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

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

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

Growing condensate in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard $k^{-5/3}$ one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to $k^{-1}$. The fluctuations decay slowly as the coherent part grows.Comment: 4 pages, 4 figures. This version includes some additional phenomenological explanations of the results, additional references and improved figure

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

Dynamics of non-equilibrium membrane bud formation

The dynamical response of a lipid membrane to a local perturbation of its molecular symmetry is investigated theoretically. A density asymmetry between the two membrane leaflets is predominantly released by in-plane lipid diffusion or membrane curvature, depending upon the spatial extent of the perturbation. It may result in the formation of non-equilibrium structures (buds), for which a dynamical size selection is observed. A preferred size in the micrometer range is predicted, as a signature of the crossover between membrane and solvent dominated dynamical membrane response.Comment: 7 pages 3 figure

Self-Organized Criticality and Stock Market Dynamics: an Empirical Study

The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that the market is in a self-organized critical state (SOC). A wavelet transform method is used in order to separate high activity periods, related to the avalanches of sandpile models, from quiescent. A statistical analysis of the filtered data show a power law behaviour in the avalanche size, duration and laminar times. The memory process, implied by the power law distribution, of the laminar times is not consistent with classical conservative models for self-organized criticality. We argue that a ``near-SOC'' state or a time dependence in the driver, which may be chaotic, can explain this behaviour.Comment: 16 pages, 13 figures. In press: Physica

Molecular insights into mitochondrial DNA replication

Mitochondria are organelles found in eukaryotic cells. These organelles produce most of the adenosine triphosphate that cells use as a source of energy. Mitochondria contain their own genomic material, a circular DNA genome (mtDNA) that encodes subunits of the respiratory chain complexes and RNA components needed for mitochondrial translation. Many aspects of mtDNA replication are still not understood and in this thesis we address some of the molecular mechanisms of this process in mammalian cells. DNA synthesis cannot be initiated de novo, but requires a short RNA primer as a starting point. We here demonstrate that the mitochondrial RNA polymerase (POLRMT) is the primase required for initiation of DNA synthesis from the origin of light strand DNA replication (OriL) in human mtDNA. Using purified POLRMT and the core factors of the mitochondrial replisome, we faithfully reconstitute OriLdependent initiation of replication in vitro. During origin activation, OriL is exposed in its single-stranded conformation and adopts a stem-loop structure. POLRMT initiates primer synthesis from a poly-dT stretch in the single-stranded loop region and after about 25 nt, POLRMT is replaced by the mitochondrial DNA polymerase ! (POL!) and DNA synthesis is initiated. Our findings also suggest that the mitochondrial single-stranded DNA binding protein directs origin-specific initiation by efficiently blocking unspecific initiation events in other regions of the mtDNA genome. To analyze the requirements of OriL in vivo, we have used saturation mutagenesis in the mouse combined with in vitro biochemistry and demonstrated that OriL is essential for mtDNA maintenance. OriL requires a stable stem-loop structure and a pyrimidine-rich sequence in the template strand for proper origin function. The OriL mechanism appears to be conserved, since bioinformatics analyses demonstrated the presence of OriL in the mtDNA of most vertebrates including birds. Our findings suggest that mtDNA replication may be performed by a common mechanism in all vertebrates and lend support to the strand-displacement model for mtDNA replication. A molecular understanding of the mitochondrial DNA replication machinery is also of medical importance. Today, more than 160 mutations in the gene encoding the catalytic subunit of POL! (POL!A) have been associated with human disease. One example is the Y955C mutation, which causes autosomal dominant progressive external ophthalmoplegia, a disorder characterized by the accumulation of multiple mtDNA deletions. The Y955C mutation decreases POL! processivity due to a decreased binding affinity for the incoming deoxyribonucleoside triphosphate. However, it is not clear why this biochemical defect leads to a dominant disease. We have used the reconstituted mammalian mtDNA replisome and studied functional consequences of the dominant Y955C mutation. Our study revealed that the POL!A:Y955C enzyme is prone to stalling at dATP insertion sites and instead enters a polymerase/exonuclease idling mode. The mutant POL!A:Y955C competes with wild-type POL!A for access to the primer template. However, once assembled in the replisome, the wild-type enzyme is no longer affected. Our data therefore provide a mechanism for the mtDNA replication phenotypes seen in patients harboring the Y955C mutation

A method for detection of structure

Context. In order to understand the evolution of molecular clouds it is important to identify the departures from self-similarity associated with the scales of self-gravity and the driving of turbulence. Aims. A method is described based on structure functions for determining whether a region of gas, such as a molecular cloud, is fractal or contains structure with characteristic scale sizes. Methods. Using artificial data containing structure it is shown that derivatives of higher order structure functions provide a powerful way to detect the presence of characteristic scales should any be present and to estimate the size of such structures. The method is applied to observations of hot H2 in the Kleinman-Low nebula, north of the Trapezium stars in the Orion Molecular Cloud, including both brightness and velocity data. The method is compared with other techniques such as Fourier transform and histogram techniques. Results. It is found that the density structure, represented by H2 emission brightness in the K-band (2-2.5micron), exhibits mean characteristic sizes of 110, 550, 1700 and 2700AU. The velocity data show the presence of structure at 140, 1500 and 3500AU. Compared with other techniques such as Fourier transform or histogram, the method appears both more sensitive to characteristic scales and easier to interpret.Comment: Astronomy and Astrophysics, in pres