145,860 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
Non-parametric PSF estimation from celestial transit solar images using blind deconvolution
Context: Characterization of instrumental effects in astronomical imaging is
important in order to extract accurate physical information from the
observations. The measured image in a real optical instrument is usually
represented by the convolution of an ideal image with a Point Spread Function
(PSF). Additionally, the image acquisition process is also contaminated by
other sources of noise (read-out, photon-counting). The problem of estimating
both the PSF and a denoised image is called blind deconvolution and is
ill-posed.
Aims: We propose a blind deconvolution scheme that relies on image
regularization. Contrarily to most methods presented in the literature, our
method does not assume a parametric model of the PSF and can thus be applied to
any telescope.
Methods: Our scheme uses a wavelet analysis prior model on the image and weak
assumptions on the PSF. We use observations from a celestial transit, where the
occulting body can be assumed to be a black disk. These constraints allow us to
retain meaningful solutions for the filter and the image, eliminating trivial,
translated and interchanged solutions. Under an additive Gaussian noise
assumption, they also enforce noise canceling and avoid reconstruction
artifacts by promoting the whiteness of the residual between the blurred
observations and the cleaned data.
Results: Our method is applied to synthetic and experimental data. The PSF is
estimated for the SECCHI/EUVI instrument using the 2007 Lunar transit, and for
SDO/AIA using the 2012 Venus transit. Results show that the proposed
non-parametric blind deconvolution method is able to estimate the core of the
PSF with a similar quality to parametric methods proposed in the literature. We
also show that, if these parametric estimations are incorporated in the
acquisition model, the resulting PSF outperforms both the parametric and
non-parametric methods.Comment: 31 pages, 47 figure
Introducing PHAEDRA: a new spectral code for simulations of relativistic magnetospheres
We describe a new scheme for evolving the equations of force-free
electrodynamics, the vanishing-inertia limit of magnetohydrodynamics. This
pseudospectral code uses global orthogonal basis function expansions to take
accurate spatial derivatives, allowing the use of an unstaggered mesh and the
complete force-free current density. The method has low numerical dissipation
and diffusion outside of singular current sheets. We present a range of one-
and two-dimensional tests, and demonstrate convergence to both smooth and
discontinuous analytic solutions. As a first application, we revisit the
aligned rotator problem, obtaining a steady solution with resistivity localised
in the equatorial current sheet outside the light cylinder.Comment: 23 pages, 18 figures, accepted for publication in MNRA
Basic Types of Coarse-Graining
We consider two basic types of coarse-graining: the Ehrenfests'
coarse-graining and its extension to a general principle of non-equilibrium
thermodynamics, and the coarse-graining based on uncertainty of dynamical
models and Epsilon-motions (orbits). Non-technical discussion of basic notions
and main coarse-graining theorems are presented: the theorem about entropy
overproduction for the Ehrenfests' coarse-graining and its generalizations,
both for conservative and for dissipative systems, and the theorems about
stable properties and the Smale order for Epsilon-motions of general dynamical
systems including structurally unstable systems. Computational kinetic models
of macroscopic dynamics are considered. We construct a theoretical basis for
these kinetic models using generalizations of the Ehrenfests' coarse-graining.
General theory of reversible regularization and filtering semigroups in
kinetics is presented, both for linear and non-linear filters. We obtain
explicit expressions and entropic stability conditions for filtered equations.
A brief discussion of coarse-graining by rounding and by small noise is also
presented.Comment: 60 pgs, 11 figs., includes new analysis of coarse-graining by
filtering. A talk given at the research workshop: "Model Reduction and
Coarse-Graining Approaches for Multiscale Phenomena," University of
Leicester, UK, August 24-26, 200
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