1,027 research outputs found
Topological Evolution of a Fast Magnetic Breakout CME in 3-Dimensions
W present the extension of the magnetic breakout model for CME initiation to a fully 3-dimensional, spherical geometry. Given the increased complexity of the dynamic magnetic field interactions in 3-dimensions, we first present a summary of the well known axisymmetric breakout scenario in terms of the topological evolution associated with the various phases of the eruptive process. In this context, we discuss the completely analogous topological evolution during the magnetic breakout CME initiation process in the simplest 3-dimensional multipolar system. We show that an extended bipolar active region embedded in an oppositely directed background dipole field has all the necessary topological features required for magnetic breakout, i.e. a fan separatrix surface between the two distinct flux systems, a pair of spine fieldlines, and a true 3-dimensional coronal null point at their intersection. We then present the results of a numerical MHD simulation of this 3-dimensional system where boundary shearing flows introduce free magnetic energy, eventually leading to a fast magnetic breakout CME. The eruptive flare reconnection facilitates the rapid conversion of this stored free magnetic energy into kinetic energy and the associated acceleration causes the erupting field and plasma structure to reach an asymptotic eruption velocity of greater than or approx. equal to 1100 km/s over an approx.15 minute time period. The simulation results are discussed using the topological insight developed to interpret the various phases of the eruption and the complex, dynamic, and interacting magnetic field structures
Sparse Deterministic Approximation of Bayesian Inverse Problems
We present a parametric deterministic formulation of Bayesian inverse
problems with input parameter from infinite dimensional, separable Banach
spaces. In this formulation, the forward problems are parametric, deterministic
elliptic partial differential equations, and the inverse problem is to
determine the unknown, parametric deterministic coefficients from noisy
observations comprising linear functionals of the solution.
We prove a generalized polynomial chaos representation of the posterior
density with respect to the prior measure, given noisy observational data. We
analyze the sparsity of the posterior density in terms of the summability of
the input data's coefficient sequence. To this end, we estimate the
fluctuations in the prior. We exhibit sufficient conditions on the prior model
in order for approximations of the posterior density to converge at a given
algebraic rate, in terms of the number of unknowns appearing in the
parameteric representation of the prior measure. Similar sparsity and
approximation results are also exhibited for the solution and covariance of the
elliptic partial differential equation under the posterior. These results then
form the basis for efficient uncertainty quantification, in the presence of
data with noise
Conditioning bounds for traveltime tomography in layered media
This paper revisits the problem of recovering a smooth, isotropic, layered
wave speed profile from surface traveltime information. While it is classic
knowledge that the diving (refracted) rays classically determine the wave speed
in a weakly well-posed fashion via the Abel transform, we show in this paper
that traveltimes of reflected rays do not contain enough information to recover
the medium in a well-posed manner, regardless of the discretization. The
counterpart of the Abel transform in the case of reflected rays is a Fredholm
kernel of the first kind which is shown to have singular values that decay at
least root-exponentially. Kinematically equivalent media are characterized in
terms of a sequence of matching moments. This severe conditioning issue comes
on top of the well-known rearrangement ambiguity due to low velocity zones.
Numerical experiments in an ideal scenario show that a waveform-based model
inversion code fits data accurately while converging to the wrong wave speed
profile
Disk and circumsolar radiances in the presence of ice clouds
The impact of ice clouds on solar disk and circumsolar radiances is investigated using a Monte Carlo radiative transfer model. The monochromatic direct and diffuse radiances are simulated at angles of 0 to 8Ā° from the center of the sun. Input data for the model are derived from measurements conducted during the 2010 Small Particles in Cirrus (SPARTICUS) campaign together with state-of-the-art databases of optical properties of ice crystals and aerosols. For selected cases, the simulated radiances are compared with ground-based radiance measurements obtained by the Sun and Aureole Measurements (SAM) instrument. First, the sensitivity of the radiances to the ice cloud properties and aerosol optical thickness is addressed. The angular dependence of the disk and circumsolar radiances is found to be most sensitive to assumptions about ice crystal roughness (or, more generally, non-ideal features of ice crystals) and size distribution, with ice crystal habit playing a somewhat smaller role. Second, in comparisons with SAM data, the ice cloud optical thickness is adjusted for each case so that the simulated radiances agree closely (i.e., within 3āÆ%) with the measured disk radiances. Circumsolar radiances at angles larger than āā3Ā° are systematically underestimated when assuming smooth ice crystals, whereas the agreement with the measurements is better when rough ice crystals are assumed. Our results suggest that it may well be possible to infer the particle roughness directly from ground-based SAM measurements. In addition, the results show the necessity of correcting the ground-based measurements of direct radiation for the presence of diffuse radiation in the instrument's field of view, in particular in the presence of ice clouds.Peer reviewe
A general wavelet-based profile decomposition in the critical embedding of function spaces
We characterize the lack of compactness in the critical embedding of
functions spaces having similar scaling properties in the
following terms : a sequence bounded in has a subsequence
that can be expressed as a finite sum of translations and dilations of
functions such that the remainder converges to zero in as
the number of functions in the sum and tend to . Such a
decomposition was established by G\'erard for the embedding of the homogeneous
Sobolev space into the in dimensions with
, and then generalized by Jaffard to the case where is a Riesz
potential space, using wavelet expansions. In this paper, we revisit the
wavelet-based profile decomposition, in order to treat a larger range of
examples of critical embedding in a hopefully simplified way. In particular we
identify two generic properties on the spaces and that are of key use
in building the profile decomposition. These properties may then easily be
checked for typical choices of and satisfying critical embedding
properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older
and BMO spaces.Comment: 24 page
Sparsity and Incoherence in Compressive Sampling
We consider the problem of reconstructing a sparse signal from a
limited number of linear measurements. Given randomly selected samples of
, where is an orthonormal matrix, we show that minimization
recovers exactly when the number of measurements exceeds where is the number of
nonzero components in , and is the largest entry in properly
normalized: . The smaller ,
the fewer samples needed.
The result holds for ``most'' sparse signals supported on a fixed (but
arbitrary) set . Given , if the sign of for each nonzero entry on
and the observed values of are drawn at random, the signal is
recovered with overwhelming probability. Moreover, there is a sense in which
this is nearly optimal since any method succeeding with the same probability
would require just about this many samples
Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn
We generalize the concept of separable dual-space Gaussian pseudopotentials
to the relativistic case. This allows us to construct this type of
pseudopotential for the whole periodic table and we present a complete table of
pseudopotential parameters for all the elements from H to Rn. The relativistic
version of this pseudopotential retains all the advantages of its
nonrelativistic version. It is separable by construction, it is optimal for
integration on a real space grid, it is highly accurate and due to its analytic
form it can be specified by a very small number of parameters. The accuracy of
the pseudopotential is illustrated by an extensive series of molecular
calculations
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