Wavelet transforms and their applications to MHD and plasma turbulence: a review

Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics based on the wavelet coefficients. We then show how to extract coherent structures out of fully developed turbulent flows using wavelet-based denoising. Finally some multiscale numerical simulation schemes using wavelets are described. Several examples for analyzing, compressing and computing one, two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201

Substructure recovery by 3D Discrete Wavelet Transforms

We present and discuss a method to identify substructures in combined angular-redshift samples of galaxies within Clusters. The method relies on the use of Discrete Wavelet Transform (hereafter DWT) and has already been applied to the analysis of the Coma cluster (Gambera et al. 1997). The main new ingredient of our method with respect to previous studies lies in the fact that we make use of a 3D data set rather than a 2D. We test the method on mock cluster catalogs with spatially localized substructures and on a N-body simulation. Our main conclusion is that our method is able to identify the existing substructures provided that: a) the subclumps are detached in part or all of the phase space, b) one has a statistically significant number of redshifts, increasing as the distance decreases due to redshift distortions; c) one knows {\it a priori} the scale on which substructures are to be expected. We have found that to allow an accurate recovery we must have both a significant number of galaxies ($\approx 200$ for clusters at z$\geq 0.4$ or about 800 at z$\leq$ 0.4) and a limiting magnitude for completeness $m_B=16$. The only true limitation to our method seems to be the necessity of knowing {\it a priori} the scale on which the substructure is to be found. This is an intrinsic drawback of the method and no improvement in numerical codes based on this technique could make up for it.Comment: Accepted for publication in MNRAS. 7 pages, 2 figure

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence

We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences

A Multiresolution Census Algorithm for Calculating Vortex Statistics in Turbulent Flows

The fundamental equations that model turbulent flow do not provide much insight into the size and shape of observed turbulent structures. We investigate the efficient and accurate representation of structures in two-dimensional turbulence by applying statistical models directly to the simulated vorticity field. Rather than extract the coherent portion of the image from the background variation, as in the classical signal-plus-noise model, we present a model for individual vortices using the non-decimated discrete wavelet transform. A template image, supplied by the user, provides the features to be extracted from the vorticity field. By transforming the vortex template into the wavelet domain, specific characteristics present in the template, such as size and symmetry, are broken down into components associated with spatial frequencies. Multivariate multiple linear regression is used to fit the vortex template to the vorticity field in the wavelet domain. Since all levels of the template decomposition may be used to model each level in the field decomposition, the resulting model need not be identical to the template. Application to a vortex census algorithm that records quantities of interest (such as size, peak amplitude, circulation, etc.) as the vorticity field evolves is given. The multiresolution census algorithm extracts coherent structures of all shapes and sizes in simulated vorticity fields and is able to reproduce known physical scaling laws when processing a set of voriticity fields that evolve over time

Rose - Buds : Intermezzo - Redowa

https://digitalcommons.library.umaine.edu/mmb-ps/2124/thumbnail.jp

Dance Of The Daisies : Intermezzo

https://digitalcommons.library.umaine.edu/mmb-ps/1472/thumbnail.jp

Effects of condensed tannins on established populations and on incoming larvae of Trichostrongylus colubriformis and Teladorsagia circumcincta in goats

The use of tanniferous plants or tannins represents one alternative approach to the control of gastrointestinal parasites in ruminants but most data have been obtained in sheep. The current study was therefore performed in goats with two objectives: firstly, to investigate the effects of condensed tannins (CT) on adult populations of Trichostrongylus colubriformis and Teladorsagia circumcincta; secondly, to examine their effects on the establishment of infective larvae of these two species. In experiment 1, two groups of kids were infected with 6 000 L3 of T. colubriformis and 6 000 L3 of T. circumcincta. After 7 weeks, quebracho extracts were administered per os for 8 days to one group. A comparable group which did not receive tannins was included as the control. The kids were slaughtered on week 11. Parasitological and pathophysiological parameters were measured weekly. Worm counts were assessed and mast cells, globule leukocytes and eosinophils were counted in the abomasal and intestinal mucosae. Tannin administration was associated with a decrease in egg excretion, and a decrease in female fecundity, but with no changes in worm numbers. These changes were associated with an increased number of intestinal mast cells. In experiment 2, 24 goats were used according to a 2 2 factorial design, depending on infection and tannin administration. Two groups were either infected with 6 000 L3 of T. colubriformis or T. circumcincta. Within each group, the goats were either drenched or undrenched with tannin extracts. Pathophysiological parameters were measured weekly. Twelve days after the cessation of tannin administration, the goats were slaughtered. Worm counts and female worm fecundity were determined. Tannin consumption was associated with a significant reduction (P < 0.001) of Trichostrongylus populations and a close to significant reduction for Teladorsagia. No effect on fecundity was observed. Our results (1) confirm the consequences of condensed tannins on nematodes in goats as in sheep and (2) indicate divergent effects depending on the parasitic stage exposed to the condensed tannins

Effects of the repeated distribution of sainfoin hay on the resistance and the resilience of goats naturally infected with gastrointestinal nematodes

Due to the high prevalence of anthelmintic resistance in goats, the need to explore novel approaches to control nematodes and to reduce the exclusive reliance on chemotherapy is strongly demanded in this host species. In sheep, several studies have shown that the consumption of tannin-rich legume forages was associated with positive effects on host resilience and resistance to parasite infection. In goats, studies on such interactions between tanniferous plants and nematode infections remain few. The objectives of the current study were to examine under natural conditions the effects of consumption of sainfoin hay by goats on the parasite populations and on host resilience. Eighteen adult cull goats naturally infected with Haemonchus contortus, Teladorsagia circumcincta and Trichostrongylus colubriformis were used in the study. At the start of the assay, the goats were allocated into two groups, balanced according to weight and the levels of egg excretion. The two groups grazed separate pastures for 3 months with similar stocking rates. Goats from group S received each month indoors, for 7 days, sainfoin hay and control goats (group C) received hay of ryegrass. The diets in both groups were made isoenergetic and isoproteic and the refusals measured. Individual parasitological and pathophysiological measurements were performed fortnightly in order to compare host resistance and resilience. At the end of the study, five goats per group were necropsied. The distribution of sainfoin was associated with: (1) a higher consumption of hay; (2) significant, lower levels of nematode egg excretion which was associated with a decrease in worm fertility but no change in worm population; however, the number of intestinal worms was reduced by 50% in group S; (3) a better host resilience. In particular, after 2 months of grazing, two control goats died and half of the remaining animals needed to be treated whereas this was not the case in group S. These differences were related to significant changes in pepsinogen and phosphate values (PCV) but not in pepsinogen and phosphate concentrations. These results demonstrate that a repeated distribution of sainfoin hay to grazing goats might be beneficial in regard of pasture contamination and host resilience. They suggest that administration of sainfoin hay might represent a valuable alternative and adjunct to reduce nematode infections in dairy goat flock. # 2004 Elsevier B.V. All rights reserved

Wavelets and Quantum Algebras

Wavelets, known to be useful in non-linear multi-scale processes and in multi-resolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators of the theory associate with any scaling equation a non-linear, two parameter algebra. This structure can be mapped onto the quantum group $su_{q}(2)$ in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding non-linear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.Comment: 27 pages Latex, 3 figure p