Properties of heavy quarkonia and B_c mesons in the relativistic quark model

The mass spectra and electromagnetic decay rates of charmonium, bottomonium and B_c mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order v^2/c^2, including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole (M1) and electric dipole (E1) transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for B_c masses and decays are compared with other quark model predictions.Comment: 31 pages, 2 figures, minor correction

Projective bundles and blow-ups of Projective spaces

The aim of this note is to investigate the relation between two types of non-singular projective varieties of Picard rank 2, namely the Projective bundles over Projective spaces and certain Blow-up of Projective spaces.Comment: Comments are welcom

Relativistic Description of Exclusive Semileptonic Decays of Heavy Mesons

Using quasipotential approach, we have studied exclusive semileptonic decays of heavy mesons with the account of relativistic effects. Due to more complete relativistic description of the $s$ quark more precise expressions for semileptonic form factors are obtained. Various differential distributions in exclusive semileptonic decays of heavy mesons are calculated. It is argued that consistent account of relativistic effects and HQET motivated choice of the parameters of quark-antiquark potential allow to get reliable value for the ratio $A_2(0)/A_1(0)$ in the $D\to K^*l\nu_l$ decay as well as the ratio~$\Gamma(D\to K^*l\nu_l)/\Gamma(D\to Kl\nu_l)$. All calculated branching ratios are in accord with available experimental data.Comment: 18 pages, LATEX, 2 figures inclosed + 4 Postscript figure

Effect of the sample geometry on the second magnetization peak in single crystalline Ba0.63_{0.63}K0.37_{0.37}BiO3_3 thick film

Magnetization hysteresis loop $M(H)$ measurements performed on a single crystalline Ba$_{0.63}$K$_{0.37}$BiO$_3$ superconducting thick film reveal pronounced sample geometry dependence of the "second magnetization peak" (SMP), i.e. a maximum in the width of $M(H)$ occurring at the field $H_{\rm SMP}(T)$. In particular, it is found that the SMP vanishes decreasing the film dimension. We argue that the observed sample geometry dependence of the SMP cannot be accounted for by models which assume a vortex pinning enhancement as the origin of the SMP. Our results can be understood considering the thermomagnetic instability effect and/or non-uniform current distribution at $H < H_{\rm SMP}$ in large enough samples.Comment: 8 pages 3 figure

Core-Core Dynamics in Spin Vortex Pairs

We investigate magnetic nano-pillars, in which two thin ferromagnetic nanoparticles are separated by a nanometer thin nonmagnetic spacer and can be set into stable spin vortex-pair configurations. The 16 ground states of the vortex-pair system are characterized by parallel or antiparallel chirality and parallel or antiparallel core-core alignment. We detect and differentiate these individual vortex-pair states experimentally and analyze their dynamics analytically and numerically. Of particular interest is the limit of strong core-core coupling, which we find can dominate the spin dynamics in the system. We observe that the 0.2 GHz gyrational resonance modes of the individual vortices are replaced with 2-6 GHz range collective rotational and vibrational core-core resonances in the configurations where the cores form a bound pair. These results demonstrate new opportunities in producing and manipulating spin states on the nanoscale and may prove useful for new types of ultra-dense storage devices where the information is stored as multiple vortex-core configurations

Algebraic approach to the spectral problem for the Schroedinger equation with power potentials

The method reducing the solution of the Schroedinger equation for several types of power potentials to the solution of the eigenvalue problem for the infinite system of algebraic equations is developed. The finite truncation of this system provides high accuracy results for low-lying levels. The proposed approach is appropriate both for analytic calculations and for numerical computations. This method allows also to determine the spectrum of the Schroedinger-like relativistic equations. The heavy quarkonium (charmonium and bottomonium) mass spectra for the Cornell potential and the sum of the Coulomb and oscillator potentials are calculated. The results are in good agreement with experimental data.Comment: 17 pages, including 6 PostScript figures (epsf style

Quantum Periods For Certain Four-Dimensional Fano Manifolds

We collect a list of known four-dimensional Fano manifolds and compute their quantum periods. This list includes all four-dimensional Fano manifolds of index greater than one, all four-dimensional toric Fano manifolds, all four-dimensional products of lower-dimensional Fano manifolds, and certain complete intersections in projective bundles

Capabilities of macroscopic forming simulation for large-scale forming processes of dry and impregnated textiles

Forming of continuously fibre-reinforced polymers (CoFRP) has a significant impact on the structural performance of composite components, underlining the importance of forming simulation for CoFRP product development processes. For an integrated development of industrial composite components, efficient forming simulation methods are in high demand. Application-oriented method development is particularly crucial for industrial needs, where large and complex multi-layer components are manufactured, commercial FE software is used, and yet high prediction accuracy is required. To meet industrial demands, this contribution gives an insight in macroscopic forming simulation approaches that utilize the FE software Abaqus in combination with user-defined material models and finite elements. Three CoFRP forming technologies are considered, which are in industrial focus due to their suitability for mass production: textile forming of dry unidirectional non-crimp fabrics (UD-NCF), thermoforming of pre-impregnated UD tapes and wet compression moulding (WCM). In addition to the highly anisotropic, large-strain material behaviour that composite forming processes have in common, the three process technologies face various process-specific modelling challenges. UD-NCFs require material models that capture the deformation behaviour and the slippage of the stitching. Thermoforming of UD tapes is highly rate- and temperature-dependent, calling for rheological membrane and bending modelling. Moreover, a thermomechanical approach including crystallisation kinetics enables the prediction of potential phase-transition during forming and resulting defects in the semi-crystalline thermoplastic matrix. For simultaneous forming and infiltration in wet compression moulding, a finite Darcy-Progression-Element is superimposed with the membrane and shell elements for forming simulation, capturing infiltration-dependent material properties. The three outlined technologies illustrate the complexity and importance of further simulation method development to support future process development

Relativistic description of the charmonium mass spectrum

The charmonium mass spectrum is considered in the framework of the constituent quark model with the relativistic treatment of the c quark. The obtained masses are in good agreement with the existing experimental data including the mass of eta_c(2S).Comment: 5 page