Willmore surfaces and Hopf tori in homogeneous 3-manifolds

Annals of Global Analysis and Geometry - Some classification results for closed surfaces in Berger spheres are presented. On the one hand, a Willmore functional for isometrically immersed surfaces...     

The circumcentered-reflection method achieves better rates than alternating projections

Computational Optimization and Applications - We study the convergence rate of the Circumcentered-Reflection Method (CRM) for solving the convex feasibility problem and compare it with the Method...     

Resolving Atomic-Scale Defects in Conjugated Polymers On-Surfaces

Atomic scale defects significantly affect the mechanical, electronic, and optical properties of π-conjugated polymers. Here, isolated atomic-scale defects are deliberately introduced into a prototypical anthracene-ethynylene π-conjugated polymer, and its local density of states is carefully examined on the atomic scale to show how individual defects modify the inherent electronic and magnetic properties of this one-dimensional systems. Scanning tunneling and atomic force microscopy experiments, supplemented with density functional theory calculations, reveal the existence of a sharp electronic resonance at the Fermi energy around certain defects, which is associated with the formation of a local magnetic moment accompanied by substantial mitigation of the mobility of charge carriers. While defects in traditionally synthesized polymers lead to arbitrary conformations, the presented results clearly reflect the preferential formation of low dimensional defects at specific polymer sites, which may introduce the possibility of engineering macroscopic defects in surface-synthesized conjugated polymers.     

Poiseuille-Number-Based Kozeny–Carman Model for Computation of Pore Shape Factors on Arbitrary Cross Sections

Porous media characterization is crucial to engineering projects where the pore shape has impact on performance gains. Membrane filters, sportswear fabrics, and tertiary oil recovery are a few examples. Kozeny–Carman (K–C) models are one of the most frequently used to understand, for instance, the relation between porosity, permeability, and other small-scale parameters. However, they have limitations, such as the inability to capture the correct dependence of permeability on porosity, the imperfect handling of the linear and nonlinear effects yielded by its fundamental quantities, and the insufficiency of geometrical parameters to predict the permeability correctly. In this paper, we cope with the problem of determining shape factors for generic geometries that represent sundry porous media configurations. Specifically, we propose a method that embeds the Poiseuille number into the classical K–C equation and returns a substitute shape factor term for its original counterpart. To the best of our knowledge, the existing formulations are unable to obtain shape factors for pores whose geometry is beyond the regular ones. We apply a Galerkin-based integral (GBI) method that determines shape factors for generic cross sections of pore channels. The approach is tested on straight capillaries with arbitrary cross sections subject to steady single-phase flow under the laminar regime. We show that shape factors for basic geometries known from experimental results are replicable exactly. Besides, we provide shape factors with precision up to 4 digits for a class of geometries of interest. As a way to demonstrate the applicability of the GBI approach, we report a case study that determines shape factors for 19 generic individual pore sections of a laboratory experiment involving flow rate measurements in an industrial arrangement of a water-agar packed bed. Porosity, flow behavior, and velocity distributions determined numerically achieve a narrow agreement with experimental values. The findings of this study provide parameters that can help to design new devices or mechanisms that depend on arbitrary pore shapes, as well as to characterize fluid flows in heterogeneous porous media.

     

Erratum to: “The penetrable-sphere fluid in the high-temperature,high-density limit” [Phys. Lett. A 323 (2004) 427]

A few misprints appearing in the paper [L. Acedo, A. Santos, Phys. Lett. A 323 (2004) 427] are corrected.     

Silver sorption isotherms onto bentonites: Comparing mathematical models

Herein is reported the application of models on sorption isotherms for removal of silver ions from aqueous solution using 2 bentonites: SWy‐2 and BaVC‐1, low‐cost sorbents. Physicochemical attributes were determined for both materials, and sorption experiments were carried out in batch system. The pH before and after sorption decreased from 7.8 to 6.1 and 8.4 to 6.7 for SWy‐2 and BaVC‐1, respectively. Langmuir, Freundlich, Sips, Toth, Kolbe‐Corrigan, Khan, and Radke‐Prausnitiz models were applied to the data. The models showed good fit with R² above 0.999 and RMSE < 2%. The adjustable parameters indicated high affinity of silver ions to BaVC‐1 sorption sites, demonstrating high sorption capacity and thermodynamic feasibility. In general, SWy‐2 showed most heterogeneous sorption sites, while BaVC‐1 showed most homogeneous sites. Moreover, BaVC‐1 has shown larger surface area and smaller particle size, which can explain its better sorption performance as compared with SWy‐2.     

Orientability of vector bundles over real flag manifolds

We investigate the orientability of a class of vector bundles over flag manifolds of real semi-simple Lie groups, which include the tangent bundle and also stable bundles of certain gradient flows. Closed formulas, in terms of roots, are provided.     

Principal component analysis and hierarchical cluster analysis for homogeneity evaluation during the preparation of a wheat flour laboratory reference material for inorganic analysis

The development of a homogeneity study during the preparation of a wheat flour laboratory reference material (LRM) for use in the quantification of metals and metalloids is reported. Inductively coupled plasma optical emission spectrometry (ICP OES) was used with validation performed using a certified reference material of wheat flour furnished by the National Institute of Standards and Technology (NIST). Copper, iron, manganese, phosphor, strontium and zinc were studied in a within-bottle homogeneity test whereas barium, copper, iron, zinc, manganese, strontium, phosphor and calcium were included in a between batch homogeneity study. Standard univariate analysis of variance (ANOVA) was performed for all analytes. Furthermore an alternative multivariate analysis for homogeneity is proposed by performing ANOVA of principal component scores and by inspection of principal component score graphs and hierarchical cluster analysis dendrograms. The ANOVA F-tests performed on both, the univariate and multivariate parameters, were not significant at the 95% confidence level and indicated homogeneous wheat flour samples. A 10 kg amount of material was processed, which was distributed in 100 bottles, each containing 100 g. For the between-bottle homogeneity test, three replicates were taken from each of 10 bottles selected of the 100 bottles obtained. The results were evaluated using an F-test, which demonstrated no significant difference for the between-bottle results. It is indicative that this material is homogeneous. Afterwards, the influence of the sample mass on the homogeneity of the material was also evaluated by quantification of the elements for 100, 300, 500, 700 and 1000 mg sample masses with all the experiments being performed in triplicate. The F-test was also used for evaluation of these results and demonstrated that the material is homogeneous for masses taken in the 100 to 1000 mg range. All these results were further evaluated employing the principal component analysis (PCA) and hierarchical cluster analysis (HCA) multivariate techniques. Both techniques also demonstrated that the material is perfectly homogeneous for use as laboratory reference material.     

Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program

Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set theoretical framework for statistical mechanics.