AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

PARTITIONED ANALYSIS FOR DIMENSIONALLY-HETEROGENEOUS HYDRAULIC NETWORKS

In this work an iterative strategy is developed to tackle the problem of coupling dimensionally-heterogeneous models in the context of fluid mechanics. The procedure proposed here makes use of a reinterpretation of the original problem as a nonlinear interface problem for which classical nonlinear solvers can be applied. Strong coupling of the partitions is achieved while dealing with different codes for each partition, each code in black-box mode. The main application for which this procedure is envisaged arises when modeling hydraulic networks in which complex and simple subsystems are treated using detailed and simplified models, correspondingly. The potentialities and the performance of the strategy are assessed through several examples involving transient flows and complex network configurations.

Generalized connectivity between any two nodes in a complex network

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

Chain motifs: The tails and handles of complex networks

A great part of the interest in complex networks has been motivated by the presence of structured, frequently nonuniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they provide the means to identify and classify several types of complex network, it becomes important to obtain meaningful measurements of the local network topology. In addition to traditional features such as the node degree, clustering coefficient, and shortest path, motifs have been introduced in the literature in order to provide complementary descriptions of the network connectivity. The current work proposes a different type of motif, namely, chains of nodes, that is, sequences of connected nodes with degree 2. These chains have been subdivided into cords, tails, rings, and handles, depending on the type of their extremities (e.g., open or connected). A theoretical analysis of the density of such motifs in random and scale-free networks is described, and an algorithm for identifying these motifs in general networks is presented. The potential of considering chains for network characterization has been illustrated with respect to five categories of real-world networks including 16 cases. Several interesting findings were obtained, including the fact that several chains were observed in real-world networks, especially the world wide web, books, and the power grid. The possibility of chains resulting from incompletely sampled networks is also investigated.

Structure of PbTe(SiO(2))/SiO(2) multilayers deposited on Si(111)

The structure of thin films composed of a multilayer of PbTe nanocrystals embedded in SiO(2), named as PbTe(SiO(2)), between homogeneous layers of amorphous SiO(2) deposited on a single-crystal Si( 111) substrate was studied by grazing-incidence small-angle X-ray scattering (GISAXS) as a function of PbTe content. PbTe(SiO(2))/SiO(2) multilayers were produced by alternately applying plasma-enhanced chemical vapour deposition and pulsed laser deposition techniques. From the analysis of the experimental GISAXS patterns, the average radius and radius dispersion of PbTe nanocrystals were determined. With increasing deposition dose the size of the PbTe nanocrystals progressively increases while their number density decreases. Analysis of the GISAXS intensity profiles along the normal to the sample surface allowed the determination of the period parameter of the layers and a structure parameter that characterizes the disorder in the distances between PbTe layers. (C) 2010 International Union of Crystallography Printed in Singapore - all rights reserved

Local atomic structure in tetragonal pure ZrO(2) nanopowders

The local atomic structures around the Zr atom of pure (undoped) ZrO(2) nanopowders with different average crystallite sizes, ranging from 7 to 40 nm, have been investigated. The nanopowders were synthesized by different wet-chemical routes, but all exhibit the high-temperature tetragonal phase stabilized at room temperature, as established by synchrotron radiation X-ray diffraction. The extended X-ray absorption fine structure (EXAFS) technique was applied to analyze the local structure around the Zr atoms. Several authors have studied this system using the EXAFS technique without obtaining a good agreement between crystallographic and EXAFS data. In this work, it is shown that the local structure of ZrO(2) nanopowders can be described by a model consisting of two oxygen subshells (4 + 4 atoms) with different Zr-O distances, in agreement with those independently determined by X-ray diffraction. However, the EXAFS study shows that the second oxygen subshell exhibits a Debye-Waller (DW) parameter much higher than that of the first oxygen subshell, a result that cannot be explained by the crystallographic model accepted for the tetragonal phase of zirconia-based materials. However, as proposed by other authors, the difference in the DW parameters between the two oxygen subshells around the Zr atoms can be explained by the existence of oxygen displacements perpendicular to the z direction; these mainly affect the second oxygen subshell because of the directional character of the EXAFS DW parameter, in contradiction to the crystallographic value. It is also established that this model is similar to another model having three oxygen subshells, with a 4 + 2 + 2 distribution of atoms, with only one DW parameter for all oxygen subshells. Both models are in good agreement with the crystal structure determined by X-ray diffraction experiments.