Heavy-light mesons on a lattice

Several excited states of Ds and Bs mesons have been discovered in the last six years: BaBar, Cleo and Belle discovered the very narrow states D(s0)*(2317)+- and D(s1)(2460)+- in 2003, and CDF and DO Collaborations reported the observation of two narrow Bs resonances, B(s1)(5830)0 and B*(s2)(5840)0 in 2007. To keep up with experiment, meson excited states should be studied from the theoretical aspect as well. The theory that describes the interaction between quarks and gluons is quantum chromodynamics (QCD). In this thesis the properties of the meson states are studied using the discretized version of the theory - lattice QCD. This allows us to perform QCD calculations from first principles, and "measure" not just energies but also the radial distributions of the states on the lattice. This gives valuable theoretical information on the excited states, as we can extract the energy spectrum of a static-light meson up to D wave states (states with orbital angular momentum L=2). We are thus able to predict where some of the excited meson states should lie. We also pay special attention to the order of the states, to detect possible inverted spin multiplets in the meson spectrum, as predicted by H. Schnitzer in 1978. This inversion is connected to the confining potential of the strong interaction. The lattice simulations can also help us understand the strong interaction better, as the lattice data can be treated as "experimental" data and used in testing potential models. In this thesis an attempt is made to explain the energies and radial distributions in terms of a potential model based on a one-body Dirac equation. The aim is to get more information about the nature of the confining potential, as well as to test how well the one-gluon exchange potential explains the short range part of the interaction.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

Kivaa ja hyödyllistä, mutta jo se riittää : Yläasteen kielikylpyoppilaiden käsityksiä ruotsinkielisestä kielikylpyopetuksesta Helsingissä

The aim of this study was to find out how immersion students experience immersion education, how they feel about the implementation of immersion education methods and what role immersion plays in immersion students’ lives outside the school context. In addition, the influence of sex, grade level, school and type of immersion education on students’ perceptions was studied. The population included all students at the lower secondary level in Helsinki who participated in Swedish immersion education during 2002–2003. The sample consisted of 128 students who represented two different forms of immersion: 47% of the students had previously participated in early total immersion while 53 % of the students had taken part in early partial immersion. The data were gathered through a questionnaire and interviews. All 128 students answered the questionnaire, and 10 students were chosen to focus interviews through purposive sampling. In addition, students’ parents were invited to fill in a questionnaire where students’ background information was requested. The data were collected during the spring of 2003. Principal Component Analysis and one-way variance analysis were used as statistical analysis methods. Also frequencies, average, correlations and cross tabs were studied. In the PCA a right-angled varimax-rotation was performed separately to every thematic entity that arose from the theoretical background. Sum variables were formed from the Principal Components by summing up all the items that received over .400 charges for the specific Principal Component. Significance testing of the mean was performed with F and t-tests. Results indicate that immersion students in lower secondary school experience immersion quite diversely as a whole. Students are satisfied with the fact that they are in the immersion class but not with the amount of teaching in Swedish. Students feel it is very important and useful to learn Swedish bearing in mind their future studies and working life. The students estimate their language skills to be very high. Yet they prefer using Finnish during classes. The fact that teachers use Swedish does not considerably affect how well the students learn the factual content in various subjects, especially if the student knows Swedish well. Theoretical subjects seemed to cause most problems. Swedish played only a very small part in students’ lives outside the school context and it was used merely when travelling abroad and in different kinds of guiding situations. Unless the students were talked to in Swedish, they kept on speaking Finnish. When asked about students’ experiences no statistically significant differences between sexes were found in this study. On the contrary, in some cases their grade level but especially their school and form of immersion had clear statistically significant differences on students’ perceptions.

