Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids : slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|3/2, and the film thickens or thins according to |x|, where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|−1, and the film thickens or thins like |t|−1, independent of N

Observation and study of baryonic B decays: B -> D(*) p pbar, D(*) p pbar pi, and D(*) p pbar pi pi

We present a study of ten B-meson decays to a D(*), a proton-antiproton pair, and a system of up to two pions using BaBar's data set of 455x10^6 BBbar pairs. Four of the modes (B0bar -> D0 p anti-p, B0bar -> D*0 p anti-p, B0bar -> D+ p anti-p pi-, B0bar -> D*+ p anti-p pi-) are studied with improved statistics compared to previous measurements; six of the modes (B- -> D0 p anti-p pi-, B- -> D*0 p anti-p pi-, B0bar -> D0 p anti-p pi- pi+, B0bar -> D*0 p anti-p pi- pi+, B- -> D+ p anti-p pi- pi-, B- -> D*+ p anti-p pi- pi-) are first observations. The branching fractions for 3- and 5-body decays are suppressed compared to 4-body decays. Kinematic distributions for 3-body decays show non-overlapping threshold enhancements in m(p anti-p) and m(D(*)0 p) in the Dalitz plots. For 4-body decays, m(p pi-) mass projections show a narrow peak with mass and full width of (1497.4 +- 3.0 +- 0.9) MeV/c2, and (47 +- 12 +- 4) MeV/c2, respectively, where the first (second) errors are statistical (systematic). For 5-body decays, mass projections are similar to phase space expectations. All results are preliminary.Comment: 28 pages, 90 postscript figures, submitted to LP0

Measurement of the branching fraction and CP content for the decay B(0) -> D(*+)D(*-)

This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APS.We report a measurement of the branching fraction of the decay B0→D*+D*- and of the CP-odd component of its final state using the BABAR detector. With data corresponding to an integrated luminosity of 20.4  fb-1 collected at the Υ(4S) resonance during 1999–2000, we have reconstructed 38 candidate signal events in the mode B0→D*+D*- with an estimated background of 6.2±0.5 events. From these events, we determine the branching fraction to be B(B0→D*+D*-)=[8.3±1.6(stat)±1.2(syst)]×10-4. The measured CP-odd fraction of the final state is 0.22±0.18(stat)±0.03(syst).This work is supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the A.P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation

Search for rare quark-annihilation decays, B --> Ds(*) Phi

We report on searches for B- --> Ds- Phi and B- --> Ds*- Phi. In the context of the Standard Model, these decays are expected to be highly suppressed since they proceed through annihilation of the b and u-bar quarks in the B- meson. Our results are based on 234 million Upsilon(4S) --> B Bbar decays collected with the BABAR detector at SLAC. We find no evidence for these decays, and we set Bayesian 90% confidence level upper limits on the branching fractions BF(B- --> Ds- Phi) Ds*- Phi)<1.2x10^(-5). These results are consistent with Standard Model expectations.Comment: 8 pages, 3 postscript figues, submitted to Phys. Rev. D (Rapid Communications

Measurement of D-s(+) and D-s(*+) production in B meson decays and from continuum e(+)e(-) annihilation at √s=10.6 GeV

