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

Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.Comment: AAS Latex file, 44 pages, accepted for publication in Ap

On the Structure and Dynamics of Sheared and Rotating Turbulence: Direct Numerical Simulations and Wavelet Based Coherent Vortex Extraction

The influence of rotation on the structure and dynamics of sheared turbulence is investigated using a series of direct numerical simulations. Five cases are considered: turbulent shear flow without rotation, with moderate rotation, and with strong rotation, where the rotation configuration is either parallel or antiparallel. For moderate rotation rates an antiparallel configuration increases the growth of the turbulent kinetic energy, while the parallel case reduces the growth as compared to the nonrotating case. For strong rotation rates decay of the energy is observed, linear effects dominate the flow, and the vorticity probability density functions tend to become Gaussian. Visualizations of vorticity show that the inclination angle of the vortical structures depends on the rotation rate and orientation. Coherent vortex extraction, based on the orthogonal wavelet decomposition of vorticity, is applied to split the flow into coherent and incoherent parts. It was found that the coherent part preserves the vortical structures using only a few percent of the degrees of freedom. The incoherent part was found to be structureless and of mainly dissipative nature. With increasing rotation rates, the number of wavelet modes representing the coherent vortices decreases, indicating an increased coherency of the flow. Restarting the direct numerical simulation with the filtered fields confirms that the coherent component preserves the temporal dynamics of the total flow, while the incoherent component is of dissipative nature

On the Structure and Dynamics of Sheared and Rotating Turbulence: Anisotropy Properties and Geometrical Scale-Dependent Statistics

This study is based on a series of nine direct numerical simulations of homogeneous turbulence, in which the rotation ratio f/S of Coriolis parameter to shear rate is varied. The presence of rotation stabilizes the flow, except for a narrow range of rotation ratios 0\u3cf/

Stability of parallel wake flows in quasigeostrophic and frontal regimes

International audienceRecent laboratory experiments [G. Perret, A. Stegner, M. Farge, and T. Pichon, Phys. Fluids 18, 036603 (2006)] have shown that the vortex-street formed in the wake of a towed cylinder in a rotating shallow-water layer could present a strong cyclone-anticyclone asymmetry. In extreme cases, only large-scale anticyclones were observed in the far wake. This asymmetry occurs in the so-called frontal regime when the Rossby number is small and the surface deviation is large. This asymmetry may have various origins and in particular may be attributed to the asymmetry of the flow around the cylinder, to the linear stability property of the wake, or to its nonlinear evolution. To discriminate between these mechanisms, we study the stability of two idealized parallel flows in the quasigeostrophic and in the frontal regimes. These parallel flows correspond to two velocity profiles measured just behind the cylinder in a region where the perturbations are negligible. According to our linear stability analysis, the most unstable mode, in the frontal regime, is localized in the anticyclonic shear region whether the base flow profile is symmetric or not. On a linear basis, it is thus more the instability that imposes the asymmetry than the base flow. Direct numerical simulations of the synthetic parallel wake flows show that nonlinearity exacerbates the dominance of the anticyclonic mode linearly selected. By numerically studying the spatio-temporal evolution of a small perturbation localized in space, we show that, unlike incompressible two-dimensional wake flows and the symmetric wake in the quasigeostrophic regime, the parallel asymmetric wake is strongly convectively unstable in the frontal regime, and not absolutely unstable. When the surface deformation becomes large, the wake instability changes from the absolute instability in the quasi-geostrophic regime to the strongly convective instability of the frontal regime. This explains well the changes. © 2006 American Institute of Physics

Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Individual quality assessment of autografting by probability estimation for clinical endpoints: a prospective validation study from the European group for blood and marrow transplantation.

