Homogenization for advection-diffusion in a perforated domain

The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor–Green velocity field

Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin

We obtain analytic expressions for the third-order corrections due to the strong interaction Coulomb potential to the S-wave Green function, energy levels and wave functions at the origin for arbitrary principal quantum number n. Together with the known non-Coulomb correction this results in the complete spectrum of S-states up to order alpha_s^5. The numerical impact of these corrections on the Upsilon spectrum and the top quark pair production cross section near threshold is estimated.Comment: 24 pages, LaTeX, v2: eq.(30) corrected (-13/8->-15/8

Improved Perturbative QCD Approach to the Bottomonium Spectrum

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the S-P splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the S-P splittings are larger than those of the boundstates themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale mu of the operator \propto C_A/(m_b r^2). The agreement of the whole spectrum with the experimental data is much better than the previous predictions when mu \simeq 3-4 GeV for alpha_S(M_Z)=0.1181. There seems to be a phenomenological preference for some suppression mechanism for the above operator.Comment: 26 pages, 16 figures. Minor changes, to be published in PR

Ultrasoft Renormalization in Non-Relativistic QCD

For Non-Relativistic QCD the velocity renormalization group correlates the renormalization scales for ultrasoft, potential and soft degrees of freedom. Here we discuss the renormalization of operators by ultrasoft gluons. We show that renormalization of soft vertices can induce new operators, and also present a procedure for correctly subtracting divergences in mixed potential-ultrasoft graphs. Our results affect the running of the spin-independent potentials in QCD. The change for the NNLL t-tbar cross section near threshold is very small, being at the 1% level and essentially independent of the energy. We also discuss implications for analyzing situations where mv^2 ~ Lambda_QCD.Comment: 31 pages, 11 fig

Comparative performance study of alternate fault-tolerant inverter configurations for direct torque control-based three-phase PM BLAC drives under single-phase open-circuit fault

This paper presents a comparative performance study of three typical fault-tolerant control (FTC) topologies [split-capacitor (SC), extra-leg split-capacitor (ELSC), and extra-leg extraswitch (ELES)] for direct torque control (DTC)-based threephase permanent magnet (PM) brushless AC (BLAC) drives under single-phase open-circuit fault (SOF). The advantages and limitations of these FTC schemes are theoretically compared and empirically validated. To achieve reliable postfault operations, control issues associated with VM-based flux estimators employed for DTC-based BLAC drives under SOF are demonstrated and relevant remedies are proposed. It is shown that although the ELES scheme can maintain the normal based speed, 6 of its 8 switching states cause phaseto-neutral short circuit in one or both two remaining phase windings resulting in high current harmonic values. Besides, during its implementation, the full DC-link voltage value is always applied to the non-short circuit phase windings leading to high possibility of winding insulation damage. Thus, for a compromise of the normal based speed by a factor of 3/2 , the ELSC drive should be used to avoid these issues. Furthermore, in the low-speed region up to half of the rated speed, the lowest copper loss, current harmonics, and torque ripples can be obtained by utilizing the SC drive

Massive Quark Production in Electron Positron Annihilation to Order αs2\alpha_s^2

Recent analytical and numerical results for the three-loop polarization function allow to present a phenomenological analysis of the cross section for massive quark production in electron positron annihilation to order $\alpha_s^2$. Numerical predictions based on fixed order perturbation theory are presented for charm and bottom production above 5 and 11.5 GeV, respectively. The contribution from these energy regions to $\alpha(M_Z^2)$, the running QED coupling constant at scale M_Z, are given. The dominant terms close to threshold, i.e. in an expansion for small quark velocity $\beta$, are presented.Comment: 26 pages (Latex), 16 figures (Postscript

Top quark pair production and decay at linear colliders: signal vs. off resonance background

Standard Model predictions for the reactions with six fermions in the final state relevant for top quark pair production and decay at linear colliders are discussed. An issue of the double resonance signal versus non doubly resonant background is addresed. Effects related to the off-mass-shell production of the t\bar{t}-pair are discussed.Comment: 9 pages, talk presented by K. Kolodziej at 6th International Symposium on Radiative Corrections RADCOR 2002 and 6th Zeuthen Workshop on Elementary Particle Theory ``Loops and Legs in Quantum Field Theory'', Kloster Banz, Germany, September 8--13, 200