19,668 research outputs found
A pseudospectral matrix method for time-dependent tensor fields on a spherical shell
We construct a pseudospectral method for the solution of time-dependent,
non-linear partial differential equations on a three-dimensional spherical
shell. The problem we address is the treatment of tensor fields on the sphere.
As a test case we consider the evolution of a single black hole in numerical
general relativity. A natural strategy would be the expansion in tensor
spherical harmonics in spherical coordinates. Instead, we consider the simpler
and potentially more efficient possibility of a double Fourier expansion on the
sphere for tensors in Cartesian coordinates. As usual for the double Fourier
method, we employ a filter to address time-step limitations and certain
stability issues. We find that a tensor filter based on spin-weighted spherical
harmonics is successful, while two simplified, non-spin-weighted filters do not
lead to stable evolutions. The derivatives and the filter are implemented by
matrix multiplication for efficiency. A key technical point is the construction
of a matrix multiplication method for the spin-weighted spherical harmonic
filter. As example for the efficient parallelization of the double Fourier,
spin-weighted filter method we discuss an implementation on a GPU, which
achieves a speed-up of up to a factor of 20 compared to a single core CPU
implementation.Comment: 33 pages, 9 figure
Fast, Scalable, and Interactive Software for Landau-de Gennes Numerical Modeling of Nematic Topological Defects
Numerical modeling of nematic liquid crystals using the tensorial Landau-de
Gennes (LdG) theory provides detailed insights into the structure and
energetics of the enormous variety of possible topological defect
configurations that may arise when the liquid crystal is in contact with
colloidal inclusions or structured boundaries. However, these methods can be
computationally expensive, making it challenging to predict (meta)stable
configurations involving several colloidal particles, and they are often
restricted to system sizes well below the experimental scale. Here we present
an open-source software package that exploits the embarrassingly parallel
structure of the lattice discretization of the LdG approach. Our
implementation, combining CUDA/C++ and OpenMPI, allows users to accelerate
simulations using both CPU and GPU resources in either single- or multiple-core
configurations. We make use of an efficient minimization algorithm, the Fast
Inertial Relaxation Engine (FIRE) method, that is well-suited to large-scale
parallelization, requiring little additional memory or computational cost while
offering performance competitive with other commonly used methods. In
multi-core operation we are able to scale simulations up to supra-micron length
scales of experimental relevance, and in single-core operation the simulation
package includes a user-friendly GUI environment for rapid prototyping of
interfacial features and the multifarious defect states they can promote. To
demonstrate this software package, we examine in detail the competition between
curvilinear disclinations and point-like hedgehog defects as size scale,
material properties, and geometric features are varied. We also study the
effects of an interface patterned with an array of topological point-defects.Comment: 16 pages, 6 figures, 1 youtube link. The full catastroph
2D Multi-Angle, Multi-Group Neutrino Radiation-Hydrodynamic Simulations of Postbounce Supernova Cores
We perform axisymmetric (2D) multi-angle, multi-group neutrino
radiation-hydrodynamic calculations of the postbounce phase of core-collapse
supernovae using a genuinely 2D discrete-ordinate (S_n) method. We follow the
long-term postbounce evolution of the cores of one nonrotating and one
rapidly-rotating 20-solar-mass stellar model for ~400 milliseconds from 160 ms
to ~550 ms after bounce. We present a multi-D analysis of the multi-angle
neutrino radiation fields and compare in detail with counterpart simulations
carried out in the 2D multi-group flux-limited diffusion (MGFLD) approximation
to neutrino transport. We find that 2D multi-angle transport is superior in
capturing the global and local radiation-field variations associated with
rotation-induced and SASI-induced aspherical hydrodynamic configurations. In
the rotating model, multi-angle transport predicts much larger asymptotic
neutrino flux asymmetries with pole to equator ratios of up to ~2.5, while
MGFLD tends to sphericize the radiation fields already in the optically
semi-transparent postshock regions. Along the poles, the multi-angle
calculation predicts a dramatic enhancement of the neutrino heating by up to a
factor of 3, which alters the postbounce evolution and results in greater polar
shock radii and an earlier onset of the initially rotationally weakened SASI.
In the nonrotating model, differences between multi-angle and MGFLD
calculations remain small at early times when the postshock region does not
depart significantly from spherical symmetry. At later times, however, the
growing SASI leads to large-scale asymmetries and the multi-angle calculation
predicts up to 30% higher average integral neutrino energy deposition rates
than MGFLD.Comment: 20 pages, 21 figures. Minor revisions. Accepted for publication in
ApJ. A version with high-resolution figures may be obtained from
http://www.stellarcollapse.org/papers/Ott_et_al2008_multi_angle.pd
Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
Based on recent work on simplicial diffeomorphisms in colored group field
theories, we develop a representation of the colored Boulatov model, in which
the GFT fields depend on variables associated to vertices of the associated
simplicial complex, as opposed to edges. On top of simplifying the action of
diffeomorphisms, the main advantage of this representation is that the GFT
Feynman graphs have a different stranded structure, which allows a direct
identification of subgraphs associated to bubbles, and their evaluation is
simplified drastically. As a first important application of this formulation,
we derive new scaling bounds for the regularized amplitudes, organized in terms
of the genera of the bubbles, and show how the pseudo-manifolds configurations
appearing in the perturbative expansion are suppressed as compared to
manifolds. Moreover, these bounds are proved to be optimal.Comment: 28 pages, 17 figures. Few typos fixed. Minor corrections in figure 6
and theorem
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