Iskanje po katalogu digitalne knjižnice

Opis: In this thesis, we study the structure and optical transmission properties of the twist-bend nematic liquid crystalline phase, made of bent dimers, confined in thin planar cells. Confinement leads to the formation of a periodic modulated structure, the formation of which is explained as follows. The twist-bend nematic phase is characterized by a heliconical modulation of the molecular long axes. Due to a short pitch of modulation (approximately 10 nm), the twist-bend nematic phase behaves as a pseudo-layered medium. At temperatures below the nematic – twist-bend nematic phase transition, the heliconical pitch and thus the thickness of the pseudo-layers reduces, which leads to a two-dimensional undulation of pseudo-layers in the direction perpendicular to the cell surfaces and along the surfaces. The undulated structure is responsible for a stripe texture observed under a polarizing microscope and acts as a diffraction grating. We constructed theoretical models to predict the pseudo-layer structure of a confined twist-bend nematic phase and to describe the properties of light diffracted on such cells. The free energy of the two-dimensional pseudo-layer structure of the twist-bend nematic phase is expressed in terms of the nematic director field, by which we describe the direction of the heliconical axis, and a complex smectic order parameter, the gradient of which gives the direction of the layer normal. At first, we assume that pseudo-layers are perpendicular to the surfaces (bookshelf geometry) and find a stable structure by assuming an ansatz for the pseudo-layer displacement from the bookshelf geometry and then minimizing the free energy at a very strong and very weak surface anchoring. In this way a threshold condition for the onset of the modulated structure is obtained, as well as the amplitude and period of modulation. Next, we assume that, at the onset of the twist-bend nematic phase, pseudo-layers are formed at some angle (pre-tilt) with respect to the surface. We find that in both cases, the bookshelf and pre-tilted one, the calculated period of modulation far from the phase transition is always approximately twice the cell thickness, which agrees with experimental observations. The properties of light diffracted by the spontaneously formed grating were studied both experimentally and theoretically. We measured the intensity and polarization properties of the first two orders of the diffracted light and the temperature dependence of the polarization of the second order diffraction peaks. To predict the observed properties of the diffracted light and to simplify the description of such gratings, we consider different preliminary models of a one-dimensional spatial variation of the optic axis, the direction of which is given by two angles. A transfer matrix method is used and a good agreement between the experimental and theoretical results is obtained. In a more comprehensive approach, we determine the spatial variation of the optic axis direction from the modeled structure. The electric field in the diffracted light is obtained by using the transfer matrix method and beam propagation method. In the case of a pre-tilt of the pseudo-layers and very strong surface anchoring both methods give good qualitative agreement with experimental results, only in the case of the temperature dependence of the second order diffraction peaks, a more complex beam propagation method is superior to the transfer matrix method. The thesis is divided into three parts. In the first part, we focus on the physical properties of the twist-bend nematic phase and its structure in thin planar cells. In the second part, a continuum model is proposed and finally, the properties of diffracted light are discussed and theoretically predicted by using the beam propagation method and transfer matrix method.
Ključne besede: Bent-dimer liquid crystals, twist-bend nematic phase, undulation of pseudo-layers, polarization, diffraction grating, beam propagation method, transfer matrix method.
Objavljeno v DKUM: 21.10.2021; Ogledov: 670; Prenosov: 61
Celotno besedilo (10,65 MB)

