The route to chaos for the Kuramoto-Sivashinsky equation

We present the results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. Our concern is with the asymptotic nonlinear dynamics as the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic (in time) attractor, to another steady fully modal attractor, to another time-periodic attractor, to a steady tetramodal attractor, to another time-periodic attractor having a full sequence of period-doublings (in the parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the lengths of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period-doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4.669201609.... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.This research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NASI-18605 while the authors were in residence at the Institute of Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665. Additional support for the second author was provided by ONR Grant N-00014-86-K-0691 while he was at UCLA.     

Sensitivity analysis of the Bagley correction to shear and extensional rheology

The excess pressure losses due to end effects in the capillary flow of two linear low-density polyethylene resins (LLDPE) were studied. These losses were first determined experimentally by using two methods: 1) by extrapolating experimental data of pressure drop versus length-to-radius ratios (L/R) to zero capillary length and 2) by means of using orifice dies (L/R≅0). Both methods resulted in practically the same end corrections. Numerical simulation was also used to model this important aspect of experimental rheology. The constitutive equations used in the simulations are a multimode K-BKZ equation, a multimode Phan-Thien/Tanner, and finally a purely viscous Carreau equation. It was found that the numerical predictions agreed qualitatively but underestimated the experimental data for the various geometries used to determine the end effects. Furthermore, it is demonstrated that the entrance pressure loss is also insensitive to extensional rheology, while it depends more strongly on the shear rheology. This finding raises doubts as to the usefulness of end pressure (known also as Bagley correction) as a method of determining the extensional viscosity of polymer melts at high rates. Received: 18 December 1997 Accepted: 21 May 1998     

A quality control method for detecting and suppressing uncorrected residual motion in fMRI studies

Motion correction is an important step in the functional magnetic resonance imaging (fMRI) analysis pipeline. While many studies simply exclude subjects who are estimated to have moved beyond an arbitrary threshold, there exists no objective method for determining an appropriate threshold. Furthermore, any criterion based only upon motion estimation ignores the potential for proper realignment. The method proposed here uses unsupervised learning (specifically k-means clustering) on features derived from the mean square derivative (MSD) of the signal before and after realignment to identify problem data. These classifications are refined through analysis of correlation between subject activation maps and the mean activation map, as well as the relationship between tasking and motion as measured through regression of the canonical hemodynamic response functions to fit both estimated motion parameters and MSD. The MSD is further used to identify specific scans containing residual motion, data which is suppressed by adding nuisance regressors to the general linear model; this statistical suppression is performed for identified problem subjects, but has potential for use over all subjects. For problem subjects, our results show increased hemodynamic activity more consistent with group results; that is, the addition of nuisance regressors resulted in a doubling of the correlation between the activation map for the problem subjects and the activation map for all subjects. The proposed method should be useful in helping fMRI researchers make more efficient use of their data by reducing the need to exclude entire subjects from studies and thus collect new data to replace excluded subjects.     

Reactions of o‐quinones with α‐methyl‐ (or methylene) substituted phosphorus ylides. Synthesis of benzo[b]furan derivatives

In Wittig reaction of some α‐methyl‐ and α‐methylene‐substituted phosphorus ylides with o‐quinones, benzo[b]furan derivatives were obtained via the cyclization of the o‐vinylphenols, initially formed from the tautomerization of the corresponding intermediate o‐quinone methides.     

Development of an HPLC multi-residue method for the determination of ten quinolones in bovine liver and porcine kidney according to the European Union Decision 2002/657/EC

A sensitive multi-residue analytical method was developed for the determination of ten quinolones: enoxacin, ofloxacin, norfloxacin, ciprofloxacin, danofloxacin, enrofloxacin, sarafloxacin, oxolinic acid, nalidixic acid, and flumequine in bovine liver and porcine kidney. A simple liquid extraction step followed by a solid phase extraction clean up procedure was applied for the extraction of quinolones from liver and kidney tissues. Recoveries of the extraction varied between 82 and 88% for bovine liver and 92 and 95% for porcine kidney. Separation was performed on an ODS-3 PerfectSil Target (250 x 4 mm) 5 microm analytical column at 25 degrees C. The mobile phase consisted of a mixture of TFA 0.1%-CH(3)CN-CH(3)OH, delivered at a flow rate of 1.2 mL/min according to a gradient program. Elution of quinolones and the internal standard (caffeine, 7.5 ng/microL) was complete within 27 min. Photodiode array detection was used for monitoring the eluants at 275 and 255 nm. The method was fully validated according to the European Union Decision 2002/657/EC, determining linearity, selectivity, decision limit, detection capability, accuracy, and precision. The LODs of the specific method of quinolone determination in bovine liver varied between 3 and 7 microg/kg and in porcine kidney between 3 and 4 microg/kg.     

