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

Enzymatic Resolution of O-Methyl-N-acetyl-DL-serine.Amino Acids. XXXII

Enzymatic resolution of O-methyl- N-acetyl-DL- serine was carried out following Greenstein\u27s procedure. The thus obtained O-methyl-L- serine was converted under partial racemisation into O-methyl-N-phthaloyl- L-serine, by reaction with phthalic anhydride

Enzymatic Resolution of O-Methyl-N-acetyl-DL-serine.Amino Acids. XXXII

Enzymatic resolution of O-methyl- N-acetyl-DL- serine was carried out following Greenstein\u27s procedure. The thus obtained O-methyl-L- serine was converted under partial racemisation into O-methyl-N-phthaloyl- L-serine, by reaction with phthalic anhydride

Extraction of coherent structures in a rotating turbulent flow experiment

The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional (3D) turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle Image Velocimetry (PIV) measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity fields exhibit vortex birth, merger, scattering, and destruction. We separate the flow into a low-entropy ``coherent'' and a high-entropy ``incoherent'' component by thresholding the coefficients of the DWPT and DWT of the vorticity fields. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWPT and DWT are necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations. The remaining small amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.Comment: experimental work aprox 17 pages, 11 figures, accepted to appear in PRE, last few figures appear at the end. clarifications, added references, fixed typo

Nonlinear non-extensive approach for identification of structured information

The problem of separating structured information representing phenomena of differing natures is considered. A structure is assumed to be independent of the others if can be represented in a complementary subspace. When the concomitant subspaces are well separated the problem is readily solvable by a linear technique. Otherwise, the linear approach fails to correctly discriminate the required information. Hence, a non extensive approach is proposed. The resulting nonlinear technique is shown to be suitable for dealing with cases that cannot be tackled by the linear one.Comment: Physica A, in pres

Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly-cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz--Toeplitz isometries as a special case.Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used for shading, accepted March 2002 for J. Funct. Ana

Extracting optimal tempo-spatial features using local discriminant bases and common spatial patterns for brain computer interfacing

Brain computer interfaces (BCI) provide a new approach to human computer communication, where the control is realised via performing mental tasks such as motor imagery (MI). In this study, we investigate a novel method to automatically segment electroencephalographic (EEG) data within a trial and extract features accordingly in order to improve the performance of MI data classification techniques. A new local discriminant bases (LDB) algorithm using common spatial patterns (CSP) projection as transform function is proposed for automatic trial segmentation. CSP is also used for feature extraction following trial segmentation. This new technique also allows to obtain a more accurate picture of the most relevant temporal–spatial points in the EEG during the MI. The results are compared with other standard temporal segmentation techniques such as sliding window and LDB based on the local cosine transform (LCT)

Towards an Inverse Scattering theory for non decaying potentials of the heat equation

The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a generic decaying potential is considered. It is shown that these potentials describe $N$ solitons superimposed by Backlund transformations to a generic background. Dressing operators and Jost solutions are constructed by solving a DBAR-problem explicitly in terms of the corresponding objects associated to the original potential. Regularity conditions of the potential in the cases N=1 and N=2 are investigated in details. The singularities of the resolvent for the case N=1 are studied, opening the way to a correct definition of the spectral data for a generically perturbed soliton.Comment: 22 pages, submitted to Inverse Problem