20,660 research outputs found
Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres
Interactions between clouds and radiation are at the root of many
difficulties in numerically predicting future weather and climate and in
retrieving the state of the atmosphere from remote sensing observations. The
large range of issues related to these interactions, and in particular to
three-dimensional interactions, motivated the development of accurate radiative
tools able to compute all types of radiative metrics, from monochromatic, local
and directional observables, to integrated energetic quantities. In the
continuity of this community effort, we propose here an open-source library for
general use in Monte Carlo algorithms. This library is devoted to the
acceleration of path-tracing in complex data, typically high-resolution
large-domain grounds and clouds. The main algorithmic advances embedded in the
library are those related to the construction and traversal of hierarchical
grids accelerating the tracing of paths through heterogeneous fields in
null-collision (maximum cross-section) algorithms. We show that with these
hierarchical grids, the computing time is only weakly sensitivive to the
refinement of the volumetric data. The library is tested with a rendering
algorithm that produces synthetic images of cloud radiances. Two other examples
are given as illustrations, that are respectively used to analyse the
transmission of solar radiation under a cloud together with its sensitivity to
an optical parameter, and to assess a parametrization of 3D radiative effects
of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2
Characteristic Evolution and Matching
I review the development of numerical evolution codes for general relativity
based upon the characteristic initial value problem. Progress in characteristic
evolution is traced from the early stage of 1D feasibility studies to 2D
axisymmetric codes that accurately simulate the oscillations and gravitational
collapse of relativistic stars and to current 3D codes that provide pieces of a
binary black hole spacetime. Cauchy codes have now been successful at
simulating all aspects of the binary black hole problem inside an artificially
constructed outer boundary. A prime application of characteristic evolution is
to extend such simulations to null infinity where the waveform from the binary
inspiral and merger can be unambiguously computed. This has now been
accomplished by Cauchy-characteristic extraction, where data for the
characteristic evolution is supplied by Cauchy data on an extraction worldtube
inside the artificial outer boundary. The ultimate application of
characteristic evolution is to eliminate the role of this outer boundary by
constructing a global solution via Cauchy-characteristic matching. Progress in
this direction is discussed.Comment: New version to appear in Living Reviews 2012. arXiv admin note:
updated version of arXiv:gr-qc/050809
Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient
technique to obtain high diversity and coding gain on a block-fading MIMO
channel. Its maximum-likelihood (ML) performance is computed under ideal
interleaving conditions, which enables a global optimization taking into
account channel coding. Thanks to a diversity upperbound derived from the
Singleton bound, an appropriate choice of the time dimension of the space-time
coding is possible, which maximizes diversity while minimizing complexity.
Based on the analysis, an optimized interleaver and a set of linear precoders,
called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed
precoders have good performance with respect to the state of the art and exist
for any number of transmit antennas and any time dimension. With turbo codes,
they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January
2006 - First review: June 200
Hyperboloidal evolution of test fields in three spatial dimensions
We present the numerical implementation of a clean solution to the outer
boundary and radiation extraction problems within the 3+1 formalism for
hyperbolic partial differential equations on a given background. Our approach
is based on compactification at null infinity in hyperboloidal scri fixing
coordinates. We report numerical tests for the particular example of a scalar
wave equation on Minkowski and Schwarzschild backgrounds. We address issues
related to the implementation of the hyperboloidal approach for the Einstein
equations, such as nonlinear source functions, matching, and evaluation of
formally singular terms at null infinity.Comment: 10 pages, 8 figure
General relativistic null-cone evolutions with a high-order scheme
We present a high-order scheme for solving the full non-linear Einstein
equations on characteristic null hypersurfaces using the framework established
by Bondi and Sachs. This formalism allows asymptotically flat spaces to be
represented on a finite, compactified grid, and is thus ideal for far-field
studies of gravitational radiation. We have designed an algorithm based on
4th-order radial integration and finite differencing, and a spectral
representation of angular components. The scheme can offer significantly more
accuracy with relatively low computational cost compared to previous methods as
a result of the higher-order discretization. Based on a newly implemented code,
we show that the new numerical scheme remains stable and is convergent at the
expected order of accuracy.Comment: 24 pages, 3 figure
Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes
We have developed the formalism necessary to employ the
discontinuous-Galerkin approach in general-relativistic hydrodynamics. The
formalism is firstly presented in a general 4-dimensional setting and then
specialized to the case of spherical symmetry within a 3+1 splitting of
spacetime. As a direct application, we have constructed a one-dimensional code,
EDGES, which has been used to asses the viability of these methods via a series
of tests involving highly relativistic flows in strong gravity. Our results
show that discontinuous Galerkin methods are able not only to handle strong
relativistic shock waves but, at the same time, to attain very high orders of
accuracy and exponential convergence rates in smooth regions of the flow. Given
these promising prospects and their affinity with a pseudospectral solution of
the Einstein equations, discontinuous Galerkin methods could represent a new
paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR
Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature
Recently, a family of exact force-free electrodynamic (FFE) solutions was
given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by
Michel, Menon and Dermer, and other authors. These solutions have been proposed
as useful models for describing the outer magnetosphere of conducting stars. As
with any exact analytical solution that aspires to describe actual physical
systems, it is vitally important that the solution possess the necessary
stability. In this paper, we show via fully nonlinear numerical simulations
that the aforementioned FFE solutions, despite being highly special in their
properties, are nonetheless stable under small perturbations. Through this
study, we also introduce a three-dimensional pseudospectral relativistic FFE
code that achieves exponential convergence for smooth test cases, as well as
two additional well-posed FFE evolution systems in the appendix that have
desirable mathematical properties. Furthermore, we provide an explicit analysis
that demonstrates how propagation along degenerate principal null directions of
the spacetime curvature tensor simplifies scattering, thereby providing an
intuitive understanding of why these exact solutions are tractable, i.e. why
they are not backscattered by spacetime curvature.Comment: 33 pages, 21 figures; V2 updated to match published versio
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