The Proper Orthogonal Decomposition, wavelets and modal approaches to the dynamics of coherent structures

We present brief précis of three related investigations. Fuller accounts can be found elsewhere. The investigations bear on the identification and prediction of coherent structures in turbulent shear flows. A second unifying thread is the Proper Orthogonal Decomposition (POD), or Karhunen-Loève expansion, which appears in all three investigations described. The first investigation demonstrates a close connection between the coherent structures obtained using linear stochastic estimation, and those obtained from the POD. Linear stochastic estimation is often used for the identification of coherent structures. The second investigation explores the use (in homogeneous directions) of wavelets instead of Fourier modes, in the construction of dynamical models; the particular problem considered here is the Kuramoto-Sivashinsky equation. The POD eigenfunctions, of course, reduce to Fourier modes in homogeneous situations, and either can be shown to converge optimally fast; we address the question of how rapidly (by comparison) a wavelet representation converges, and how the wavelet-wavelet interactions can be handled to construct a simple model. The third investigation deals with the prediction of POD eigenfunctions in a turbulent shear flow. We show that energy-method stability theory, combined with an anisotropic eddy viscosity, and erosion of the mean velocity profile by the growing eigenfunctions, produces eigenfunctions very close to those of the POD, and the same eigenvalue spectrum at low wavenumbers.Prepared for presentation at International Union of Theoretical and Applied Mechanics Symposium Eddy Structure Identification in Free Turbulent Shear Flows, Poitiers, France, 12–14 October 1992. Supported in part by: the U.S. Air Force Office of Scientific Research, The U.S. Office of Naval Research (Mechanics Branch and Physical Oceanography Program), and the U.S. National Science Foundation (program in Physical Oceanography).     

Averaged dynamics of time-periodic advection diffusion equations in the limit of small diffusivity

We study the effect of advection and small diffusion on passive tracers. The advecting velocity field is assumed to have mean zero and to possess time-periodic stream lines. Using a canonical transform to action-angle variables followed by a Lie transform, we derive an averaged equation describing the effective motion of the tracers. An estimate for the time validity of the first-order approximation is established. For particular cases of a regularized vortical flow we present explicit formulas for the coefficients of the averaged equation both at first and at second order. Numerical simulations indicate that the validity of the above first-order estimate extends to the second order.     

New cyclic aminimides containing pyrazolone skeleton

The synthetic route to 1,1-dimethylpyrazolin-5-on-1,2-aminimides ($\text{2}$), is described, involving the cyclization of diethyl acylmalonates ($\text{1}$) with 1,1-dimethylhydrazine.     

Electronic and ESR Spectra of Copper(II) Complexes with N,N-Dialkyl Amino Acids

Five N,N-dialkylamino acids were synthesised [4]: N,N-dimethylisoleucine (DMIL), N,N-dimethyl-alloisoleucine (DMAIL), N,N-dimethylvaline (DMV), N,N-diethyl-alanine (DEA), and N,N-diethylvaline (DEV), as well as their complexes with copper(II): Cu(DMIL)₂, Cu(DMAIL)₂, Cu(DMV)₂, Cu(DMIL)(DMV), Cu(DEA)₂, and Cu(DEV)₂. UV/VIS spectra of the complexes were recorded in CH₂Cl₂ solutions and the ESR spectra in CH₂Cl₂, CD₃OD, and D₂O solutions. By applying the analysis of variance, ESR spectra were shown to be influenced by the solvent and substituent differences, the former effect being related to the degree of covalency of the copper-ligand bonds. The effect of the ligand's spatial configuration (diastereoisomerism) upon the ESR spectrum of the complex was demonstrated and explained.     

Stereoselective oxidation of gem-disulphides with aspergillus niger

A strain of Aspergillus niger was used to prepare optically active gem-disulphide S-oxides 2 and 3 and the (s)-meso-disulphoxide 4. The structural assignment was made by intercorrelating the senses of NMR non-equivalence in pseudoasymmetric disulphoxides 4 and 5 of established configurations with the configurationally related monosulphoxides 2 and 3. The enantiomeric composition and absolute configurations were determined using the chiral solvent NMR method. The stereoselectivity in the microbial oxidation was found to be independent of the configuration of the incipient chiral centre at carbon.     

Determination of organotin compounds (OTC) at low levels in seawater by solid-phase extraction (SPE) and gas chromatography-pulsed flame photometric detection (GC-PFPD)

In this work, a simple, sensitive and affordable analytical method for the simultaneous determination of nine organotin compounds (butyltins, phenyltins and methyltins) in seawater using solid-phase extraction (SPE) and gas chromatography-pulsed flame photometric detection was developed and validated. The performance of three different SPE cartridges (Envi C₁₈, Oasis HLB and Oasis MCX) and three elution solvents of different polarity (hexane, methanol and acetonitrile) was evaluated. The extraction parameters, such as solvent volume, presence of complexing and ion-pairing reagents, sample volume and pH and breakthrough volume, were also investigated. Tributyltin, as the organotin compound of special interest, was efficiently extracted using any of the cartridges and solvents tested. However, the simultaneous extraction of all nine organotin compounds was the most efficient using reversed-phase Envi C₁₈ cartridge and 0.1% (w/v) tropolone in methanol as eluent. The optimised method resulted in good recovery, precision and linearity for all compounds, particularly for tri- and disubstituted species. Method detection limits ranged from 0.22 to 1.27 ng(Sn) L^?1 for butyltins, 0.37 to 4.91 ng(Sn) L^?1 for phenyltins and 0.45 to 1.16 ng(Sn) L^?1 for methyltins. The accuracy of butyltins determination was further verified by the comparison with purchased derivatised standards. The developed method was successfully applied to the environmental samples.     

Correction to: Development of electrochemistry in Serbia-challenges and perspectives

Journal of Solid State Electrochemistry -