By enlarging the spatial and temporal spectral problems within a certain Lie algebra, a hierarchy of integrable couplings of the Kaup-Newell soliton equations is constructed. The recursion operator of the resulting hierarchy of integrable couplings is explicitly computed. The integrability of the new coupling hierarchy is exhibited by showing the existence of infinitely many commuting symmetries.

Curling deformation of thin elastic surfaces appears in numerous natural and man-made structures where a spontaneous curvature is present. In this thesis, we couple theoretical approaches and macroscopic experiments on elastic ribbons to understand the dynamics of curling of opened bio-membranes, motivated by the need to better understand recent microscopic observations during egress of Malaria infected red blood cells (MIRBC) and bursting of artificial polymersomes.In a first part, we study theoretically pore stability and curling propagation of an initially opened spherical bio-membrane. We model geometrically curling deformation as the revolution of a decentered Archimedean spiral, leading to a prescribed toroidal wrapping of the membrane. In this configuration, we show how the stability of a pore to curling depends strongly on both line-tension and shear elasticity and we discuss these results in relation to the curling of MIRBCs membranes. Moreover, taking into account viscous dissipations, the consequent dynamics we calculate agrees quantitatively well with experimental data obtained during opening of MIRBCs. Our approach shows in particular how the membrane dissipation resulting from the surface redistribution dominates curling dynamics over outer viscous dissipation.However, the complexity of the spherical geometry and the lack of detailed images in microscopic observations hamper the development of more accurate models where the coupling between flow and deformation is fully understood. Subsequently, we study in a second part the curling deformation of macroscopic naturally curved elastic ribbons in different viscous media and elastic conditions. At high Reynolds numbers, due to the tendency of ribbons to localize bending deformations when a curling front travels down the material, we show that curling reaches rapidly a constant propagating velocity. In this regime, the ribbon wraps itself into a compact roll whose size is predicted through the solitary wave solution of the associated Elastica. At low Reynolds numbers, however, closer to the hydrodynamic conditions of curling in microscopic membranes, we show that the strong lubrication forces induce a non-compact curling. The overall size of the spiraling ribbon increases in time leading to a temporal decrease of the released elastic power and therefore a consequent decrease in velocity. We discuss how such discovery sheds a new light on the modeling of curling in MIRBCs and polymersomes.

This thesis is twofold. In the first part, a proof of the interpolation inequality along geodesics in p-Wasserstein spaces is given and a new curvature condition on abstract metric measure spaces is defined. In the second part of the thesis a proof of the identification of the q-heat equation with the gradient flow of the Renyi (3-p)-Renyi entropy functional in the p-Wasserstein space is given. For that, a further study of the q-heat flow is presented including a condition for its mass preservation.

A theoretical explanation of the existence of lipid rafts in cell membranes remains a topic of lively debate. Large, micrometer sized rafts are readily observed in artificial membranes and can be explained using thermodynamic models for phase separation and coarsening. In live cells such domains are not observed and various models are proposed to describe why the systems do not coarsen. We review these attempts critically and show within a phase field approach that membrane bound proteins have the potential to explain the different behaviour observed in vitro and in vivo. Large scale simulations are performed to compute scaling laws and size distribution functions under the influence of membrane bound proteins and to observe a significant slow down of the domain coarsening at longer times and a breakdown of the self-similarity of the size-distribution function. / Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.

<p>The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist infinitely many spacetimes, not necessarily spherically symmetric or static, that admit smooth global solutions to inverse mean curvature vector flow. Prior to our work, such solutions were only known in spherically symmetric and static spacetimes. The technique used in this thesis might be important to prove the Spacetime Penrose Conjecture, which remains open today. </p><p>Given a spacetime $(N^{4}, \gbar)$ and a spacelike hypersurface $M$. For any closed surface $\Sigma$ embedded in $M$ satisfying some natural conditions, one can ``steer'' the spacetime metric $\gbar$ such that the mean curvature vector field of $\Sigma$ becomes tangential to $M$ while keeping the induced metric on $M$. This can be used to construct more examples of smooth solutions to inverse mean curvature vector flow from smooth solutions to inverse mean curvature flow in a spacelike hypersurface.</p> / Dissertation

This thesis explored how asphaltene and naphthenic amphiphile species influence the formation (morphology and size) and stability of heavy crude oil (bitumen) emulsions. It was experimentally shown that asphaltenes produce water-in-oil emulsions. Naphthenic amphiphiles on the other hand flip the emulsion morphology to oil-in-water. It was further demonstrated that the size and stability of these emulsions is influenced by physicochemical effects such as the pH, solvent-bitumen-water ratios, solvent aromaticity, and temperature. In view of these findings, the hydrophilic-lipophilic deviation (HLD) and net-average curvature (NAC) models were looked at as potential means for predicting the formation and stability of emulsions. Owing to the complexity of bitumen emulsions, however, the HLD and NAC models were instead tested against well-defined sodium dihexyl sulfosuccinate-toluene-water emulsions. The morphologies of these emulsions were predicted as a function of the formulation salinity whereas corresponding droplet sizes were predicted as a function of the continuous phase density and interfacial tension (γow). Emulsion stability trends were in turn predicted using a collision-coalescence-separation assumption. From this assumption, emulsion stability was expressed as a function of the emulsion droplet collision frequency and activation energy. The key parameters of the highly scrutinized activation energy term included the γow, interfacial rigidity, and critical film thickness. In applying the same modeling approach to the stability of other emulsions already published in the literature, it was found that the rigidity of adsorbed multilayer/liquid crystal films cannot yet be fully accounted for. This shortcoming was the reason for which only minimum stability times were reported for bitumen emulsions.

