Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.Comment: 22 pages, 3 figure

Structures and waves in a nonlinear heat-conducting medium

The paper is an overview of the main contributions of a Bulgarian team of researchers to the problem of finding the possible structures and waves in the open nonlinear heat conducting medium, described by a reaction-diffusion equation. Being posed and actively worked out by the Russian school of A. A. Samarskii and S.P. Kurdyumov since the seventies of the last century, this problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer Proceedings in Mathematics and Statistics, Numerical Methods for PDEs: Theory, Algorithms and their Application

Hadrons with Charm and Beauty

By combining potential models and QCD spectral sum rules (QSSR), we discuss the spectroscopy of the $(b\bar c)$ mesons and of the $(bcq)$, $(ccq)$ and $(bbq)$ baryons (${q}\equiv {d}$ or $s$), the decay constant and the (semi)leptonic decay modes of the $B_c$ meson. For the masses, the best predictions come from potential models and read: $M_{B_c} = (6255 \pm 20)$~MeV, $M_{B^*_c} = (6330 \pm 20)$~MeV, $M_{\Lambda(bcu)} = (6.93\pm 0.05)$~GeV, $M_{\Omega(bcs)} = (7.00\pm 0.05)$~GeV, $M_{\Xi^*(ccu)} =(3.63\pm 0.05)$~GeV and $M_{\Xi^*(bbu)} = (10.21\pm 0.05)$~GeV. The decay constant $f_{B_c} = (2.94 \pm 0.21) f_\pi$ is well determined from QSSR and leads to: $\Gamma(B_c \rightarrow \nu_\tau \tau) = (3.0 \pm 0.4)( V_{cb}/0.037 )^2$ $\times 10^{10}$ s$^{-1}$.The uses of the vertex sum rules for the semileptonic decays of the $B_c$ show that the $t$-dependence of the form factors is much stronger than predicted by vector meson dominance. It also predicts the almost equal strength of about 0.30 $\times 10^{10}$ sec$^{-1}$ for the semileptonic rates $B_c$ into $B_s, B^*_s,\eta_c$ and J/$\psi$. Besides these phenomenological results, we also show explicitly how the Wilson coefficients of the $\langle\alpha_s G^2\rangle$ and $\langle G^3\rangle$ gluon condensates already contain the full heavy quark- ($\langle\bar QQ\rangle$) and mixed- ($\langle\bar QGQ\rangle$) condensate contributions in the OPE.}Comment: 32 pages, LaTeX, no changes in the 1994 paper, latex errors corrected in 201

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

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2, 6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405) who find no evidence for a correlation between the power of ballistic jets and black hole spi

Search for Heavy Neutral and Charged Leptons in e+ e- Annihilation at LEP

A search for exotic unstable neutral and charged heavy leptons as well as for stable charged heavy leptons is performed with the L3 detector at LEP. Sequential, vector and mirror natures of heavy leptons are considered. No evidence for their existence is found and lower limits on their masses are set

Production of singlet P-wave ccˉc \bar c and bbˉb \bar b states

No spin-singlet $b \bar b$ quarkonium state has yet been observed. In this paper we discuss the production of the singlet P-wave $b\bar{b}$ and $c\bar{c}$ $^1P_1$ states $h_b$ and $h_c$. We consider two possibilities. In the first the $^1P_1$ states are produced via the electromagnetic cascades \ups(3S) \to \eta_b(2S) + \gamma \to h_b + \gamma \gamma \to \eta_b +\gamma\gamma\gamma and $\psi'\to \eta_c' + \gamma \to h_c + \gamma \gamma \to \eta_c + \gamma\gamma\gamma$. A more promising process consists of single pion transition to the $^1P_1$ state followed by the radiative transition to the $1^1S_0$ state: \ups(3S)\to h_b + \pi^0 \to \eta_b + \pi^0 +\gamma and $\psi' \to h_c + \pi^0 \to \eta_c + \pi^0 +\gamma$. For a million \ups(3S) or $\psi'$'s produced we expect these processes to produce several hundred events.Comment: 13 pages, LaTeX, 1 figure, to be published Phys. Rev. D. Some equation numbers and one table number correcte

Metal complex of the Bronze Age from an Alakul burial ground (typology and manufacturing techniques)

The article deals with metal artifacts from an Alakul burial ground, which is considered to be one of the largest and brightest monuments of the Alakul culture in the Trans-Urals. There is a description of morphological and typological characteristics of the metal complex which determined the main types of objects, a circle of cultural analogies, and also artifacts which aren't found among materials of other monuments. The main raw materials for production of artifacts were tin bronze (71,6 %). Concentration of tin in jewelry markers of the Alakul culture (cross-shaped pendants) could reach 25–30 %. The obtained data reflect the extent of expansion of use of tin alloy with simultaneous reduction of number of products made of pure copper by the Alakul populations, in comparison with the previous Petrovka culture. This process was promoted by the established relations with sources of metal raw materials and, in particular, of tin alloy arriving in the form of small rectangular bars with concentration of tin of 2–5 %, possibly from centers of production of metal in Central Kazakhstan and the Altai. The metallographic analysis revealed 8 technological schemes applied to produce an inventory complex and jewelry with a prevalence of high-temperature modes. The fact that masters of the Alakul burial ground chose from such big variety of technological schemes calls attention, because they adopted traditional methods of Petrovka metal working. However, the increase in share of forge technologies of molding in combination with forging hot metal processing at temperatures of full red heat, increase in application of preliminary homogenization annealing, which is necessary when working with high tin bronze, were, undoubtedly, a progressive phenomenon. The received data characterize the studied metal complex as traditional for the entire Alakul culture of the Tobol river basin, on the one hand, and as original and unique, on the other hand