Spinor Bose-Einstein Condensates and Topological Defects

This thesis concentrates on the topological defects of spin-1 and spin-2 Bose-Einstein condensates, the ground states of spin-3 condensates, and the inert states of spinor condensates with arbitrary spin. Our work is based on the description of a spinor condensate of spin-S atoms in terms of a state vector of a spin-S particle. The results of the homotopy theory are used to study the existence and structure of the topological defects in spinor condensates. We construct examples of defects, study their energetics, and examine how their stability is affected by the presence of an external magnetic field. The ground states of spin-3 condensates are calculated using analytical and numerical means. Special emphasis is put on the ground states of a chromium condensate, whose dependence on the magnetic dipole-dipole interaction is studied. A simple geometrical method for the calculation of inert states of spinor condensates is presented. This method is used to find candidates for the ground states of spin-S condensates.

Measuring irregularities and surface defects from printed patterns

Quality inspection and assurance is a veryimportant step when today's products are sold to markets. As products are produced in vast quantities, the interest to automate quality inspection tasks has increased correspondingly. Quality inspection tasks usuallyrequire the detection of deficiencies, defined as irregularities in this thesis. Objects containing regular patterns appear quite frequently on certain industries and science, e.g. half-tone raster patterns in the printing industry, crystal lattice structures in solid state physics and solder joints and components in the electronics industry. In this thesis, the problem of regular patterns and irregularities is described in analytical form and three different detection methods are proposed. All the methods are based on characteristics of Fourier transform to represent regular information compactly. Fourier transform enables the separation of regular and irregular parts of an image but the three methods presented are shown to differ in generality and computational complexity. Need to detect fine and sparse details is common in quality inspection tasks, e.g., locating smallfractures in components in the electronics industry or detecting tearing from paper samples in the printing industry. In this thesis, a general definition of such details is given by defining sufficient statistical properties in the histogram domain. The analytical definition allowsa quantitative comparison of methods designed for detail detection. Based on the definition, the utilisation of existing thresholding methodsis shown to be well motivated. Comparison of thresholding methods shows that minimum error thresholding outperforms other standard methods. The results are successfully applied to a paper printability and runnability inspection setup. Missing dots from a repeating raster pattern are detected from Heliotest strips and small surface defects from IGT picking papers.

Surface Studies of Thiolate Adsorbates on Some Metals

The results and discussions in this thesis are based on my studies about selfassembled thiol layers on gold, platinum, silver and copper surfaces. These kinds of layers are two-dimensional, one molecule thick and covalently organized at the surface. They are an easy way to modify surface properties. Self-assembly is today an intensive research field because of the promise it holds for producing new technology at nanoscale, the scale of atoms and molecules. These kinds of films have applications for example, in the fields of physics, biology, engineering, chemistry and computer science. Compared to the extensive literature concerning self-assembled monolayers (SAMs) on gold, little is known about the structure and properties of thiolbased SAMs on other metals. In this thesis I have focused on thiol layers on gold, platinum, silver and copper substrates. These studies can be regarded as a basic study of SAMs. Nevertheless, an understanding of the physical and chemical nature of SAMs allows the correlation between atomic structure and macroscopic properties. The results can be used as a starting point for many practical applications. X-ray photoelectron spectroscopy (XPS) and synchrotron radiation excited high resolution photoelectron spectroscopy (HR-XPS) together with time-offlight secondary ion mass spectrometry (ToF-SIMS) were applied to investigate thin organic films formed by the spontaneous adsorption of molecules on metal surfaces. Photoelectron spectroscopy was the main method used in these studies. In photoelectron spectroscopy, the sample is irradiated with photons and emitted photoelectrons are energy-analyzed. The obtained spectra give information about the atomic composition of the surface and about the chemical state of the detected elements. It is widely used in the study of thin layers and is a very powerful tool for this purpose. Some XPS results were complemented with ToF-SIMS measurements. It provides information on the chemical composition and molecular structure of the samples. Thiol (1-Dodecanethiol, CH3(CH2)11SH) solution was used to create SAMs on metal substrates. Uniform layers were formed on most of the studied metal surfaces. On platinum, surface aligned molecules were also detected in investigations by XPS and ToF-SIMS. The influence of radiation on the layer structure was studied, leading to the conclusion that parts of the hydrocarbon chains break off due to radiation and the rest of the layer is deformed. The results obtained showed differences depending on the substrate material. The influence of oxygen on layer formation was also studied. Thiol molecules were found to replace some of the oxygen from the metal surfaces.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

Solid-state reference and ion-selective electrodes : towards portable potentiometric sensing

Potentiometric sensors are very attractive tools for chemical analysis because of their simplicity, low power consumption and low cost. They are extensively used in clinical diagnostics and in environmental monitoring. Modern applications of both fields require improvements in the conventional construction and in the performance of the potentiometric sensors, as the trends are towards portable, on-site diagnostics and autonomous sensing in remote locations. The aim of this PhD work was to improve some of the sensor properties that currently hamper the implementation of the potentiometric sensors in modern applications. The first part of the work was concentrated on the development of a solid-state reference electrode (RE) compatible with already existing solid-contact ion-selective electrodes (ISE), both of which are needed for all-solid-state potentiometric sensing systems. A poly(vinyl chloride) membrane doped with a moderately lipophilic salt, tetrabutylammonium-tetrabutylborate (TBA-TBB), was found to show a satisfactory stability of potential in sample solutions with different concentrations. Its response time was nevertheless slow, as it required several minutes to reach the equilibrium. The TBA-TBB membrane RE worked well together with solid-state ISEs in several different situations and on different substrates enabling a miniature design. Solid contacts (SC) that mediate the ion-to-electron transduction are crucial components of well-functioning potentiometric sensors. This transduction process converting the ionic conduction of an ion-selective membrane to the electronic conduction in the circuit was studied with the help of electrochemical impedance spectroscopy (EIS). The solid contacts studied were (i) the conducting polymer (CP) poly(3,4-ethylienedioxythiophene) (PEDOT) and (ii) a carbon cloth having a high surface area. The PEDOT films were doped with a large immobile anion poly(styrene sulfonate) (PSS-) or with a small mobile anion Cl-. As could be expected, the studied PEDOT solid-contact mediated the ion-toelectron transduction more efficiently than the bare glassy carbon substrate, onto which they were electropolymerized, while the impedance of the PEDOT films depended on the mobility of the doping ion and on the ions in the electrolyte. The carbon cloth was found to be an even more effective ion-to-electron transducer than the PEDOT films and it also proved to work as a combined electrical conductor and solid contact when covered with an ion-selective membrane or with a TBA-TBB-based reference membrane. The last part of the work was focused on improving the reproducibility and the potential stability of the SC-ISEs, a problem that culminates to the stability of the standard potential E°. It was proven that the E° of a SC-ISE with a conducting polymer as a solid contact could be adjusted by reducing or oxidizing the CP solid contact by applying current pulses or a potential to it, as the redox state of the CP solid-contact influences the overall potential of the ISE. The slope and thus the analytical performance of the SC-ISEs were retained despite the adjustment of the E°. The shortcircuiting of the SC-ISE with a conventional large-capacitance RE was found to be a feasible instrument-free method to control the E°. With this method, the driving force for the oxidation/reduction of the CP was the potential difference between the RE and the SC-ISE, and the position of the adjusted potential could be controlled by choosing a suitable concentration for the short-circuiting electrolyte. The piece-to-piece reproducibility of the adjusted potential was promising, and the day-today reproducibility for a specific sensor was excellent. The instrumentfree approach to control the E° is very attractive considering practical applications.