Turbulent premixed propane/air and methane/air flames were studied using planar Rayleigh scattering and particle image velocimetry on a stabilized Bunsen type burner. The fuel-air equivalence ratio was varied from Φ=0.7 to 1.0 for propane flames, and from Φ=0.6 to 1.0 for methane flames. The non-dimensional turbulence intensity, u'/SL (ratio of fluctuation velocity to laminar burning velocity), covered the range from 3 to 24, equivalent to conditions of corrugated flamelets and thin reaction zones regimes. Temperature gradients decreased with the increasing u'/SL and levelled off beyond u'/SL > 10 for both propane and methane flames. Flame front thickness increased slightly as u'/SL increased for both mixtures, although the thickness increase was more noticeable for propane flames, which meant the thermal flame front structure was being thickened. A zone of higher temperature was observed on the average temperature profile in the preheat zone of the flame front as well as some instantaneous temperature profiles at the highest u'/SL. Curvature probability density functions were similar to the Gaussian distribution at all u'/SL for both mixtures and for all the flame sections. The mean curvature values decreased as a function of u'/SL and approached zero. Flame front thickness was smaller when evaluated at flame front locations with zero curvature than that with curvature. Temperature gradients and FSD were larger when the flame curvature was zero. The combined thickness and FSD data suggest that the curvature effect is more dominant than that of the stretch by turbulent eddies during flame propagation. Integrated flame surface density for both propane and methane flames exhibited no dependance on u'/SL regardless of the FSD method used for evaluation. This observation implies that flame surface area may not be the dominant factor in increasing the turbulent burning velocity and the flamelet assumption may not be valid under the conditions studied. Dκ term, the product of diffusivity evaluated at conditions studied and the flame front curvature, was a magnitude smaller than or the same magnitude as the laminar burning velocity.

The user of an image database often wishes to retrieve all images similar to the one (s)he already has. In this thesis, shape analysis methods for retrieving shape are investigated. Shape analysis methods can be classified in two groups as contour-based and region-based according to the shape information used. In such a classification, curvature scale space (CSS) representation and angular radial transform (ART) are promising methods for shape similarity retrieval respectively. The CSS representation operates by decomposing the shape contour into convex and concave sections. CSS descriptor is extracted by using the curvature zero-crossings behaviour of the shape boundary while smoothing the boundary with Gaussian filter. The ART descriptor decomposes the shape region into a number of orthogonal 2-D basis functions defined on a unit disk. ART descriptor is extracted using the magnitudes of ART coefficients. These methods are implemented for similarity comparison of binary images and the retrieval performances of descriptors for changing number of sampling points of boundary and order of ART coefficients are investigated. The experiments are done using 1000 images from MPEG7 Core Experiments Shape-1. Results show that for different classes of shape, different descriptors are more successful. When the choice of approach depends on the properties of the query shape, similarity retrieval performance increases.

ABSTRACT AN ANALYTICAL STUDY ON THE MINIMUM CONFINEMENT IN SPIRAL COLUMNS &Ouml / zkaya, Cenan M.S., Department of Civil Engineering Supervisor: Prof. Dr. G&uuml / ney &Ouml / zcebe Co-Supervisor: Prof. Dr. Ugur Ersoy July 2005, 135 pages The minimum spiral ratio equation given in the codes is derived by equating the strength at the second peak to the strength at the first peak for spiral columns tested under uniaxial load. In this study, specimen behavior under combined bending and axial load was taken as basis while deriving proposed equations. Analyses were carried out by using a Moment-Curvature program. For normal strength concrete, one regression and one simplified equation giving minimum spiral ratio are proposed. Difference between two equations arises from the number in front of (Ac/Ack). In regression equation, this number is calculated by means of a function. In simplified equation, this number is a constant. For high strength concrete, a different regression equation is proposed which is valid for concrete strengths up to 95 MPa. Simplified equation proposed for normal strength concrete is also proposed for high strength concrete up to concrete strengths of 120 MPa. It was found that / (i) Simplified equation proposed for normal and high strength concrete yielded consistent results in the range of variables studied / (ii) Except some points, regression equations yielded consistent results / (iii) It is recommended to use simplified equation instead of regression and code equations since it yields more consistent results than code and regression equations. Keywords: Confined Concrete, Ductility, Moment-Curvature, Minimum Spiral Volumetric Ratio

abstract: The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle. / Dissertation/Thesis / Ph.D. Mathematics 2011