1,027 research outputs found

    Topological Evolution of a Fast Magnetic Breakout CME in 3-Dimensions

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    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

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    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 NN 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

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    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

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    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 3ā€Æ%) with the measured disk radiances. Circumsolar radiances at angles larger than ā‰ˆā€‰3Ā° 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

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    We characterize the lack of compactness in the critical embedding of functions spaces XāŠ‚YX\subset Y having similar scaling properties in the following terms : a sequence (un)nā‰„0(u_n)_{n\geq 0} bounded in XX has a subsequence that can be expressed as a finite sum of translations and dilations of functions (Ļ•l)l>0(\phi_l)_{l>0} such that the remainder converges to zero in YY as the number of functions in the sum and nn tend to +āˆž+\infty. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space X=HĖ™sX=\dot H^s into the Y=LpY=L^p in dd dimensions with 0<s=d/2āˆ’d/p0<s=d/2-d/p, and then generalized by Jaffard to the case where XX 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 XX and YY that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of XX and YY 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

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    We consider the problem of reconstructing a sparse signal x0āˆˆRnx^0\in\R^n from a limited number of linear measurements. Given mm randomly selected samples of Ux0U x^0, where UU is an orthonormal matrix, we show that ā„“1\ell_1 minimization recovers x0x^0 exactly when the number of measurements exceeds mā‰„Constā‹…Ī¼2(U)ā‹…Sā‹…logā”n, m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n, where SS is the number of nonzero components in x0x^0, and Ī¼\mu is the largest entry in UU properly normalized: Ī¼(U)=nā‹…maxā”k,jāˆ£Uk,jāˆ£\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|. The smaller Ī¼\mu, the fewer samples needed. The result holds for ``most'' sparse signals x0x^0 supported on a fixed (but arbitrary) set TT. Given TT, if the sign of x0x^0 for each nonzero entry on TT and the observed values of Ux0Ux^0 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

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    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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