677 research outputs found
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
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
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
High Order Upwind Schemes for Multidimensional Magnetohydrodynamics
A general method for constructing high order upwind schemes for
multidimensional magnetohydrodynamics (MHD), having as a main built-in
condition the divergence-free constraint \divb=0 for the magnetic field
vector \bb, is proposed. The suggested procedure is based on {\em
consistency} arguments, by taking into account the specific operator structure
of MHD equations with respect to the reference Euler equations of gas-dynamics.
This approach leads in a natural way to a staggered representation of the \bb
field numerical data where the divergence-free condition in the cell-averaged
form, corresponding to second order accurate numerical derivatives, is exactly
fulfilled. To extend this property to higher order schemes, we then give
general prescriptions to satisfy a order accurate \divb=0
relation for any numerical \bb field having a order interpolation
accuracy. Consistency arguments lead also to a proper formulation of the upwind
procedures needed to integrate the induction equations, assuring the exact
conservation in time of the divergence-free condition and the related
continuity properties for the \bb vector components. As an application, a
third order code to simulate multidimensional MHD flows of astrophysical
interest is developed using ENO-based reconstruction algorithms. Several test
problems to illustrate and validate the proposed approach are finally
presented.Comment: 34 pages, including 14 figure
Solving One Dimensional Scalar Conservation Laws by Particle Management
We present a meshfree numerical solver for scalar conservation laws in one
space dimension. Points representing the solution are moved according to their
characteristic velocities. Particle interaction is resolved by purely local
particle management. Since no global remeshing is required, shocks stay sharp
and propagate at the correct speed, while rarefaction waves are created where
appropriate. The method is TVD, entropy decreasing, exactly conservative, and
has no numerical dissipation. Difficulties involving transonic points do not
occur, however inflection points of the flux function pose a slight challenge,
which can be overcome by a special treatment. Away from shocks the method is
second order accurate, while shocks are resolved with first order accuracy. A
postprocessing step can recover the second order accuracy. The method is
compared to CLAWPACK in test cases and is found to yield an increase in
accuracy for comparable resolutions.Comment: 15 pages, 6 figures. Submitted to proceedings of the Fourth
International Workshop Meshfree Methods for Partial Differential Equation
Dispersive wave runup on non-uniform shores
Historically the finite volume methods have been developed for the numerical
integration of conservation laws. In this study we present some recent results
on the application of such schemes to dispersive PDEs. Namely, we solve
numerically a representative of Boussinesq type equations in view of important
applications to the coastal hydrodynamics. Numerical results of the runup of a
moderate wave onto a non-uniform beach are presented along with great lines of
the employed numerical method (see D. Dutykh et al. (2011) for more details).Comment: 8 pages, 6 figures, 18 references. This preprint is submitted to
FVCA6 conference proceedings. Other author papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Athena: A New Code for Astrophysical MHD
A new code for astrophysical magnetohydrodynamics (MHD) is described. The
code has been designed to be easily extensible for use with static and adaptive
mesh refinement. It combines higher-order Godunov methods with the constrained
transport (CT) technique to enforce the divergence-free constraint on the
magnetic field. Discretization is based on cell-centered volume-averages for
mass, momentum, and energy, and face-centered area-averages for the magnetic
field. Novel features of the algorithm include (1) a consistent framework for
computing the time- and edge-averaged electric fields used by CT to evolve the
magnetic field from the time- and area-averaged Godunov fluxes, (2) the
extension to MHD of spatial reconstruction schemes that involve a
dimensionally-split time advance, and (3) the extension to MHD of two different
dimensionally-unsplit integration methods. Implementation of the algorithm in
both C and Fortran95 is detailed, including strategies for parallelization
using domain decomposition. Results from a test suite which includes problems
in one-, two-, and three-dimensions for both hydrodynamics and MHD are given,
not only to demonstrate the fidelity of the algorithms, but also to enable
comparisons to other methods. The source code is freely available for download
on the web.Comment: 61 pages, 36 figures. accepted by ApJ
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