The density and pressure are positive physical quantities in magnetohydrodynamics (MHD). Design of provably positivity-preserving (PP) numerical schemes for ideal compressible MHD is highly desired, but remains a challenge especially in the multi-dimensional cases. In this paper, we develop uniformly high-order discontinuous Galerkin (DG) schemes which provably preserve the positivity of densit...

For the understandings of the magnetohydrodynamic (MHD) characteristics in plasma, the spectrum of the resistive MHD modes are investigated in detail by solving the eigenvalue problem of the reduced MHD equations in cylindrical tokamak plasmas. The eigenvalues and eigenfunctions of the resistive MHD modes are clarified for small toroidal and poloidal mode numbers, and the discrete eigenvalues w...

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. Formation of the pedestal and the L-H transition is the direct result of ~ Er × ~ B flow shear suppression of anomalous transport. The periodic ELM crashes...

The Monty Hall Dilemma (MHD) is a striking example of the human tendency to base probability judgment on intuitive, erroneous heuristics instead of an analytic, normative reasoning process. Two experiments tested the claim (e.g., Stanovich & West, 2000) that correct, normative reasoning draws on executive, working memory resources (WM) whereas heuristic reasoning would be purely automatic. Expe...

We analyze 3D numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic field. We find that the time scale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions we show that the turbulent motions in the plane ...

We construct magnetohydrodynamic (MHD) similarity rebound shocks joining ‘quasistatic’ asymptotic solutions around the central degenerate core to explore an MHD model for the evolution of random magnetic field in supernova explosions. This provides a theoretical basis for further studying synchrotron diagnostics, MHD shock acceleration of cosmic rays, and the nature of intense magnetic field in...

Results from a three-dimensional axisymmetric resistive magnetohydrodynamic ~MHD! simulation are compared to experimental data from the Swarthmore Spheromak Experiment ~SSX! @M. R. Brown, Phys. Plasmas 6, 1717 ~1999!#. The MHD simulation is run under conditions and with dimensionless parameters similar to the experiment ~Lundquist number S51000, plasma beta b 50.1). The simulation is shown to r...

Wave and oscillatory activity is observed with modern imaging and spectral instruments in the visible light, EUV, X-ray and radio bands in all parts of the solar corona. Magnetohydrodynamic (MHD) wave theory gives satisfactory interpretation of these phenomena in terms of MHD modes of coronal structures. The paper reviews the current trends in the observational study of coronal oscillations, re...

Photonic crystal microcavities with multi-hole defects were simulated using finite difference time domain (FDTD) analysis. Subwavelength, multi-hole defects (MHD) offer a significant increase in defect surface area without compromising the quality factor of the photonic crystal. Calculations of the increase in surface area compared to a traditional, single hole defect are performed for MHD stru...

We investigate hydromagnetic turbulence of primordial magnetic fields using magnetohydrodynamics ~MHD! in an expanding universe. We present the basic, covariant MHD equations, find solutions for MHD waves in the early universe, and investigate the equations numerically for random magnetic fields in two spatial dimensions. We find the formation of magnetic structures at larger and larger scales ...