Opis: This doctoral dissertation is devoted to the studies of some qualitative properties of certain polynomial systems of ordinary differential equations. The main problems that are considered in this thesis are the problems of integrability and cyclicity. Some results on the classification of the global phase portraits of a family of cubic systems are presented as well. In the first chapter basic notions and results of the qualitative theory of systems of ODE's are introduced. Since one of important tools for our study of these problems is the commutative computational algebra, some main notions and properties of polynomial ideals and their varieties, including various algorithms related to them, are also presented in the introduction. In the second chapter methods for investigation of trajectories near degenerated singularities are presented. They are further used for the classification of global phase portraits of a family of cubic systems with the nilpotent center at the origin. In the third chapter the main problem of these thesis is studied, the problem of integrability. The problem of integrability which is connected to the problem of distinguishing between a center and a focus is studied for two different families of cubic polynomial systems of ODE's. With the computational algebra approach the necessary conditions for the existence of the first integral of these systems were obtained. For all but one condition was proven, using various approaches, the existence of the first integrals. The center problem for the real systems can be generalized to the complex systems. The origin of the system obtained after the complexification of the real system is the so-called 1:-1 resonant singular point, from which one additional generalization follows. This is the generalization to the p:-q resonant center. In the third chapter the :-3 resonant singular point of a quadratic family of complex systems is studied. The fourth chapter is devoted to the study of the problem of integrability of a three dimensional polynomial system with quadratic nonlinearities. The problem of existence of two independent first integrals and the existence of one first integral in the system was investigated. In the last chapter local bifurcations of limit cycles of a family of cubic systems are studied. Estimations for the number of limit cycles bifurcated from each components of the center variety are obtained.
Ključne besede: planar systems of ODE's, higher dimensional systems of ODE's, phase portrait, nilpotent center, limit cylces, Poincaré compactification, center problem, Bautin ideal, focus quantities, time-reversibility, integrability problem, Darboux method, linearizability, limit cycle, cyclicity
Objavljeno v DKUM: 19.07.2016; Ogledov: 1592; Prenosov: 247
Celotno besedilo (12,26 MB)

Opis: The thesis is comprised of three main categories. The first part of dissertation covers investigations of phase equilibria of compounds from natural materials in conventional and also non conventional supercritical fluids. In details, the impact of pressure and/or temperature on the system behaviour (miscibility, solubility, phase inversion) is investigated, quantitative and qualitative analyses to evaluate and identify compounds contained after performing preliminary extraction experiments from different natural tissues are presented. The impact of operating parameters (pre-treatment of the raw material with SFE; different extraction solvents: propane, CO2, non conventional SCFs; different extraction temperatures and pressures) on extraction kinetics is observed. Following substances were taken into consideration: vanillins, caffeine, carnosoic acid extract and lecithin. Second part of dissertation covers studies of phase equilibria of the systems bio oil/gas, which is crucial in biorefinery process design. In this part of dissertation, which covers studies of phase equilibria of binary and ternary systems, the impact of pressure and/or temperature on the system behaviour (miscibility, solubility, phase inversion) for binary system bio oil/supercritical fluid (bio oil/CO2) and (bio oil/H2) was studied. Additionally, phase behaviour of ternary systems of (bio oil/diesel/CO2) and (bio oil/tail water/CO2) under the impact of pressure and/or temperature is observed. These data are of a high importance for bio refineries as an important part of necessary sustainable development. In recent years, studies on biodiesel synthesis have focused on development of process intensification technologies to resolve some of these issues. Fundamental data to design fractionation process of components of bio oil are crucial for an efficient hydrogenation process of bio oil. In the third part of dissertation observation of phase equilibria and determination of the parameters like diffusion coefficient, density and viscosity for the systems polymer/CO2 at elevated pressures is investigated. An overview of different methods applied to determine the parameters like diffusion coefficient, density and viscosity of the systems polymer (PEG)/CO2 at elevated pressures is offered. Observation of phase equilibria of the binary system PEG/CO2, determination of the impact of pressure and/or temperature on the system behaviour (miscibility, solubility, phase inversion), determination of thermodynamically and physically properties of the system with new applicative methods and finally, comparison of the results obtained by different methods is provided. The interfacial tension (IFT) at the (PEG)/CO2 interface has been determined by using an experimental technique developed to study the interfacial interactions of the liquids in equilibrium with gas in a glass-windowed equilibrium cell by the means of Capillary Rise (CR) method. Advantages and disadvantages of methods that were applied are exposed and discussed.
Ključne besede: phase equilibria, natural materials, conventional and non conventional supercritical fluids, extraction, bio oil, data for biorefinery process design, systems polymer (PEG)/CO2, diffusion coefficient, density, viscosity, surface tension, Capillary Rise (CR) method.
Objavljeno v DKUM: 28.10.2014; Ogledov: 2377; Prenosov: 338
Celotno besedilo (4,46 MB)