Nonlocal surface-wave solitons

We demonstrate, experimentally and theoretically, surface-wave solitons occurring at the interface between a dielectric medium (air) and a nonlinear material with a very long-range nonlocal response. These surface solitons are always attracted toward the surface, and unlike their Kerr-like counterparts, they do not exhibit a power threshold.     

Development and validation of an HPLC confirmatory method for residue analysis of ten quinolones in tissues of various food-producing animals, according to the European Union Decision 2002/657/EC

The aim of this work was to develop an HPLC method for the simultaneous determination of ten quinolones: enoxacin, ofloxacin, norfloxacin, ciprofloxacin, danofloxacin, enrofloxacin, sarafloxacin, oxolinic acid, nalidixic acid, and flumequine, in various tissues of food-producing animals. Separation was achieved on a PerfectSil Target column (250 mm x 4 mm, ODS-3, 5 microm), by MZ-Analysentechnik (Germany), at room temperature. The mobile phase consisted of 0.1% TFA-CH(3)OH-CH(3)CN and was delivered by a gradient program of 35 min. The detection and quantitation was performed on a photodiode array detector at 275 and 255 nm. Caffeine (7.5 ng/microL) was used as the internal standard (IS). Analytes were isolated from tissue samples by 0.1% methanolic TFA solution. SPE, using LiChrolut RP-18 cartridges, was applied for further purification. The extraction protocol was optimized and the final recoveries varied between 92.0 and 107.4%. The method was fully validated according to Commission Decision 2002/657/EC. Limits of quantitation for the examined quinolones extracted from each tissue were much lower than the respective Maximum Residue Levels, ranging between 30 and 50 microg/kg for bovine tissue, between 30 and 55 microg/kg for ovine tissue, and between 40 and 50 microg/kg for porcine tissue.     

Elemental concentrations in sediments of the Patras Harbour, Greece, using INAA, ICP-MS and AAS

Twenty marine sediment samples, selected downcore from six sediment cores, which were retrieved from the Patras Harbour, were studied for their elemental composition using three analytical techniques: INAA, ICP-MS and AAS. Standard reference materials were used to verify the accuracy of the analysis techniques. In total, the concentrations of 30 major, minor and trace elements were measured. The vertical distribution of most elements in the examined cores could be characterized as relatively uniform. The eastern part of the harbour seems to be more polluted in respect to some elements (Ag, Br, Cd, Cr, Cu, Pb and Zn) compared to the western one. The concentrations of a number of elements (As, Cd, Cr, Cu, Ni, Pb and Zn) determined in the sediment samples of the present work are discussed regarding to those obtained from other harbours in the world and compared against sediment quality guidelines (SQGs) to assess the ecotoxicological significance of the sediment contaminants to benthic biota.     

Synthesis of oxadiazoloquinoxaline,oxathiadiazoloquinoxaline and oxadiazolobenzothiazine derivatives

Bis‐amidoxime 1 reacts with phosgene, thiophosgene and thionylchloride to give the corresponding bisfused oxadiazolo‐ and oxathiadiazoloquinoxalines 2, 4, 5 along with the unexpected furazano‐derivative 3 , while monoamidoximes 9, 13 by treatment with ethyl chloroformate affords the oxadiazoloquinoxaline and the oxadiazolobenzothiazine derivatives 14, 15 along with the dicarboxylated product 16 .     

Brane Cosmology From Heterotic String Theory

We consider brane cosmologies within the context of five-dimensional effective actions with higher curvature corrections. The actions are compatible with bulk string amplitude calculations from heterotic string theory. We find wrapped solutions that satisfy the field equations in an approximate but acceptable manner given their complexity, where the internal, four-dimensional, scale factor is naturally inflating, having an exponential De-Sitter form. The temporal dependence of the metric components is nontrivial so that this metric cannot be factored as in a conformally flat case. The effective Planck mass is finite and the brane solutions can localize four-dimensional gravity while the four-dimensional gravitational constant varies with time. The Hubble constant can be freely specified through the initial value of the scalar field, to conform with recent data.