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.

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.

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.

Dimensional Reduction Near the Deconfinement Transition

When ordinary nuclear matter is heated to a high temperature of ~ 10^12 K, it undergoes a deconfinement transition to a new phase, strongly interacting quark-gluon plasma. While the color charged fundamental constituents of the nuclei, the quarks and gluons, are at low temperatures permanently confined inside color neutral hadrons, in the plasma the color degrees of freedom become dominant over nuclear, rather than merely nucleonic, volumes. Quantum Chromodynamics (QCD) is the accepted theory of the strong interactions, and confines quarks and gluons inside hadrons. The theory was formulated in early seventies, but deriving first principles predictions from it still remains a challenge, and novel methods of studying it are needed. One such method is dimensional reduction, in which the high temperature dynamics of static observables of the full four-dimensional theory are described using a simpler three-dimensional effective theory, having only the static modes of the various fields as its degrees of freedom. A perturbatively constructed effective theory is known to provide a good description of the plasma at high temperatures, where asymptotic freedom makes the gauge coupling small. In addition to this, numerical lattice simulations have, however, shown that the perturbatively constructed theory gives a surprisingly good description of the plasma all the way down to temperatures a few times the transition temperature. Near the critical temperature, the effective theory, however, ceases to give a valid description of the physics, since it fails to respect the approximate center symmetry of the full theory. The symmetry plays a key role in the dynamics near the phase transition, and thus one expects that the regime of validity of the dimensionally reduced theories can be significantly extended towards the deconfinement transition by incorporating the center symmetry in them. In the introductory part of the thesis, the status of dimensionally reduced effective theories of high temperature QCD is reviewed, placing emphasis on the phase structure of the theories. In the first research paper included in the thesis, the non-perturbative input required in computing the g^6 term in the weak coupling expansion of the pressure of QCD is computed in the effective theory framework at an arbitrary number of colors. The two last papers on the other hand focus on the construction of the center-symmetric effective theories, and subsequently the first non-perturbative studies of these theories are presented. Non-perturbative lattice simulations of a center-symmetric effective theory for SU(2) Yang-Mills theory show --- in sharp contrast to the perturbative setup --- that the effective theory accommodates a phase transition in the correct universality class of the full theory. This transition is seen to take place at a value of the effective theory coupling constant that is consistent with the full theory coupling at the critical temperature.

Simulations of dimensionally reduced effective theories of high temperature QCD

Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by performing lattice simulations in EQCD. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The finite chemical potential results are optained using analytic continuation. The diagonal susceptibility approaches the perturbative result above 20T_c$, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c.

On cluster approximations of cellular automata

In this thesis I examine one commonly used class of methods for the analytic approximation of cellular automata, the so-called local cluster approximations. This class subsumes the well known mean-field and pair approximations, as well as higher order generalizations of these. While a straightforward method known as Bayesian extension exists for constructing cluster approximations of arbitrary order on one-dimensional lattices (and certain other cases), for higher-dimensional systems the construction of approximations beyond the pair level becomes more complicated due to the presence of loops. In this thesis I describe the one-dimensional construction as well as a number of approximations suggested for higher-dimensional lattices, comparing them against a number of consistency criteria that such approximations could be expected to satisfy. I also outline a general variational principle for constructing consistent cluster approximations of arbitrary order with minimal bias, and show that the one-dimensional construction indeed satisfies this principle. Finally, I apply this variational principle to derive a novel consistent expression for symmetric three cell cluster frequencies as estimated from pair frequencies, and use this expression to construct a quantitatively improved pair approximation of the well-known lattice contact process on a hexagonal lattice.

Polymeereillä stabiloitu amorfinen formulaatio

Nowadays growing number of new active pharmaceutical ingredients (API) have large molecular weight and are hydrophobic. The energy of their crystal lattice is bigger and polarity has decreased. This leads to weakened solubility and dissolution rate of the drug. These properties can be enhanced for example by amorphization. Amorphous form has the best dissolution rate in the solid state. In the amorphous form drug molecules are randomly arranged, so the energy required to dissolve molecules is lower compared to the crystalline counterpart. The disadvantage of amorphous form is that it is unstable. Amorphous form tends to crystallize. Stability of amorphous form can be enhanced by adding an adjuvant to drug product. Adjuvant is usually a polymer. Polymers prevent crystallization both by forming bonds with API molecules and by steric hindrance. The key thing in stabilizing amorphous form is good miscibility between API and polymer. They have to be mixed in a molecular level so that the polymer is able to prevent crystallization. The aim of this work was to study miscibility of drug and polymer and stability of their dispersion with different analytical methods. Amorphous dispersions were made by rotary evaporator and freeze dryer. Amorphicity was confirmed with X-ray powder diffraction (XRPD) right after preparation. Itraconazole and theophylline were the chosen molecules to be stabilized. Itraconazole was expected to be easier and theophylline more difficult to stabilize. Itraconazole was stabilized with HPMC and theophylline was stabilized with PVP. Miscibility was studied with XRPD and differential scanning calorimetry (DSC). In addition it was studied with polarized light microscope if miscibility was possible to see visually. Dispersions were kept in stressed conditions and the crystallization was analyzed with XRPD. Stability was also examined with isothermal microcalorimetry (IMC). The dispersion of itraconazole and theophylline 40/60 (w/w) was completely miscible. It was proved by linear combination of XRPD results and single glass transition temperature in DSC. Homogenic well mixed film was observed with light microscope. Phase separation was observed with other compositions. Dispersions of theophylline and PVP mixed only partly. Stability of itraconazole dispersions were better than theophylline dispersions which were mixed poorer. So miscibility was important thing considering stability. The results from isothermal microcalorimetry were similar to results from conventional stability studies. Complementary analytical methods should be used when studying miscibility so that the results are more reliable. Light microscope is one method in addition to mostly used XRPD and DSC. Analyzing light microscope photos is quite subjective but it gives an idea of miscibility. Isothermal microcalorimetry can be one option for conventional stability studies. If right conditions can be made where the crystallization is not too fast, it may be possible to predict stability with isothermal microcalorimetry.