We have implemented non-ideal Magneto-Hydrodynamics (MHD) effects in the Adaptive Mesh Refinement (AMR) code RAMSES, namely ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test and the Alfven wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.

The ratio of the CKM quark-mixing matrix elements |V ub |/|V cb | has been measured using B hadron semileptonic decays. The analysis uses the reconstructed mass M X of the secondary hadronic system produced in association with an identified lepton. Since B → X u ℓν transitions are characterised by hadronic masses below those of the D mesons produced in B → X c ℓν transitions, events with a reconstructed value of M X significantly below the D mass are selected. Further signal enrichments are obtained using the topology of reconstructed decays and hadron identification. A fit to the numbers of decays in the b → u enriched and depleted samples with M X above and below 1.6 GeV/c 2 and to the shapes of the lepton energy distribution in the B rest frame gives |V ub |/|V cb | = 0.103 +0.011 −0.012 (stat.) ± 0.016 (syst.) ± 0.010 (model) and, correspondingly, a charmless semileptonic B decay branching fraction of BR(B → X u ℓν) = (1.57 ± 0.35 (stat.) ± 0.48 (syst.) ± 0.27 (model)) × 10 −3 .

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Infrared and collinear safe event shape distributions and their mean values are determined using the data taken at five different centre of mass energies above M Z with the DELPHI detector at LEP. From the event shapes, the strong coupling α s is extracted in O(α 2 s ), NLLA and a combined scheme using hadronisation corrections evaluated with fragmentation model generators as well as using an analytical power ansatz. Comparing these measurements to those obtained at M Z , the energy dependence (running) of α s is accessible. The logarithmic energy slope of the inverse strong coupling is measured to bein good agreement with the QCD expectation of 1.27.

Context. We analyse the presence of nonradial oscillations in Cepheids, a problem that has not been theoretically revised since the work of Dziembowski (1977, Acta Astron., 27, 95) and Osaki (1977, PASJ, 29, 235). Our analysis is motivated by a work of Moskalik et al. (2004, ASPC, 310, 498), which reports the detection of low-amplitude periodicities in a few Cepheids of the large Magellanic cloud. These newly discovered periodicities were interpreted as nonradial modes. Aims. Based on linear nonadiabatic stability analysis, our goal is to reanalyse the presence and stability of nonradial modes, taking into account improvement in the main input physics required for the modelling of Cepheids. Methods. We compare the results obtained from two different numerical methods used to solve the set of differential equations: a matrix method and the Ricatti method. Results. We show the limitation of the matrix method for finding low-order p-modes (l < 6), because of their dual character in evolved stars such as Cepheids. For higher order p-modes, we find excellent agreement between the two methods. Conclusions. No nonradial instability is found below l = 5, whereas many unstable nonradial modes exist for higher orders. We also find that nonradial modes remain unstable, even at hotter effective temperatures than the blue edge of the Cepheid instability strip, where no radial pulsations are expected.