Vibrationally induced fourth-order magnetic anisotropy and tunnel splittings in Mn_{12}

From density-functional-theory (DFT) based methods we calculate the vibrational spectrum of the Mn_{12}O_{12}(COOH)_{16}(H_2 O)_4 molecular magnet. Calculated infrared intensities are in accord with experimental studies. There have been no ab initio attempts at determining which interactions account for the fourth-order anisotropy. We show that vibrationally induced distortions of the molecule contribute to the fourth-order anisotropy Hamiltonian and that the magnitude and sign of the effect (-6.2 K) is in good agreement with all experiments. Vibrationally induced tunnel splittings in isotopically pure and natural samples are predicted.Comment: corres. author: [email protected] 4 pages, final version, accepted PR

Optimal Accuracy of Discontinuous Galerkin for Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106460/1/AIAA2013-2691.pd

Analysis and Implementation of Recovery-Based Discontinuous Galerkin for Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76575/1/AIAA-2009-3786-303.pd

Optimal multistage schemes for Euler equations with residual smoothing

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76583/1/AIAA-12860-858.pd

Bilinear forms for the recovery-based discontinuous Galerkin method for diffusion

The present paper introduces bilinear forms that are equivalent to the recovery-based discontinuous Galerkin formulation introduced by Van Leer in 2005. The recovery method approximates the solution of the diffusion equation in a discontinuous function space, while inter-element coupling is achieved by a local L2 projection that recovers a smooth continuous function underlying the discontinuous approximation. Here we introduce the concept of a local “recovery polynomial basis” - smooth polynomials that are in the weak sense indistinguishable from the discontinuous basis polynomials - and show it allows us to eliminate the recovery procedure. The recovery method reproduces the symmetric discontinuous Galerkin formulation with additional penalty-like terms depending on the targeted accuracy of the method. We present the unique link between the recovery method and discontinuous Galerkin bilinear forms

Two-Fluid MHD Simulations of Converging HI Flows in the Interstellar Medium. I: Methodology and Basic Results

We develop an unconditionally stable numerical method for solving the coupling between two fluids (frictional forces/heatings, ionization, and recombination), and investigate the dynamical condensation process of thermally unstable gas that is provided by the shock waves in a weakly ionized and magnetized interstellar medium by using two-dimensional two-fluid magnetohydrodynamical simulations. If we neglect the effect of magnetic field, it is known that condensation driven by thermal instability can generate high density clouds whose physical condition corresponds to molecular clouds (precursor of molecular clouds). In this paper, we study the effect of magnetic field on the evolution of supersonic converging HI flows and focus on the case in which the orientation of magnetic field to converging flows is orthogonal. We show that the magnetic pressure gradient parallel to the flows prevents the formation of high density and high column density clouds, but instead generates fragmented, filamentary HI clouds. With this restricted geometry, magnetic field drastically diminishes the opportunity of fast molecular cloud formation directly from the warm neutral medium, in contrast to the case without magnetic field.Comment: ApJ accepte

Multi-Dimensional Astrophysical Structural and Dynamical Analysis I. Development of a Nonlinear Finite Element Approach

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.). The technique employed is the Finite Element Method (FEM), commonly used to solve engineering structural problems. The approach developed herein has the following key features: 1. The computational mesh can extend into the time dimension, as well as space, perhaps only a few cells, or throughout spacetime. 2. Virtually all equations describing the astrophysics of continuous media, including the field equations, can be written in a compact form similar to that routinely solved by most engineering finite element codes. 3. The transformations that occur naturally in the four-dimensional FEM possess both coordinate and boost features, such that (a) although the computational mesh may have a complex, non-analytic, curvilinear structure, the physical equations still can be written in a simple coordinate system independent of the mesh geometry. (b) if the mesh has a complex flow velocity with respect to coordinate space, the transformations will form the proper arbitrary Lagrangian- Eulerian advective derivatives automatically. 4. The complex difference equations on the arbitrary curvilinear grid are generated automatically from encoded differential equations. This first paper concentrates on developing a robust and widely-applicable set of techniques using the nonlinear FEM and presents some examples.Comment: 28 pages, 9 figures; added integral boundary conditions, allowing very rapidly-rotating stars; accepted for publication in Ap.

Comment on Viscous Stability of Relativistic Keplerian Accretion Disks

Recently Ghosh (1998) reported a new regime of instability in Keplerian accretion disks which is caused by relativistic effects. This instability appears in the gas pressure dominated region when all relativistic corrections to the disk structure equations are taken into account. We show that he uses the stability criterion in completely wrong way leading to inappropriate conclusions. We perform a standard stability analysis to show that no unstable region can be found when the relativistic disk is gas pressure dominated.Comment: 9 pages, 4 figures, uses aasms4.sty, submitted for ApJ Letter

Fix for solution errors near interfaces in two-fluid computations

A finite-volume method is considered for the computation of flows of two compressible, immiscible fluids at very different densities. A level-set technique is employed to distinguish between the two fluids. A simple ghost-fluid method is presented as a fix for the solution errors (‘pressure oscillations’) that may occur near two-fluid interfaces when applying a capturing method. Computations with it for compressible two-fluid flows with arbitrarily large density ratios yield perfectly sharp, pressure-oscillation-free interfaces. The masses of the separate fluids appear to be conserved up to first-order accuracy

Riemann-problem and level-set approaches for two-fluid flow computations II. Fixes for solution errors near interfaces.

Fixes are presented for the solution errors (`pressure oscillations') that may occur near two-fluid interfaces when applying a capturing method. The fixes are analyzed and tested. For two-fluid flows with arbitrarily large density ratios, a variant of the ghost-fluid method appears to be a perfect remedy. Results are presented for compressible water-air flows. The results are promising for a further elaboration of this important application area. The paper contributes to the state-of-the-art in computing two-fluid flows