Integral Equations, Dichotomy of Evolution Families on the Half-Line and Applications

The purpose of this paper is to provide a new, unified and complete study for uniform dichotomy and exponential dichotomy on the half-line. First we deduce conditions for the existence of uniform dichotomy, using classes of function spaces over _+{\mathbb {R}_+} which are invariant under translations. After that, we obtain a classification of the main classes of function spaces over \mathbb R₊{\mathbb {R}_+}, in order to deduce necessary and sufficient conditions for the existence of exponential dichotomy, emphasizing on the main technical qualitative properties of the underlying spaces. We motivate our approach by illustrative examples and show that the main hypotheses cannot be dropped. We provide optimal methods regarding the input space in the study of dichotomy and deduce as particular cases some interesting situations as well as several dichotomy results published in the past few years.     

Dissimilar electro-osmotic flow and ionic current recirculation patterns in porous media detected by NMR mapping experiments

Random-site percolation clusters were milled into ceramic (polar) and polystyrene (nonpolar) plates as a paradigm for porous media or complex microsystem channel networks. The pore space was filled with electrolyte solutions. Using NMR microscopy techniques, maps of the following quantities were recorded: (i) flow velocity driven by external pressure gradient, (ii) electro-osmotic flow (EOF) velocity, (iii) ionic current density in the presence of EOF, (iv) ionic current density in the absence of EOF. As far as possible, the experiments were supplemented by computational fluid dynamics simulations. It is shown that electro-osmotic flow as well as the electric current density include vortices and recirculation patterns. Remarkably, all transport patterns turned out to be dissimilar, and the occurrence and positions of vortices do not coincide in the different maps.     

Asymptotically optimal estimating equation with strongly consistent solutions for longitudinal data

In this article, we introduce a conditional marginal model for longitudinal data, in which the residuals form a martingale difference sequence. This model allows us to consider a rich class of estimating equations which contains several estimating equations proposed in the literature. A particular sequence of estimating equations in this class contains a random matrix R _i−1^*(β) as a replacement for the “true” conditional correlation matrix of the ith individual. Using the approach of [12], we identify some sufficient conditions under which this particular sequence of equations is asymptotically optimal (in our class). In the second part of the article, we identify a second set of conditions under which we prove the existence and strong consistency of a sequence of estimators of β defined as roots of estimation equations which are martingale transforms (in particular, roots of the sequence of asymptotically optimal equations).     

Long Non-crossing Configurations in the Plane

We revisit some maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1995). Given a set of n points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching, (b) a Hamiltonian path, and (c) a spanning tree. We obtain some new results for (b) and (c), as well as for the Hamiltonian cycle problem.     

Fluorescence Study of Intermolecular Interactions in Diluted Aqueous Solutions of Some Cationic Amphiphilic Polysaccharides

The intermolecular hydrophobic association in diluted aqueous solutions of some cationic amphiphilic polysaccharides was investigated using fluorescence techniques. Dextran and dextran carrying N-alkyl-N,N-dimethyl-N(2-hydroxypropylene) ammonium chloride groups as side chains were single labeled with pyrene or naphthalene. The intensity of the pyrene excimer peak and the ratio I₃/I₁ determined from the fluorescence emission spectra of pyrene-labeled amphiphilic polymer increased with increasing polymer concentration and were higher than in the solution containing pyrene-labeled dextran. Emission spectra of diluted solution (0.008–0.2 g/dl) containing mixtures of pyrene and naphthalene single-labeled amphiphilic polymers proved the occurrence of a nonradiative energy transfer between labels at very a low polymer concentration (<10^?2 g/dl). The energy transfer was not observed in mixtures of single-labeled unmodified dextran. All these results suggest that the intermolecular hydrophobic association of alkyl substituents takes place at a very low concentration of amphiphilic polymers.     

Stable isotope study of precipitation and cave drip water in Florida (USA): implications for speleothem-based paleoclimate studies†

Stable isotopes of hydrogen and oxygen were used to examine how the isotopic signal of meteoric water is modified as it travels through soil and epikarst into two caves in Florida. Surface and cave water samples were collected every week from February 2006 until March 2007. The isotopic composition of precipitation at the investigated sites is highly variable and shows little seasonal control. The δ¹⁸O vs. δ²H plot shows a mixing line having a slope of 5.63, suggesting evaporation effects dominate the isotopic composition of most rainfall events of less than 8 cm/day, as indicated by their low d-excess values. The δ¹⁸O values of the drip water show little variability (<0.6‰), which is loosely tied to local variations in the seasonal amount of precipitation. This is only seen during wintertime at the Florida Caverns site.

The lag time of over two months and the lack of any relationship between rainfall amount and the increase in drip rate indicate a dominance of matrix flow relative to fracture/conduit flow at each site. The long residence time of the vadose seepage waters allows for an effective isotopic homogenisation of individual and seasonal rainfall events. We find no correlation between rainfall and drip water δ¹⁸O at any site. The isotopic composition of drip water in both caves consistently tends to resemble the amount-weighted monthly mean rainfall input. This implies that the δ¹⁸O of speleothems from these two caves in Florida cannot record seasonal cycle in rainfall δ¹⁸O, but are suitable for paleoclimate reconstructions at inter-annual time scales.? Revised version of a paper presented at the 9th, Symposium of the European Society for Isotope Research (ESIR), 23 to 28 June 2007, Cluj-Napoca, Romania.      

Dirichlet problem for the general Beltrami equation in Jordan domains

We study the Dirichlet problem for the general degenerate Beltrami equations $ \bar{\partial}f=\mu \partial f+\nu \overline{{\partial f}} $ in a Jordan domain. Some criteria for the existence of regular solutions are given.     

Influence of pitching on performance of VAWTs

Self- starting is the major obstacle to be overcome for successful design of a vertical axis wind turbine (VAWT). In the past has been suggested that pitching the turbine blades such that pitch angle is not 90 degrees allows for self-starting. To understand the physics surrounding pitching, an analysis is carried out for a common airfoil profile, NACA 0012. The vortex model is used to predict aerodynamic performance of VAWT with pitched blades at various angles. As a result of the analysis carried out for the airfoil at various pitch angles, it was shown that the “dead band” phenomenon could be overcome, but only slightly. At the same time, to overcome the “dead band” with a level on confidence, torques in the tip speed ratio (TSR ) range of 0.75 to 2.75 must be increased to values further above zero. The paper aimed at giving an insight into the small wind turbine starting behavior and its influence parameters. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical investigation on the dynamic stall of a vertical axis wind turbine

In the last years, for home user, the wind turbine with vertical axis (VAWT) began to be more attractive due benefits in exploitation. In terms of aerodynamics, when the wind speed approaches the speed of operation (low value of tip speed ratio -TSR) the blade airfoil exceeds the critical angle of incidence for static conditions. Angle of incidence varies quickly across blade and the blade works in dynamic stall condition. The goal of the present work is to investigate the two-dimensional dynamic stall phenomenon around the NACA 0012 airfoil at relatively low Reynolds. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unsteady Flow and its Influence to Aerodynamic and Aeroacoustic of VAWT's

A study is reported of the influence of unsteady flow on the aerodynamics and aeroacoustics of vertical axis wind turbines by numerical simulation. The combination of aerodynamic predictions with a discrete vortex method and aeroacoustic predictions based on Ffowcs Williams-Hawkings equation is used to achieve this goal. The numerical results show that unsteady flow of the turbine has a significant influence on the turbine aerodynamics and can lead to a decrease in generated noise as compared to the conventional horizontal axis wind turbine at the similar aerodynamic performance. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)