324,838 research outputs found
Three Dimensional Magneto Hydrodynamical Simulations of Gravitational Collapse of a 15Msun Star
We introduce our newly developed two different, three dimensional magneto
hydrodynamical codes in detail. One of our codes is written in the Newtonian
limit (NMHD) and the other is in the fully general relativistic code (GRMHD).
Both codes employ adaptive mesh refinement and, in GRMHD, the metric is evolved
with the "Baumgarte-Shapiro-Shibata-Nakamura" formalism known as the most
stable method at present. We did several test problems and as for the first
practical test, we calculated gravitational collapse of a star.
Main features found from our calculations are; (1) High velocity bipolar
outflow is driven from the proto-neutronstar and moves through along the
rotational axis in strongly magnetized models; (2) A one-armed spiral structure
appears which is originated from the low- instability; (3) By comparing
GRMHD and NMHD models, the maximum density increases about in GRMHD
models due to the stronger gravitational effect. These features agree very well
with previous studies and our codes are thus reliable to numerical simulation
of gravitational collapse of massive stars.Comment: Accepted by ApJS, 55 pages, 34 figure
Error Analysis of Band Matrix Method
Numerical error in the solution of the band matrix method based on the elimination method in single precision is investigated theoretically and experimentally, and the behaviour of the truncation error and the roundoff error is clarified. Some important suggestions for the useful application of the band solver are proposed by using the results of above error analysis
Relativistic MHD and black hole excision: Formulation and initial tests
A new algorithm for solving the general relativistic MHD equations is
described in this paper. We design our scheme to incorporate black hole
excision with smooth boundaries, and to simplify solving the combined Einstein
and MHD equations with AMR. The fluid equations are solved using a finite
difference Convex ENO method. Excision is implemented using overlapping grids.
Elliptic and hyperbolic divergence cleaning techniques allow for maximum
flexibility in choosing coordinate systems, and we compare both methods for a
standard problem. Numerical results of standard test problems are presented in
two-dimensional flat space using excision, overlapping grids, and elliptic and
hyperbolic divergence cleaning.Comment: 22 pages, 8 figure
Comparing Cost Functions in Resource Analysis
Cost functions provide information about the amount of resources required to execute a program in terms of the sizes of input arguments. They can provide an upper-bound, a lower-bound, or the average-case cost. Motivated by the existence of a number of automatic cost analyzers which produce cost functions, we propose an approach for automatically proving that a cost function is smaller than another one. In all applications of resource analysis, such as resource-usage verification, program synthesis and optimization, etc., it is essential to compare cost functions. This allows choosing an implementation with smaller cost or guaranteeing that the given resource-usage bounds are preserved. Unfortunately, automatically generated cost functions for realistic programs tend to be rather intricate, defined by multiple cases, involving non-linear subexpressions (e.g., exponential, polynomial and logarithmic) and they can contain multiple variables, possibly related by means of constraints. Thus, comparing cost functions is far from trivial. Our approach first syntactically transforms functions into simpler forms and then applies a number of su!cient conditions which guarantee that a set of expressions is smaller than another expression. Our preliminary implementation in the COSTA system indicates that the approach can be useful in practic
Statistical Mechanics of maximal independent sets
The graph theoretic concept of maximal independent set arises in several
practical problems in computer science as well as in game theory. A maximal
independent set is defined by the set of occupied nodes that satisfy some
packing and covering constraints. It is known that finding minimum and
maximum-density maximal independent sets are hard optimization problems. In
this paper, we use cavity method of statistical physics and Monte Carlo
simulations to study the corresponding constraint satisfaction problem on
random graphs. We obtain the entropy of maximal independent sets within the
replica symmetric and one-step replica symmetry breaking frameworks, shedding
light on the metric structure of the landscape of solutions and suggesting a
class of possible algorithms. This is of particular relevance for the
application to the study of strategic interactions in social and economic
networks, where maximal independent sets correspond to pure Nash equilibria of
a graphical game of public goods allocation
Numerical simulations with a first order BSSN formulation of Einstein's field equations
We present a new fully first order strongly hyperbolic representation of the
BSSN formulation of Einstein's equations with optional constraint damping
terms. We describe the characteristic fields of the system, discuss its
hyperbolicity properties, and present two numerical implementations and
simulations: one using finite differences, adaptive mesh refinement and in
particular binary black holes, and another one using the discontinuous Galerkin
method in spherical symmetry. The results of this paper constitute a first step
in an effort to combine the robustness of BSSN evolutions with very high
accuracy numerical techniques, such as spectral collocation multi-domain or
discontinuous Galerkin methods.Comment: To appear in Physical Review
A Hybrid Godunov Method for Radiation Hydrodynamics
From a mathematical perspective, radiation hydrodynamics can be thought of as
a system of hyperbolic balance laws with dual multiscale behavior (multiscale
behavior associated with the hyperbolic wave speeds as well as multiscale
behavior associated with source term relaxation). With this outlook in mind,
this paper presents a hybrid Godunov method for one-dimensional radiation
hydrodynamics that is uniformly well behaved from the photon free streaming
(hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and
to the strong equilibrium diffusion (hyperbolic) limit. Moreover, one finds
that the technique preserves certain asymptotic limits. The method incorporates
a backward Euler upwinding scheme for the radiation energy density and flux as
well as a modified Godunov scheme for the material density, momentum density,
and energy density. The backward Euler upwinding scheme is first-order accurate
and uses an implicit HLLE flux function to temporally advance the radiation
components according to the material flow scale. The modified Godunov scheme is
second-order accurate and directly couples stiff source term effects to the
hyperbolic structure of the system of balance laws. This Godunov technique is
composed of a predictor step that is based on Duhamel's principle and a
corrector step that is based on Picard iteration. The Godunov scheme is
explicit on the material flow scale but is unsplit and fully couples matter and
radiation without invoking a diffusion-type approximation for radiation
hydrodynamics. This technique derives from earlier work by Miniati & Colella
2007. Numerical tests demonstrate that the method is stable, robust, and
accurate across various parameter regimes.Comment: accepted for publication in Journal of Computational Physics; 61
pages, 15 figures, 11 table
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