The aim of supportive autografting is to reduce the side effects from stem cell transplantation and avoid procedure-related health disadvantages for patients at the lowest possible cost and resource expenditure. Economic evaluation of health care is becoming increasingly important. We report clinical and laboratory data collected from 397 consecutive adult patients (173 non-Hodgkin lymphoma, 30 Hodgkin lymphoma, 160 multiple myeloma, 7 autoimmune diseases, and 28 acute leukemia) who underwent their first autologous peripheral blood stem cell transplantation (PBSCT). We considered primary endpoints evaluating health economic efficacy (eg, antibiotic administration, transfusion of blood components, and time in hospital), secondary endpoints evaluating toxicity (in accordance with Common Toxicity Criteria), and tertiary endpoints evaluating safety (ie, the risk of regimen-related death or disease progression within the first year after PBSCT). A time-dependent grading of efficacy is proposed with day 21 for multiple myeloma and day 25 for the other disease categories (depending on the length of the conditioning regimen) as the acceptable maximum time in hospital, which together with antibiotics, antifungal, or transfusion therapy delineates four groups: favorable (≤7 days on antibiotics and no transfusions; ≤21 [25] days in hospital), intermediate (from 7 to 10 days on antibiotics and 7 days on antibiotics, >3 but 30/34 days in hospital after transplantation), and very unfavorable (>10 days on antibiotics, >6 transfusions; >30 to 34 days in hospital). The multivariate analysis showed that (1) PBSC harvests of ≥4 × 106/kg CD34 + cells in 1 apheresis procedure were associated with a favorable outcome in all patient categories except acute myelogenous leukemia and acute lymphoblastic leukemia (P = .001), (2) ≥5 × 106/kg CD34 + cells infused predicted better transplantation outcome in all patient categories (P 500 mL) (P = .002), and (5) patients with a central venous catheter during both collection and infusion of PBSC had a more favorable outcome post-PBSCT than peripheral access (P = .007). The type of mobilization regimen did not affect the outcome of auto-PBSCT. The present study identified predictive variables, which may be useful in future individual pretransplantation probability evaluations with the goal to improve supportive care

Cumulants as non-Gaussian qualifiers

We discuss the requirements of good statistics for quantifying non-Gaussianity in the Cosmic Microwave Background. The importance of rotational invariance and statistical independence is stressed, but we show that these are sometimes incompatible. It is shown that the first of these requirements prefers a real space (or wavelet) formulation, whereas the latter favours quantities defined in Fourier space. Bearing this in mind we decide to be eclectic and define two new sets of statistics to quantify the level of non-Gaussianity. Both sets make use of the concept of cumulants of a distribution. However, one set is defined in real space, with reference to the wavelet transform, whereas the other is defined in Fourier space. We derive a series of properties concerning these statistics for a Gaussian random field and show how one can relate these quantities to the higher order moments of temperature maps. Although our frameworks lead to an infinite hierarchy of quantities we show how cosmic variance and experimental constraints give a natural truncation of this hierarchy. We then focus on the real space statistics and analyse the non-Gaussian signal generated by points sources obscured by large scale Gaussian fluctuations. We conclude by discussing the practical implementations of these techniques

Numerical simulation of a new type of cross flow tidal turbine using OpenFOAM - Part II: Investigation of turbine-to-turbine interaction

Copyright © 2013 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Renewable Energy. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Renewable Energy, Volume 50 (2013), DOI: 10.1016/j.renene.2012.08.064Prediction of turbine-to-turbine interaction represents a significant challenge in determining the optimized power output from a tidal stream farm, and this is an active research area. This paper presents a detailed work which examines the influence of surrounding turbines on the performance of a base case (isolated turbine). The study was conducted using a new CFD based, Immersed Body Force (IBF) model, which was validated in the first paper, and an open source CFD software package OpenFOAM was used for the simulations. The influence of the surrounding turbines was investigated using randomly chosen initial lateral and longitudinal spacing among the turbines. The initial spacing was then varied to obtain four configurations to examine the relative effect that positioning can have on the performance of the base turbine

Straightening of Thermal Fluctuations in Semi-Flexible Polymers by Applied Tension

We investigate the propagation of a suddenly applied tension along a thermally excited semi-flexible polymer using analytical approximations, scaling arguments and numerical simulation. This problem is inherently non-linear. We find sub-diffusive propagation with a dynamical exponent of 1/4. By generalizing the internal elasticity, we show that tense strings exhibit qualitatively different tension profiles and propagation with an exponent of 1/2.Comment: Latex file; with three postscript figures; .ps available at http://dept.physics.upenn.edu/~nelson/pull.p