This is the pre-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2002 APSNew measurements of Ds+ and Ds*+ meson production rates from B decays and from qq̅ continuum events near the Υ(4S) resonance are presented. Using 20.8 fb-1 of data on the Υ(4S) resonance and 2.6 fb-1 off-resonance, we find the inclusive branching fractions B(B⃗Ds+X)=(10.93±0.19±0.58±2.73)% and B(B⃗Ds*+X)=(7.9±0.8±0.7±2.0)%, where the first error is statistical, the second is systematic, and the third is due to the Ds+→φπ+ branching fraction uncertainty. The production cross sections σ(e+e-→Ds+X)×B(Ds+→φπ+)=7.55±0.20±0.34pb and σ(e+e-→Ds*±X)×B(Ds+→φπ+)=5.8±0.7±0.5pb are measured at center-of-mass energies about 40 MeV below the Υ(4S) mass. The branching fractions ΣB(B⃗Ds(*)+D(*))=(5.07±0.14±0.30±1.27)% and ΣB(B⃗Ds*+D(*))=(4.1±0.2±0.4±1.0)% are determined from the Ds(*)+ momentum spectra. The mass difference m(Ds+)-m(D+)=98.4±0.1±0.3MeV/c2 is also measured.This work was supported by DOE and NSF (USA), NSERC (Canada), IHEP (China), CEA and CNRS-IN2P3 (France), BMBF (Germany), INFN (Italy), NFR (Norway), MIST (Russia), and PPARC (United Kingdom). Individuals have received support from the Swiss NSF, A. P. Sloan Foundation, Research Corporation, and Alexander von Humboldt Foundation

Measurement of CP-violation asymmetries in D0 to Ks pi+ pi-

We report a measurement of time-integrated CP-violation asymmetries in the resonant substructure of the three-body decay D0 to Ks pi+ pi- using CDF II data corresponding to 6.0 invfb of integrated luminosity from Tevatron ppbar collisions at sqrt(s) = 1.96 TeV. The charm mesons used in this analysis come from D*+(2010) to D0 pi+ and D*-(2010) to D0bar pi-, where the production flavor of the charm meson is determined by the charge of the accompanying pion. We apply a Dalitz-amplitude analysis for the description of the dynamic decay structure and use two complementary approaches, namely a full Dalitz-plot fit employing the isobar model for the contributing resonances and a model-independent bin-by-bin comparison of the D0 and D0bar Dalitz plots. We find no CP-violation effects and measure an asymmetry of ACP = (-0.05 +- 0.57 (stat) +- 0.54 (syst))% for the overall integrated CP-violation asymmetry, consistent with the standard model prediction.Comment: 15 page

Measurement of the branching fraction for B−→D0K∗−B^- \to D^0 K^{*-}

We present a measurement of the branching fraction for the decay B- --> D0 K*- using a sample of approximately 86 million BBbar pairs collected by the BaBar detector from e+e- collisions near the Y(4S) resonance. The D0 is detected through its decays to K- pi+, K- pi+ pi0 and K- pi+ pi- pi+, and the K*- through its decay to K0S pi-. We measure the branching fraction to be B.F.(B- --> D0 K*-)= (6.3 +/- 0.7(stat.) +/- 0.5(syst.)) x 10^{-4}

A Precision Measurement of the Lambda_c Baryon Mass

The $\Lambda_c^+$ baryon mass is measured using $\Lambda_c^+\to\Lambda K^0_S K^+$ and $\Lambda_c^+\to\Sigma^0 K^0_S K^+$ decays reconstructed in 232 fb$^{-1}$ of data collected with the BaBar detector at the PEP-II asymmetric-energy $e^+e^-$ storage ring. The $\Lambda_c^+$ mass is measured to be $2286.46\pm0.14\mathrm{MeV}/c^2$. The dominant systematic uncertainties arise from the amount of material in the tracking volume and from the magnetic field strength.Comment: 14 pages, 8 postscript figures, submitted to Phys. Rev.

Observation of a significant excess of π0π0\pi^{0}\pi^{0} events in B meson decays

We present an observation of the decay $B^{0} \to \pi^{0} \pi^{0}$ based on a sample of 124 million $B\bar{B}$ pairs recorded by the BABAR detector at the PEP-II asymmetric-energy $B$ Factory at SLAC. We observe $46 \pm 13 \pm 3$ events, where the first error is statistical and the second is systematic, corresponding to a significance of 4.2 standard deviations including systematic uncertainties. We measure the branching fraction \BR(B^{0} \to \pi^{0} \pi^{0}) = (2.1 \pm 0.6 \pm 0.3) \times 10^{-6}, averaged over $B^{0}$ and $\bar{B}^{0}$ decays