Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics II. Dust and the Critical Speed for C Shocks

This is the second in a series of papers on the effects of dust on multifluid, MHD shock waves in weakly ionized molecular gas. We investigate the influence of dust on the critical shock speed, v_crit, above which C shocks cease to exist. Chernoff showed that v_crit cannot exceed the grain magnetosound speed, v_gms, if dust grains are dynamically well coupled to the magnetic field. We present numerical simulations of steady shocks where the grains may be well- or poorly coupled to the field. We use a time-dependent, multifluid MHD code that models the plasma as a system of interacting fluids: neutral particles, ions, electrons, and various ``dust fluids'' comprised of grains with different sizes and charges. Our simulations include grain inertia and grain charge fluctuations but to highlight the essential physics we assume adiabatic flow, single-size grains, and neglect the effects of chemistry. We show that the existence of a phase speed v_phi does not necessarily mean that C shocks will form for all shock speeds v_s less than v_phi. When the grains are weakly coupled to the field, steady, adiabatic shocks resemble shocks with no dust: the transition to J type flow occurs at v_crit = 2.76 v_nA, where v_nA is the neutral Alfven speed, and steady shocks with v_s > 2.76 v_nA are J shocks with magnetic precursors in the ion-electron fluid. When the grains are strongly coupled to the field, v_crit = min(2.76 v_nA, v_gms). Shocks with v_crit < v_s < v_gms have magnetic precursors in the ion-electron-dust fluid. Shocks with v_s > v_gms have no magnetic precursor in any fluid. We present time-dependent calculations to study the formation of steady multifluid shocks. The dynamics differ qualitatively depending on whether or not the grains and field are well coupled.Comment: 43 pages with 17 figures, aastex, accepted by The Astrophysical Journa

Strategic alliances and competitive strategies in the European aerospace industry: the case of BMW Rolls-Royce GmbH

Strategic alliances are an important feature of the aerospace industry and there have been many studies that have sought to evaluate their performance. Most have taken a policy perspective exploring the economic and political benefits claimed for collaboration of this type. The perspective is a reflection of the political origins of many aerospace alliances. This study seeks to evaluate, from a managerial perspective, one of the newer alliances established on a strictly commercial basis,. It focuses on BMW Rolls-Royce GmbH, one of a small number of truly European alliances. The study concludes that although Rolls-Royce bought out its German partner after a decade of operation, the alliance was a success. The two engines developed by the alliance over this period were a technical success, overall sales were well on target and the alliance was about to break even. In addition, the study concludes that the alliance formed a key element in Rolls-Royce‟s successful strategy to extend its product portfolio, a strategy that elevated the company to second place in the global aero engine market

Benefits to be derived from meteorological satellite technology

The benefits derived from satellite technology in educational communication and meteorology are cited

Optical observation of "band‐to‐band" scattering by time‐resolved phosphorescence line narrowing: Exciton dephasing in a quasi‐one‐dimensional solid

Abstract Unavailable