Publications (19) View all
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Article: A multifractal formalism for vector-valued random fields based on wavelet analysis: application to turbulent velocity and vorticity 3D numerical data
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ABSTRACT: Extreme atmospheric events are intimately related to the statistics of atmospheric turbulent velocities. These, in turn, exhibit multifractal scaling, which is determining the nature of the asymptotic behavior of velocities, and whose parameter evaluation is therefore of great interest currently. We combine singular value decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued random fields. The so-called Tensorial Wavelet Transform Modulus Maxima (TWTMM) method is calibrated on synthetic self-similar 2D vector-valued multifractal measures and monofractal 3D vector-valued fractional Brownian fields. We report the results of some application of the TWTMM method to turbulent velocity and vorticity fields generated by direct numerical simulations of the incompressible Navier–Stokes equations. This study reveals the existence of an intimate relationship Dv(h+1)=D\varvecw(h),{D_{{\bf v}}(h+1)=D_{\varvec{\omega}}(h)}, between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.Stochastic Environmental Research and Risk Assessment 04/2012; 22(3):421-435. · 1.52 Impact Factor -
Article: Characterising Complexity in Solar Magnetogram Data using a Wavelet-based Segmentation Method
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ABSTRACT: The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive space-scale partition of the fractal distribution under study, from which one can extract the multifractal singularity spectrum. We describe the implementation of a multiscale image processing segmentation procedure based on the partitioning of the WT skeleton which allows the disentangling of the information concerning the multifractal properties of active regions from the surrounding quiet-Sun field. The quiet Sun exhibits a average H\"older exponent $\sim -0.75$, with observed multifractal properties due to the supergranular structure. On the other hand, active region multifractal spectra exhibit an average H\"older exponent $\sim 0.38$ similar to those found when studying experimental data from turbulent flows. Comment: accepted for publication in ApJ05/2010; -
Article: Characterizing Complexity in Solar Magnetogram Data Using a Wavelet-based Segmentation Method
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ABSTRACT: The multifractal nature of solar photospheric magnetic structures are studied using the 2D wavelet transform modulus maxima (WTMM) method. This relies on computing partition functions from the wavelet transform skeleton defined by the WTMM method. This skeleton provides an adaptive space-scale partition of the fractal distribution under study, from which one can extract the multifractal singular-ity spectrum. We describe the implementation of a multiscale image processing segmentation procedure based on the partitioning of the WT skeleton which allows the disentangling of the information concerning the multifractal properties of active regions from the surrounding quiet-Sun field. The quiet Sun exhibits a average Hölder exponent ∼ −0.75, with observed multifractal properties due to the supergranular struc-ture. On the other hand, active region multifractal spectra exhibit an average Hölder exponent ∼ 0.38 similar to those found when studying experimental data from turbulent flows.04/2010; -
Article: Automated Detection of Coronal Loops using a Wavelet Transform Modulus Maxima Method
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ABSTRACT: We propose and test a wavelet transform modulus maxima method for the au- tomated detection and extraction of coronal loops in extreme ultraviolet images of the solar corona. This method decomposes an image into a number of size scales and tracks enhanced power along each ridge corresponding to a coronal loop at each scale. We compare the results across scales and suggest the optimum set of parameters to maximise completeness while minimising detection of noise. For a test coronal image, we compare the global statistics (e.g., number of loops at each length) to previous automated coronal-loop detection algorithms.02/2010; -
Conference Proceeding: Accelerating Euler Equations Numerical Solver on Graphics Processing Units.
Algorithms and Architectures for Parallel Processing, 10th International Conference, ICA3PP 2010, Busan, Korea, May 21-23, 2010. Proceedings. Part II; 01/2010
