106,927 research outputs found
Spectral Numerical Exterior Calculus Methods for Differential Equations on Radial Manifolds
We develop exterior calculus approaches for partial differential equations on
radial manifolds. We introduce numerical methods that approximate with spectral
accuracy the exterior derivative , Hodge star , and their
compositions. To achieve discretizations with high precision and symmetry, we
develop hyperinterpolation methods based on spherical harmonics and Lebedev
quadrature. We perform convergence studies of our numerical exterior derivative
operator and Hodge star operator
showing each converge spectrally to and . We show how the
numerical operators can be naturally composed to formulate general numerical
approximations for solving differential equations on manifolds. We present
results for the Laplace-Beltrami equations demonstrating our approach.Comment: 22 pages, 13 figure
Quasiequilibrium sequences of black-hole--neutron-star binaries in general relativity
We construct quasiequilibrium sequences of black hole-neutron star binaries
for arbitrary mass ratios by solving the constraint equations of general
relativity in the conformal thin-sandwich decomposition. We model the neutron
star as a stationary polytrope satisfying the relativistic equations of
hydrodynamics, and account for the black hole by imposing equilibrium boundary
conditions on the surface of an excised sphere (the apparent horizon). In this
paper we focus on irrotational configurations, meaning that both the neutron
star and the black hole are approximately nonspinning in an inertial frame. We
present results for a binary with polytropic index n=1, mass ratio
M_{irr}^{BH}/M_{B}^{NS}=5 and neutron star compaction
M_{ADM,0}^{NS}/R_0=0.0879, where M_{irr}^{BH} is the irreducible mass of the
black hole, M_{B}^{NS} the neutron star baryon rest-mass, and M_{ADM,0}^{NS}
and R_0 the neutron star Arnowitt-Deser-Misner mass and areal radius in
isolation, respectively. Our models represent valid solutions to Einstein's
constraint equations and may therefore be employed as initial data for
dynamical simulations of black hole-neutron star binaries.Comment: 5 pages, 1 figure, revtex4, published in Phys.Rev.
Star Formation with Adaptive Mesh Refinement Radiation Hydrodynamics
I provide a pedagogic review of adaptive mesh refinement (AMR) radiation
hydrodynamics (RHD) methods and codes used in simulations of star formation, at
a level suitable for researchers who are not computational experts. I begin
with a brief overview of the types of RHD processes that are most important to
star formation, and then I formally introduce the equations of RHD and the
approximations one uses to render them computationally tractable. I discuss
strategies for solving these approximate equations on adaptive grids, with
particular emphasis on identifying the main advantages and disadvantages of
various approximations and numerical approaches. Finally, I conclude by
discussing areas ripe for improvement.Comment: 8 pages, to appear in the Proceedings of IAU Symposium 270:
Computational Star Formatio
The topological AC effect on noncommutative phase space
The Aharonov-Casher (AC) effect in non-commutative(NC) quantum mechanics is
studied. Instead of using the star product method, we use a generalization of
Bopp's shift method. After solving the Dirac equations both on noncommutative
space and noncommutative phase space by the new method, we obtain the
corrections to AC phase on NC space and NC phase space respectively.Comment: 8 pages, Latex fil
A -product solver with spectral accuracy for non-autonomous ordinary differential equations
A new method for solving non-autonomous ordinary differential equations is
proposed, the method achieves spectral accuracy. It is based on a new result
which expresses the solution of such ODEs as an element in the so called
-algebra. This algebra is equipped with a product, the -product,
which is the integral over the usual product of two bivariate distributions.
Expanding the bivariate distributions in bases of Legendre polynomials leads to
a discretization of the -product and this allows for the solution to be
approximated by a vector that is obtained by solving a linear system of
equations. The effectiveness of this approach is illustrated with numerical
experiments
Weyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
The knowledge of quantum phase flow induced under the Weyl's association rule
by the evolution of Heisenberg operators of canonical coordinates and momenta
allows to find the evolution of symbols of generic Heisenberg operators. The
quantum phase flow curves obey the quantum Hamilton's equations and play the
role of characteristics. At any fixed level of accuracy of semiclassical
expansion, quantum characteristics can be constructed by solving a coupled
system of first-order ordinary differential equations for quantum trajectories
and generalized Jacobi fields. Classical and quantum constraint systems are
discussed. The phase-space analytic geometry based on the star-product
operation can hardly be visualized. The statement "quantum trajectory belongs
to a constraint submanifold" can be changed e.g. to the opposite by a unitary
transformation. Some of relations among quantum objects in phase space are,
however, left invariant by unitary transformations and support partly geometric
relations of belonging and intersection. Quantum phase flow satisfies the
star-composition law and preserves hamiltonian and constraint star-functions.Comment: 27 pages REVTeX, 6 EPS Figures. New references added. Accepted for
publication to JM
Hydro-without-Hydro Framework for Simulations of Black Hole-Neutron Star Binaries
We introduce a computational framework which avoids solving explicitly
hydrodynamic equations and is suitable to study the pre-merger evolution of
black hole-neutron star binary systems. The essence of the method consists of
constructing a neutron star model with a black hole companion and freezing the
internal degrees of freedom of the neutron star during the course of the
evolution of the space-time geometry. We present the main ingredients of the
framework, from the formulation of the problem to the appropriate computational
techniques to study these binary systems. In addition, we present numerical
results of the construction of initial data sets and evolutions that
demonstrate the feasibility of this approach.Comment: 16 pages, 7 figures. To appear in the Classical and Quantum Gravity
special issue on Numerical Relativit
Constraints on the braneworld from compact stars
According to the braneworld idea, ordinary matter is confined on a
3-dimensional space (brane) that is embedded in a higher-dimensional space-time
where gravity propagates. In this work, after reviewing the limits coming from
general relativity, finiteness of pressure and causality on the brane, we
derive observational constraints on the braneworld parameters from the
existence of stable compact stars. The analysis is carried out by solving
numerically the brane-modified Tolman-Oppenheimer-Volkoff equations, using
different representative equations of state to describe matter in the star
interior. The cases of normal dense matter, pure quark matter and hybrid matter
are considered.Comment: 13 pages, 11 figures, 2 tables; new EoS considered, references and
comments adde
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