On the functional ordering of biomembranes : Implications for drug binding

Cells are packed with membrane structures, defining the inside and outside, and the different subcellular compartments. These membranes consisting mainly of phospholipids have a variety of functions in addition to providing a permeability barrier for various compounds. These functions involve cellular signaling, where lipids can act as second messengers, or direct regulation of membrane associating proteins. The first part of this study focuses on relating some of the physicochemical properties of membrane lipids to the association of drug compounds to membranes. A fluorescence based method is described allowing for determination of the membrane association of drugs. This method was subsequently applied to a novel drug, siramesine, previously shown to have anti-cancer activity. Siramesine was found to associate with anionic lipids. Especially interesting is its strong affinity for a second messenger lipid phosphatidic acid. This is the first example of a small molecule drug compound specifically interacting with a cellular lipid. Phosphatidic acid in cells is required for the activation of many signaling pathways mediating growth and proliferation. This provides an intriguing possibility for a simple molecular mechanism of the observed anti-cancer activity of siramesine. In the second part the thermal behavior and self assembly of charged and uncharged membrane assemblies was studied. Strong inter-lamellar co-operativity was observed for multilamellar DPPC vesicles using fluorescence techniques together with calorimetry. The commonly used membrane models, large unilamellar vesicles (LUV) and multilamellar vesicles (MLV) were found to possess different biophysical properties as interlamellar interactions of MLVs drive segregation of a pyrene labeled lipid analogue into clusters. The effect of a counter-ion lattice on the self assembly of a cationic gemini surfactant was studied. The presence of NaCl strongly influenced the thermal phase behavior of M-1 vesicles, causing formation of giant vesicles upon exceeding a phase transition temperature, followed by a subsequent transition into a more homogenous dispersion. Understanding the underlying biophysical aspects of cellular membranes is of fundamental importance as the complex picture of the structure and function of cells is evolving. Many of the cellular reactions take place on membranes and membranes are known to regulate the activity of many peripheral and intergral membrane associating proteins. From the point of view of drug design and gene technology, membranes can provide an interesting target for future development of drugs, but also a vehicle sensitive for environmental changes allowing for encapsulating drugs and targeting them to the desired site of action.

Properties of Ammonium Nitrate based fertilisers

The text is divided into three parts; Properties, Application and Safety of Ammonium Nitrate (AN) based fertilisers. In Properties, the structures and phase transitions of ammonium and potassium nitrate are reviewed. The consequences of phase transitions affect the proper use of fertilisers. Therefore the products must be stabilised against the volume changes and consequent loss of bulk density and hardness, formation of dust and finally caking of fertilisers. The effect of different stabilisers is discussed. Magnesium nitrate, ammonium sulphate and potassium nitrate are presented as a good compromise. In the Application part, the solid solutions in the systems (K+,NH4+)NO3- and (NH4+,K+)(Cl-,NO3-) are presented based on studies made with DSC and XRD. As there are clear limits for solute content in the solvent lattice, a number of disproportionation transitions exist in these process phases, e.g., N3 (solid solution isomorphous to NH4NO3-III) disproportionates to phases K3 (solid solution isomorphous to KNO3-III) and K2 (solid solution isomorphous to KNO3-II). In the crystallisation experiments, the formation of K3 depends upon temperature and the ratio K/(K+NH4). The formation of phases K3, N3, and K2 was modelled as a function of temperature and the mole ratios. In introducing chlorides, two distinct maxima for K3 were found. Confirmed with commercial potash samples, the variables affecting the reaction of potassium chloride with AN are the particle size, time, temperature, moisture content and amount of organic coating. The phase diagrams obtained by crystallisation studies were compared with a number of commercial fertilisers and, with regard to phase composition, the temperature and moisture content are critical when the formation and stability of solid solutions are considered. The temperature where the AN-based fertiliser is solidified affects the amount of compounds crystallised at that point. In addition, the temperature where the final moisture is evaporated affects the amount and type of solid solution formed at this temperature. The amount of remaining moisture affects the stability of the K3 phase. The K3 phase is dissolved by the moisture and recrystallised into the quantities of K3, which is stable at the temperature where the sample is kept. The remaining moisture should not be free; it should be bound as water in the final product. The temperatures during storage also affect the quantity of K3 phase. As presented in the figures, K3 phase is not stable at temperatu¬res below 30 °C. If the temperature is about 40 °C, the K3 phase can be formed due to the remaining moisture. In the Safety part, self-sustaining decomposition (SSD), oxidising and energetic properties of fertilisers are discussed. Based on the consequence analysis of SSD, early detection of decomposition in warehouses and proper temperature control in the manufacturing process is important. SSD and oxidising properties were found in compositions where K3 exists. It is assumed that potassium nitrate forms a solid matrix in which AN can decompose. The oxidising properties can be affected by the form of the product. Granular products are inherently less oxidising. Finally energetic properties are reviewed. The composition of the fertiliser has an importance based on theoretical calculations supported by experimental studies. Materials such as carbonates and sulphates act as diluents. An excess of ammonium ions acts as a fuel although this is debatable. Based on the experimental work, the physical properties have a major importance over the composition. A high bulk density is of key importance for detonation resistance.

Boundedness of weakly singular integral operators on domains

The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.