This paper is a study of T-sets of normed linear spaces. Geometrical properties of normed linear spaces are developed in terms of intersection properties shared by a subcollection of T-sets of the space and in terms of special spanning properties shared by each T-set of a subcollection of T-sets of the space. A characterization of the extreme points of the unit ball of the dual of a normed linear space is given in terms of the T-sets of the space. Conditions on the collection of T-sets of a normed linear space are determined so that the normed linear space has the property that extreme points of the unit ball of the dual space map canonically to extreme points of the unit ball of the third dual space.

Mineral dust aerosol plays an important role in determining the physical and chemical equilibrium of the atmosphere. The radiative balance of the Earth's atmosphere can be affected by mineral dust through both direct and indirect means. Mineral dust can directly scatter or absorb incoming visible solar radiation and outgoing terrestrial IR radiation. Dust particles can also serve as cloud condensation nuclei, thereby increasing albedo, or provide sites for heterogeneous reactions with trace gas species, which are indirect effects. Unfortunately, many of these processes are poorly understood due to incomplete knowledge of the physical and chemical characteristics of the particles including dust concentration and global distribution, as well as aerosol composition, mixing state, and size and shape distributions. Much of the information about mineral dust aerosol loading and spatial distribution is obtained from remote sensing measurements which often rely on measuring the scattering or absorption of light from these particles and are thus subject to errors arising from an incomplete understanding of the scattering processes. The light scattering properties of several key mineral components of atmospheric dust have been measured at three different wavelengths in the visible. In addition, measurements of the scattering were performed for several authentic mineral dust aerosols, including Saharan sand, diatomaceous earth, Iowa loess soil, and palagonite. These samples include particles that are highly irregular in shape. Using known optical constants along with measured size distributions, simulations of the light scattering process were performed using both Mie and T-Matrix theories. Particle shapes were approximated as a distribution of spheroids for the T-Matrix calculations. It was found that the theoretical model simulations differed markedly from experimental measurements of the light scattering, particularly near the mid-range and near backscattering angles. In many cases, in the near backward direction, theoretical models predicted scattering intensities for near spherical particles that were up to 3 times higher than the experimentally measured values. It was found that better agreement between simulations and experiments could be obtained for the visible scattering by using a much wider range of more eccentric particle shapes.

Author: Mgr. Břetislav Šopík Thesis advisor: doc. Pavel Lipavský, CSc. Ph.D. thesis Superconductivity in disordered systems Abstract We study some aspects of the superconductivity in disordered systems - namely the superconductivity in a boron-doped diamond. We also apply theoretical methods originally developed in the field of the disordered systems to the theory of superconductivity. In the case of the boron-doped diamond we focus on the question of the dependence of the critical temperature Tc on boron doping. We discuss the impact of the boron distribution correlations on the Tc as well. First, we evaluate the density of states at the Fermi energy N0 within the dynamical cluster approximation. We discuss the Tc as a function of N0 within the BCS, the McMillan and the Belitz theory. In the case of 100 samples, the simplified Belitz theory gives the best agreement with experimental data. For 111 samples the McMillan theory is sufficient. We also show that the difference of 100 and 111 samples in the N0 dependence of Tc can be explained as given by attractive correlations in the boron distribution. Applying the concept of the coherent potential approximation, we re- move a self-interaction from the Galitskii-Feynman T-matrix approxima- tion. This correction has no effect in the normal state but makes the...

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The importance of the T-matrix method is well-known when frequency domain scattering problems are of interest. With the relatively recent and wide-spread interest in time domain scattering problems, similar applications of the T-matrix method are expected to be useful in the time domain. In this thesis, the time domain spherical scalar wave functions are introduced, translational addition theorems for the time domain spherical scalar wave functions necessary for the solution of multiple scattering problems are given, and the formulation of time domain scattering of scalar waves by two spheres and by two scatterers of arbitrary shape is presented. The whole analysis is performed in the time domain requiring no inverse Fourier integrals to be evaluated. Scattering examples are studied in order to check the numerical accuracy, and demonstrate the utility of the expressions.

Nanometer-scale particles of the noble metals have been used for decades as contrast enhancement agents in electron microscopy. Over the past several years it has been demonstrated that these particles also function as excellent contrast agents for optical imaging techniques. The resonant optical scattering they exhibit enables scattering cross sections that may be many orders of magnitude greater than the analogous efficiency factor for fluorescent dye molecules. Biologically relevant labeling with nanoparticles generally results in aggregates containing a few to several tens of particles. The electrodynamic coupling between particles in these aggregates produces observable shifts in the resonance-scattering spectrum. This dissertation provides a theoretical analysis of the scattering from nanoparticle aggregates. The key objectives are to describe this scattering behavior qualitatively and to provide numerical codes usable for modeling its application to biomedical engineering. Considerations of the lowest-order dipole-dipole coupling lead to simple qualitative predictions of the behavior of the spectral properties of the optical cross sections as they depend on number of particles, inter-particle spacing, and aggregate aspect ratio. More comprehensive analysis using the multiple-particle T-matrix formalism allows the elaboration of more subtle cross-section spectral features depending on the interactions of the electrodynamic collective-modes of the aggregate, of individual-particle modes, and of modes associated with groups of particles within the aggregate sub-structure. In combination these analyses and the supporting numerical code-base provide a unified electrodynamic approach which facilitates interpretation of experimental cross section spectra, guides the design of new biophysical experiments using nanoparticle aggregates, and enables optimal fabrication of nanoparticle structures for biophysical applications. / text

