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Vector Potential (vector + potential)
Selected AbstractsA simple method to calculate the signal-to-noise ratio of a circular-shaped coil for MRICONCEPTS IN MAGNETIC RESONANCE, Issue 6 2006K. Ocegueda Abstract The introduction of the ultrafast imaging sequences has renewed the interest in development of RF coils. The theoretical frame of the SNR of MRI coils is a challenge because it requires a deep mathematical background to master the associated concepts. Here, a simpler method is proposed based on Legendre polynomials. This approximation method, together with a quasi-static approach, was used to derive a signal-to-noise ratio expression for a circular-shaped coil. Legendre polynomials were used instead of a weighting function to simplify the vector potential of the power loss, and an SNR formula was then derived. The simplified version of the SNR formula of a circular coil was compared with the weighting function-derived SNR expression using the quasi-static approach. SNR-vs.-depth plots were computed to theoretically compare both SNR formulas. Results showed a strong agreement between SNR values for the circular-shaped coil. This approach can be used as a tool to derive SNR expressions for more complex geometries. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 422,429, 2006 [source] Leakage field distribution of a transformer for conventional and superconducting conditionsEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 4 2002P. Raitsios The overall distribution of leakage field and current density in a transformer model with cylindrical windings in proximity to the core yokes is investigated from a different viewpoint than that of Kapp or Rogowski, i.e. by taking into consideration the conductivity of the conductive material. Using Maxwell's differential equations and the vector potential and by considering the conductivity of the conductive material, general equations are obtained for the components of the magnetic induction in a two dimensional space. From these components the leakage inductance is calculated and its application for conventional and superconducting conditions is examined. The distribution of current density in the windings is obtained from the vector potential. [source] Piecewise divergence-free discontinuous Galerkin methods for Stokes flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2008Peter Hansbo Abstract In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix,Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Error analysis and Hertz vector approach for an electromagnetic interaction between a line current and a conducting plateINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 3 2003M.T. Attaf Abstract In the present paper we first introduce the Hertz vector potential and examine how the specific case of electromagnetic field diffusion problems can be formulated in terms of this potential. Its connection to other commonly used potentials is presented and a basic approach in the form of a suitable set of equations is introduced. The suggested method is then successfully applied to solve the case of an electromagnetic interaction between a straight conductor carrying sinusoidal current and a finite thickness fixed plate. Due to the oscillatory aspect of the integral solution obtained, an appropriate numerical treatment is investigated and various curves are shown to illustrate the convergence behaviour. Copyright © 2003 John Wiley & Sons, Ltd. [source] Relativistic and electron-correlation effects on magnetizabilities investigated by the Douglas-Kroll-Hess method and the second-order Møller-Plesset perturbation theoryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2009Terutaka Yoshizawa Abstract Isotropic and anisotropic magnetizabilities for noble gas atoms and a series of singlet and triplet molecules were calculated using the second-order Douglas-Kroll-Hess (DKH2) Hamiltonian containing the vector potential A and in part using second-order generalized unrestricted Møller-Plesset (GUMP2) theory. The DKH2 Hamiltonian was resolved into three parts (spin-free terms, spin-dependent terms, and magnetic perturbation terms), and the magnetizabilities were decomposed into diamagnetic and paramagnetic terms to investigate the relativistic and electron-correlation effects in detail. For Ne, Kr, and Xe, the calculated magnetizabilities approached the experimental values, once relativistic and electron-correlation effects were included. For the IF molecule, the magnetizability was strongly affected by the spin-orbit interaction, and the total relativistic contribution amounted to 22%. For group 17, 16, 15, and 14 hydrides, the calculated relativistic effects were small (less than 3%), and trends were observed in relativistic and electron-correlation effects across groups and periods. The magnetizability anisotropies of triplet molecules were generally larger than those of similar singlet molecules. The so-called relativistic-correlation interference for the magnetizabilities computed using the relativistic GUMP2 method can be neglected for the molecules evaluated, with exception of triplet SbH. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009 [source] Equatorial magnetic helicity flux in simulations with different gaugesASTRONOMISCHE NACHRICHTEN, Issue 1 2010D. Mitra Abstract We use direct numerical simulations of forced MHD turbulence with a forcing function that produces two different signs of kinetic helicity in the upper and lower parts of the domain. We show that the mean flux of magnetic helicity from the small-scale field between the two parts of the domain can be described by a Fickian diffusion law with a diffusion coefficient that is approximately independent of the magnetic Reynolds number and about one third of the estimated turbulent magnetic diffusivity. The data suggest that the turbulent diffusive magnetic helicity flux can only be expected to alleviate catastrophic quenching at Reynolds numbers of more than several thousands. We further calculate the magnetic helicity density and its flux in the domain for three different gauges. We consider the Weyl gauge, in which the electrostatic potential vanishes, the pseudo-Lorenz gauge, where the speed of light is replaced by the sound speed, and the ,resistive gauge' in which the Laplacian of the magnetic vector potential acts as a resistive term. We find that, in the statistically steady state, the time-averaged magnetic helicity density and the magnetic helicity flux are the same in all three gauges (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||