Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics

We present a constrained formulation of Dedner et al's hyperbolic/parabolic divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we impose is that energy removed must either be conserved or dissipated, such that the scheme is guaranteed to decrease the overall magnetic energy. This is shown to require use of conjugate numerical operators for evaluating \nabla\dot B and \nabla{\psi} in the SPMHD cleaning equations. The resulting scheme is shown to be stable at density jumps and free boundaries, in contrast to an earlier implementation by Price & Monaghan (2005). Optimal values of the damping parameter are found to be {\sigma} = 0.2-0.3 in 2D and {\sigma} = 0.8-1.2 in 3D. With these parameters, our constrained Hamiltonian formulation is found to provide an effective means of enforcing the divergence constraint in SPMHD, typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to an order of magnitude better than artificial resistivity without the associated dissipation in the physical field. Furthermore, when applied to realistic, 3D simulations we find an improvement of up to two orders of magnitude in momentum conservation with a corresponding improvement in numerical stability at essentially zero additional computational expense.Comment: 28 pages, 25 figures, accepted to J. Comput. Phys. Movies at http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted figs 1,4,6, and several color bar

Article 9: Secured Transactions (Comment) of Uniform Commercial Code Annotations

Review of SCHLEIMER V. ARROWHEAD GARAGE, INC. 260 N.Y.S.2d 271 (Civ. Ct. 1965

Article 1: General Provisions (Comment) of Uniform Commercial Code Annotations

Review of: KORESKA V. UNITED CARGO CORP. 258 N.Y.S.2d 432 (App. Div. 1965) GREATER LOUISVILLE AUTO AUCTION, INC. V. OGLE BUICK, INC. 387 S.W.2d 17 (Ky. 1965) IN RE KING FURNITURE CITY, INC. 240 F. Supp. 453 (E.D. Ark. 1965) IN THE MATTER OF WHEATLAND ELEC. PROD, Co. 237 F. Supp. 820 (W.D. Pa. 1965

Experience with the Quality Assurance of the Superconducting Electrical Circuits of the LHC Machine

The coherence between the powering reference database for the LHC and the Electrical Quality Assurance (ELQA) is guaranteed on the procedural level. However, a challenge remains the coherence between the database, the magnet test and assembly procedures, and the connection of all superconducting circuits in the LHC machine. In this paper, the methods, tooling, and procedures for the ELQA during the assembly phase of the LHC will be presented in view of the practical experience gained in the LHC tunnel. Some examples of detected polarity errors and electrical non-conformities will be presented. The parameters measured at ambient temperature, such as the dielectric insulation of circuits, will be discussed

Automatic System for the D.C. High Voltage Qualification of the Superconducting Electrical Circuits of the LHC Machine

A d.c. high voltage test system has been developed to verify automatically the insulation resistance of the powering circuits of the LHC. In the most complex case, up to 72 circuits share the same volume inside cryogenic lines. Each circuit can have an insulation fault versus any other circuit or versus ground. The system is able to connect up to 80 circuits and apply a voltage up to 2 kV D.C. The leakage current flowing through each circuit is measured within a range of 1 nA to 1.6 mA. The matrix of measurements allows characterizing the paths taken by the currents and locating weak points of the insulation between circuits. The system is composed of a D.C. voltage source and a data acquisition card. The card is able to measure with precision currents and voltages and to drive up to 5 high voltage switching modules offering 16 channels each. A LabVIEW application controls the system for an automatic and safe operation. This paper describes the hardware and software design, the testing methodology and the results obtained during the qualification of the LHC superconducting circuits

Protostellar outflows with Smoothed Particle Magnetohydrodynamics (SPMHD)

The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D AMR/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the Smoothed Particle Hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show, that Smoothed Particle Magnetohydrodynamics (SPMHD) is able to handle the magnetorotational processes connected with outflow phenomena, and to produce meaningful results which are in good agreement with findings reported in the literature. Especially, our numerical scheme allows for a quantitative analysis of the evolution of the ratio of the toroidal to the poloidal magnetic field, which we performed in this work.Comment: 5 pages, 4 figures. Accepted to MNRAS Letter