking, previously the main paradigm for
studying states of matter. This has led also to the development of new topological theories for describing the novel properties. In this dissertation an investigation in this
frontier research area is presented, which looks at the interplay between the quantum geometry of these states, defects and disorder. After a brief introduction to the topological quantum states of matter considered herein, some aspects of my work in this area are described. First, the disorder-induced band structure engineering of topological insulator surface states is considered, which is possible due to their resilience from Anderson localization, and believed to be a consequence of their topological origin.
Next, the idiosyncratic behavior of these same surface states is considered, as observed in experiments on thin film topological insulators, in response to competition between
hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the
topologically-protected charge response of two dimensional gapped electronic topological states to a special kind of 0-dimensional boundary – a disclination – that encodes spatial curvature. Finally, an intriguing relation between the gravitational response of quantum Hall states, and their response to an apparently unrelated perturbation – nonuniform electric fields is reported.