(EN) Thesis deals with an approximation of static moduli in wells from dynamic moduli determined by acoustic well logging using T-matrix model. Proposed approach makes possible to determine moduli values, which are close to values of static moduli, which would be determined by loading tests. This approach is based on an idea, that an intact rock with sufficiently high compressional strength sc and sufficiently high value of static Young's modulus Es, manifests more or less linear elastic behaviour. In such case, the values of static and dynamic moduli are identical. This fact has been experimentally verified for rocks with values of sc and Es in order of higher tens of MPa and GPa respectively. In case of a rock damage presence in such rock, it's behaviour becomes nonlinearly elastic. The amount of nonlinearity is proportional to increasing amount of rock damage. This results in the difference between values of static and dynamic moduli. T-matrix model is used to quantify this difference. This model is based on an anisotropic rock matrix with ellipsoidal inclusions. These inclusions can affect each other. The result of this model calculation is a group of values of elastic constants, which we call effective moduli. These effective moduli include the effect of porosity in the rock as well and they...

In dieser Dissertation werden das Anregungsspektrum und das Phasendiagramm wechselwirkender Fermi- und Bosegase untersucht. Zu diesem Zweck wird eine neuartige renormierte Kadanoff-Martin-Näherung vorgestellt, die Selbstwechselwirkung von Teilchen vermeidet und somit eine einheitliche Beschreibung sowohl der normalen als auch der kondensierten Phase ermöglicht. Für Fermionen findet man den BCS-Zustand, benannt nach Bardeen, Cooper und Schrieffer, welcher entscheidend ist für das Phänomen der Supraleitung. Charakteristisch für diesen Zustand ist eine Energielücke im Anregungsspektrum an der Fermi-Energie. Weiterhin tritt für Bosonen eine Bose-Einstein-Kondensation (BEC) auf, bei der das Anregungsspektrum für kleine Impulse linear ist. Letzteres führt zum Phänomen der Suprafluidität. Über die bereits bekannten Phänomene hinaus findet man eine dem BCS-Zustand ähnliche Kondensation von Zweiteilchenbindungszuständen, sowohl für Fermionen als auch für Bosonen. Für Fermionen tritt ein Übergang zwischen der Kondensation von Bindungszuständen und dem BCS-Zustand auf, der sogenannte BEC-BCS-Übergang. Die Untersuchung der Zustandsgleichung zeigt, dass im Gegensatz zu Fermi-Gasen und Bose-Gasen mit abstoßender Wechselwirkung Bose-Gase mit anziehender Wechselwirkung zu einer Flüssigkeit kondensieren oder sich verfestigen, bevor es zur Kondensation von Bindungszuständen oder zur Bose-Einstein-Kondensation kommt. Daher können diese Phänomene voraussichtlich nicht in der Gasphase beobachtet werden. Zusammenfassend lässt sich sagen, dass das vorgestellte Näherungsverfahren sehr gut geeignet ist, die erwähnten Phänomene im Zusammenhang mit der Bose-Einstein-Kondensation zu beschreiben.

In dieser Dissertation werden das Anregungsspektrum und das Phasendiagramm wechselwirkender Fermi- und Bosegase untersucht. Zu diesem Zweck wird eine neuartige renormierte Kadanoff-Martin-Näherung vorgestellt, die Selbstwechselwirkung von Teilchen vermeidet und somit eine einheitliche Beschreibung sowohl der normalen als auch der kondensierten Phase ermöglicht. Für Fermionen findet man den BCS-Zustand, benannt nach Bardeen, Cooper und Schrieffer, welcher entscheidend ist für das Phänomen der Supraleitung. Charakteristisch für diesen Zustand ist eine Energielücke im Anregungsspektrum an der Fermi-Energie. Weiterhin tritt für Bosonen eine Bose-Einstein-Kondensation (BEC) auf, bei der das Anregungsspektrum für kleine Impulse linear ist. Letzteres führt zum Phänomen der Suprafluidität. Über die bereits bekannten Phänomene hinaus findet man eine dem BCS-Zustand ähnliche Kondensation von Zweiteilchenbindungszuständen, sowohl für Fermionen als auch für Bosonen. Für Fermionen tritt ein Übergang zwischen der Kondensation von Bindungszuständen und dem BCS-Zustand auf, der sogenannte BEC-BCS-Übergang. Die Untersuchung der Zustandsgleichung zeigt, dass im Gegensatz zu Fermi-Gasen und Bose-Gasen mit abstoßender Wechselwirkung Bose-Gase mit anziehender Wechselwirkung zu einer Flüssigkeit kondensieren oder sich verfestigen, bevor es zur Kondensation von Bindungszuständen oder zur Bose-Einstein-Kondensation kommt. Daher können diese Phänomene voraussichtlich nicht in der Gasphase beobachtet werden. Zusammenfassend lässt sich sagen, dass das vorgestellte Näherungsverfahren sehr gut geeignet ist, die erwähnten Phänomene im Zusammenhang mit der Bose-Einstein-Kondensation zu beschreiben.

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<br>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<br>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.<br>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<br>hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the<br>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. <br>