A Divergence-Free Upwind Code for Multidimensional Magnetohydrodynamic Flows

A description is given for preserving {\bmsy\nabla}\cdot{\vec B}=0 in a magnetohydrodynamic (MHD) code that employs the upwind, Total Variation Diminishing (TVD) scheme and the Strang-type operator splitting for multi-dimensionality. The method is based on the staggered mesh technique to constrain the transport of magnetic field: the magnetic field components are defined at grid interfaces with their advective fluxes on grid edges, while other quantities are defined at grid centers. The magnetic field at grid centers for the upwind step is calculated by interpolating the values from grid interfaces. The advective fluxes on grid edges for the magnetic field evolution are calculated from the upwind fluxes at grid interfaces. Then, the magnetic field can be maintained with {\bmsy\nabla}\cdot{\vec B}=0 exactly, if this is so initially, while the upwind scheme is used for the update of fluid quantities. The correctness of the code is demonstrated through tests comparing numerical solutions either with analytic solutions or with numerical solutions from the code using an explicit divergence-cleaning method. Also the robustness is shown through tests involving realistic astrophysical problems.Comment: 15 pages of text, 8 figures (in degraded gif format), to appear in The Astrophysical Journal (Dec. 10, 1998), original quality figures available via anonymous ftp at ftp://ftp.msi.umn.edu/pub/users/twj/mhddivb5.uu or ftp://canopus.chungnam.ac.kr/ryu/mhddivb5.u

Holographic classification of Topological Insulators and its 8-fold periodicity

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table

Hydrodynamic Simulations of Oscillating Shock Waves in a Sub-Keplerian Accretion Flow Around Black Holes

We study the accretion processes on a black hole by numerical simulation. We use a grid based finite difference code for this purpose. We scan the parameter space spanned by the specific energy and the angular momentum and compare the time-dependent solutions with those obtained from theoretical considerations. We found several important results (a) The time dependent flow behaves close to a constant height model flow in the pre-shock region and a flow with vertical equilibrium in the post-shock region. (c) The infall time scale in the post-shock region is several times higher than the free-fall time scale. (b) There are two discontinuities in the flow, one being just outside of the inner sonic point. Turbulence plays a major role in determining the locations of these discontinuities. (d) The two discontinuities oscillate with two different frequencies and behave as a coupled harmonic oscillator. A Fourier analysis of the variation of the outer shock location indicates higher power at the lower frequency and lower power at the higher frequency. The opposite is true when the analysis of the inner shock is made. These behaviours will have implications in the spectral and timing properties of black hole candidates.Comment: 19 pages, 13 figures, 1 Table MNRAS (In press

Analytical Models for the Energetics of Cosmic Accretion Shocks, their Cosmological Evolution, and the Effect of Environment

We present an analytical description of the energetics of the population of cosmic accretion shocks, for a concordance cosmology. We calculate how the shock-processed accretion power and mass current are distributed among different shock Mach numbers, and how they evolve with cosmic time. We calculate the cumulative energy input of cosmic accretion shocks of any Mach number to the intergalactic medium as a function of redshift, and we compare it with the energy output of supernova explosions as well as with the energy input required to reionize the universe. In addition, we investigate and quantify the effect of environmental factors, such as local clustering properties and filament preheating on the statistical properties of these shocks. We find that the energy processed by accretion shocks is higher than the supernova energy output for z<3 and that it becomes more than an order of magnitude higher in the local universe. The energy processed by accretion shocks alone becomes comparable to the energy required to reionize the universe by z~3.5. Finally, we establish both qualitative and quantitatively that both local clustering as well as filament compression and preheating are important factors in determining the statistical properties of the cosmic accretion shock population.Comment: 13 pages, 5 figures, emulateap

Growth of Magnetic Fields Induced by Turbulent Motions

We present numerical simulations of driven magnetohydrodynamic (MHD) turbulence with weak/moderate imposed magnetic fields. The main goal is to clarify dynamics of magnetic field growth. We also investigate the effects of the imposed magnetic fields on the MHD turbulence, including, as a limit, the case of zero external field. Our findings are as follows. First, when we start off simulations with weak mean magnetic field only (or with small scale random field with zero imposed field), we observe that there is a stage at which magnetic energy density grows linearly with time. Runs with different numerical resolutions and/or different simulation parameters show consistent results for the growth rate at the linear stage. Second, we find that, when the strength of the external field increases, the equilibrium kinetic energy density drops by roughly the product of the rms velocity and the strength of the external field. The equilibrium magnetic energy density rises by roughly the same amount. Third, when the external magnetic field is not very strong (say, less than ~0.2 times the rms velocity when measured in the units of Alfven speed), the turbulence at large scales remains statistically isotropic, i.e. there is no apparent global anisotropy of order B_0/v. We discuss implications of our results on astrophysical fluids.Comment: 16 pages, 18 figures; ApJ, accepte

Empirical Comparisons of Virtual Environment Displays

There are many different visual display devices used in virtual environment (VE) systems. These displays vary along many dimensions, such as resolution, field of view, level of immersion, quality of stereo, and so on. In general, no guidelines exist to choose an appropriate display for a particular VE application. Our goal in this work is to develop such guidelines on the basis of empirical results. We present two initial experiments comparing head-mounted displays with a workbench display and a foursided spatially immersive display. The results indicate that the physical characteristics of the displays, users' prior experiences, and even the order in which the displays are presented can have significant effects on performance

Topological delocalization of two-dimensional massless Dirac fermions

The beta function of a two-dimensional massless Dirac Hamiltonian subject to a random scalar potential, which e.g., underlies the theoretical description of graphene, is computed numerically. Although it belongs to, from a symmetry standpoint, the two-dimensional symplectic class, the beta function monotonically increases with decreasing $g$. We also provide an argument based on the spectral flows under twisting boundary conditions, which shows that none of states of the massless Dirac Hamiltonian can be localized.Comment: 4 pages, 2 figure