Weak compactness of wave maps and harmonic maps

We show that a weak limit of a sequence of wave maps in (1 + 2) dimensions with uniformly bounded energy is again a wave map. Essential ingredients in the proof are Hodge structures related to harmonic maps, ¹ estimates for Jacobians, ¹-BMO duality, a “monotonicity” formula in the hyperbolic context and the concentration compactness method. Application of similar ideas in the elliptic context yields a drastically shortened proof of recent results by Bethuel on Palais-Smale sequences for the harmonic map functional on two dimensional domains and on limits of almost H-surfaces.     

Accuracy and time performance of different schemes of the local field correction PIV technique

Local field correction particle image velocimetry (LFC-PIV) has become an established alternative among high-resolution PIV techniques. Previous works by the authors introduced its implementation by means of simple algorithms. In these works the initial limitation of the method, which was related to the mean distance between particles, was removed. Comparison with other contemporary high-resolution techniques indicates that it offers advantages in robustness and accuracy. The trade-off for this better performance is a heavier computing load. Until now, the computing time that this load requires has not been characterized in detail, since this computing time could be substantially reduced by accepting a reduction in accuracy. This paper focuses on the characterization of the trade-off between time and accuracy, thus offering a new perspective to PIV. In this field, LFC-PIV offers a wide range of possibilities that are described in the paper. Several alternative schemes for LFC-PIV are tested, together with an analysis of the influence of the number of iterations. Performance figures for both accuracy and expended time are given. Metrological evaluation is carried out over synthetic images. A test of coherence between these results and the performance on real images is also presented. The paper shows that even for a limited number of iterations this technique offers advantages.     

Hysteretic resistance spikes in quantum hall ferromagnets without domains

We use spin-density-functional theory to study recently reported hysteretic magnetoresistance rho(xx) spikes in Mn-based 2D electron gases [Phys. Rev. Lett. 89, 266802 (2002)10.1103/PhysRevLett.89.266802]. We find hysteresis loops in our calculated Landau fan diagrams and total energies signaling quantum Hall ferromagnet phase transitions. Spin-dependent exchange-correlation effects are crucial to stabilize the relevant magnetic phases arising from distinct symmetry-broken excited- and ground-state solutions of the Kohn-Sham equations. Besides hysteretic spikes in rho(xx), we predict hysteretic dips in the Hall resistance rho(xy). Our theory, without domain walls, satisfactorily explains the recent data.     

Stress and Strain Analysis of Pipelines with Localized Metal Loss

This paper presents the analysis of stress and strain data acquired with the finite element method and with tests that used post-yielding strain gages bonded onto the external surface of pipes that suffered thickness metal loss and that had been loaded with internal pressure. These metal loss areas were produced by three different processes: actual internal corrosion, careful machining of external patches by spark-erosion, and milling of internal or external patches to simulate limited or extensive strip corrosion defects with depths up to 70% of the pipe’s thickness. Results show that: (1) the extensive longitudinal internal or external defect areas behave as extensive strips with a high degree of freedom to deform elastically and plastically in the circumferential and thickness directions, and (2) large restraints are offered to the longitudinal strains by the non-corroded thick walls parallel to the strip. Using the above experimental observation, a simple mathematical model was developed to predict the burst pressure of pipes with longitudinal extensive and reasonably constant depths of metal loss. This model employed thin-pipe-strength-of-material equations associated to a bulging correction factor, the material’s uniaxial ultimate strength and the von Mises criterion. The onset of plastic collapse predicted by the simple model was successfully compared with results determined from actual hydrostatic tests that were carried out with full scale pipe specimens and from finite element results generated by the use of a commercial program. The developed model was also helpful in showing that the yield and burst behaviors of new or corroded pipeline specimens under laboratory test conditions can be directly compared and extended to the yield and burst behaviors of buried pipeline in field operation.     

Enhancing Intersystem Crossing in Phenotiazinium Dyes by Intercalation into DNA

Phenothiazinium dyes are used as photosensitizers in photodynamic therapy. Their mode of action is related to the generation of triplet excited states by intersystem crossing. Therefore, rationalizing the factors that influence intersystem crossing is crucial to improve the efficacy of photodynamic therapy. Here we employ quantum mechanics/molecular mechanics calculations to investigate the effect of aqueous and nucleic acid environments on the intersystem crossing mechanism in methylene blue. We find that the mechanism by which the triplet states are generated depends strongly on the environment. While intersystem crossing in water is mediated exclusively by vibronic spin–orbit coupling, it is enhanced in DNA due to a second pathway driven by electronic spin–orbit coupling. Competing charge‐transfer processes, which are also possible in the presence of DNA, can therefore be suppressed by a suitable structural functionalization, thereby increasing the efficacy of photodynamic therapy.     

Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions

Elsewhere in this volume (Nogueira et al. (2005) Exp Fluids, in press), the conceptual background that explains the possibility of resolving wavelengths smaller than the size of the interrogation window, with no basic restrictions but sampling, has been explained. Here, a practical implementation of the concepts is performed. To achieve this resolution in iterative PIV processing, an appropriate weighting function can be used, as commented in that reference. Here, the constraints for the design of such weighting functions are presented and analysed. This opens a line of work on possible weighting functions to develop, since the weightings used in these iterative methods, like local field correction particle image velocimetry (LFC-PIV) (Nogueira et al. (1999) Exp Fluids 27(2):107–116), have not been optimised yet. As an example, different weighting functions are commented and tested both on synthetic and real images. The results on these new weightings indicate that the current ones can be improved and the optimisation criteria are open for further advancement.     

Limits on the resolution of correlation PIV iterative methods. Fundamentals

The spatial resolution of correlation particle image velocimetry (PIV) is a frequently addressed issue that still raises scientific interest. In conventional non-iterative PIV, the spatial resolution limits are of common knowledge (Willert and Gharib (1991) Exp Fluids 10:181–193; Raffel et al. (1998) ISBN 3-540-63683-8, Springer, Berlin Heidelberg New York, among others). On the contrary, those advanced iterative multipass methods that use image distortion techniques or multigrid techniques present a more complex scenario. One of the concepts that raises more debate is the limiting effect of the interrogation window size. This paper focuses on the subject, trying to clarify key points. The results indicate that iterative algorithms using an appropriate weighting function eliminate the window size from the ensemble of spatial resolution limits.     

Analysis of Hopf and Takens–Bogdanov Bifurcations in a Modified van der Pol–Duffing Oscillator

We analyze a modified van der Pol–Duffing electronic circuit, modeled by a tridimensional autonomous system of differential equations with Z₂-symmetry. Linear codimension-one and two bifurcations of equilibria give rise to several dynamical behaviours, including periodic, homoclinic and heteroclinic orbits. The local analysis provides, in first approximation, the different bifurcation sets. These local results are used as a guide to apply the adequate numerical methods to obtain a global understanding of the bifurcation sets. The study of the normal form of the Hopf bifurcation shows the presence of cusps of saddle-node bifurcations of periodic orbits. The existence of a codimension-four Hopf bifurcation is also pointed out. In the case of the Takens–Bogdanov bifurcation, several degenerate situations of codimension-three are analyzed in both homoclinic and heteroclinic cases. The existence of a Hopf–Shil'nikov singularity is also shown.     

Near wall characterization of the flow over a two-dimensional steep smooth hill

Near-wall data for the strongly perturbed flow in a neutrally stable boundary layer encountering a steep, smooth, two-dimensional hill are presented. Observations were made on the centerplane of a water channel at thirteen stations relative to the hill by laser Doppler anemometry. The large reverse flow region that is formed on the lee of the hill was particularly scrutinized through seven measuring stations. Results are presented for the mean and turbulent properties of the flow. Wall shear stress was evaluated through fitting procedures that resorted to the near wall behavior of the velocity profile. Logarithmic fits as well as predictions through the Reynolds stress profiles are also presented.     

Investigating the formation and the properties of monoalkyl carbonates in aqueous medium using capillary electrophoresis with capacitively coupled contactless conductivity detection

Although alkyl carbonic acids (ACAs) and their salts are referred to as instable species in aqueous medium, we demonstrate that a monoalkyl carbonate (MAC) can in fact be easily formed from bicarbonate and an alcohol even in the presence of a high amount of water. A CE system with two capacitively coupled contactless conductivity detectors (C?Ds) was used to obtain different parameters about these species and their reactions. Based on the mobilities obtained for a series of alcohols ranging from 1 to 5 carbons, the coefficients of diffusion and the hydrodynamic radii were calculated. When compared with the equivalent carboxylates, MACs have radii systematically smaller. Although the precise pK(a) values of the ACAs could not be obtained, because of the fast decomposition in acid medium, it was possible, for the first time, to show that they are below 4.0. This result suggests that the acidity of an ACA is quite similar to the first hydrogen of H?CO?. Using a new approach to indirectly calibrate the C?D, the kinetic constants and the equilibrium constants of formation were also obtained. The results suggest that the increase in the chain length makes the MACs less stable and more inert.