Periodic orbits of oval billiards on surfaces of constant curvature

In this paper, we define and study the billiard problem on bounded regions on surfaces of constant curvature. We show that this problem defines a two-dimensional conservative and reversible dynamical system, defined by a Twist diffeomorphism, if the boundary of the region is an oval. Using these properties and defining good perturbations for billiards, we show that having only a finite number of nondegenerate periodic orbits for each fixed period is an open property for billiards on surfaces of constant curvature and a dense one on the hyperbolic plane. We finish this paper studying the stability of these nondegenerate orbits.     

Characterization of the phosphatic mineral of the barnacle Ibla cumingi at atomic level by solid-state nuclear magnetic resonance: comparison with other phosphatic biominerals

Ibliform barnacles are among the few invertebrate animals harnessing calcium phosphate to construct hard tissue. The ³¹P solid-state NMR (SSNMR) signal from the shell plates of Ibla cumingi (Iblidae) is broader than that of bone, and shifted by ca 1 ppm to low frequency. ¹H–³¹P heteronuclear correlation (HETCOR) experiments show a continuum of different phosphorus/phosphate atomic environments, close to hydrogen populations with resonance frequencies between ca 10 and 20 ppm. Associated ¹H and ³¹P chemical shifts argue the coexistence of weakly (high ³¹P frequency, low ¹H frequency) to more strongly (lower ³¹P frequency, higher ¹H frequency) hydrogen-bonded hydrogen phosphate-like molecular/ionic species. There is no resolved signal from discrete OH⁻ ions. ¹³C SSNMR shows chitin, protein and other organic biomolecules but, unlike bone, there are no significant atomic scale organic matrix–mineral contacts. The poorly ordered hydrogen phosphate-like iblid mineral is strikingly different, structurally and compositionally, from both vertebrate bone mineral and the more crystalline fluoroapatite of the linguliform brachiopods. It probably represents a previously poorly characterized calcium phosphate biomineral, the evolution of which may have reflected either the chemical conditions of ancestral seas or the mechanical advantages of phosphatic biomineralization over a calcium carbonate equivalent.     

Genetic parameters for hoof health traits estimated with linear and threshold models using alternative cohorts

A national genetic evaluation program for hoof health could be achieved by using hoof lesion data collected directly by hoof trimmers. However, not all cows in the herds during the trimming period are always presented to the hoof trimmer. This preselection process may not be completely random, leading to erroneous estimations of the prevalence of hoof lesions in the herd and inaccuracies in the genetic evaluation. The main objective of this study was to estimate genetic parameters for individual hoof lesions in Canadian Holsteins by using an alternative cohort to consider all cows in the herd during the period of the hoof trimming sessions, including those that were not examined by the trimmer over the entire lactation. A second objective was to compare the estimated heritabilities and breeding values for resistance to hoof lesions obtained with threshold and linear models. Data were recorded by 23 hoof trimmers serving 521 herds located in Alberta, British Columbia, and Ontario. A total of 73,559 hoof-trimming records from 53,654 cows were collected between 2009 and 2012. Hoof lesions included in the analysis were digital dermatitis, interdigital dermatitis, interdigital hyperplasia, sole hemorrhage, sole ulcer, toe ulcer, and white line disease. All variables were analyzed as binary traits, as the presence or the absence of the lesions, using a threshold and a linear animal model. Two different cohorts were created: Cohort 1, which included only cows presented to hoof trimmers, and Cohort 2, which included all cows present in the herd at the time of hoof trimmer visit. Using a threshold model, heritabilities on the observed scale ranged from 0.01 to 0.08 for Cohort 1 and from 0.01 to 0.06 for Cohort 2. Heritabilities estimated with the linear model ranged from 0.01 to 0.07 for Cohort 1 and from 0.01 to 0.05 for Cohort 2. Despite a low heritability, the distribution of the sire breeding values showed large and exploitable variation among sires. Higher breeding values for hoof lesion resistance corresponded to sires with a higher prevalence of healthy daughters. The rank correlations between estimated breeding values ranged from 0.96 to 0.99 when predicted using either one of the 2 cohorts and from 0.94 to 0.99 when predicted using either a threshold or a linear model.     

Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions

In the analysis of crystallographic texture, the orientation distribution function (ODF) of the grains is generally expressed as a linear combination of the generalized spherical harmonics. Recently, an alternative expansion of the ODF, as a linear combination of the hyperspherical harmonics, has been proposed, with the advantage that this is a function of the angles that directly describe the axis and angle of each grain rotation, rather than of the Euler angles. This article provides the formulas required to convert between the generalized spherical harmonics and the hyperspherical harmonics, and between the coefficients appearing in their respective expansions of the ODF. A short discussion of the phase conventions surrounding these expansions is also presented.     

Characterization of low-flammability electrolytes for lithium-ion batteries

In an effort to develop low-flammability electrolytes for a new generation of Li-ion batteries, we have evaluated physical and electrochemical properties of electrolytes with two novel phosphazene additives. We have studied performance quantities including conductivity, viscosity, flash point, and electrochemical window of electrolytes as well as formation of solid electrolyte interphase (SEI) films. In the course of study, the necessity for a simple method of SEI characterization was realized. Therefore, a new method and new criteria were developed and validated on 10 variations of electrolyte/electrode substrates. Based on the summation of determined physical and electrochemical properties of phosphazene-based electrolytes, one structure of phosphazene compound was found better than the other. This capability helps to direct our further synthetic work in phosphazene chemistry.     

Phase Stability and Optoelectronic Properties of the Bixbyite Phase in the Gallium–Indium–Tin–Oxide System

X‐ray diffraction techniques were used to determine the phase boundaries of the In₂O₃ solid solution phase in the Ga₂O₃–In₂O₃–SnO₂ ternary system. The effects of Ga and Sn content on the unit cell dimensions of the bixbyite phase were calculated by a linear regression fit, the results of which indicate the two substitutive cations have opposite and independent effects on the lattice parameter. These results suggest that the cations do not strongly interact with each other in the crystal. Measurements of optoelectronic properties were also taken on single‐phase bulk specimens within the solid solution to establish their dependence on composition. As anticipated, Sn doping yields corresponding increases in conductivity, reduction in the absolute value of Seebeck coefficient, and increase in optical band gap. In contrast, these properties are not significantly affected by varying Ga content, confirming that Ga behaves as an isovalent dopant at the low doping levels involved.     

Confirmation of the Dominant Defect Mechanism in Amorphous In–Zn–O Through the Application of In Situ Brouwer Analysis

The dominant point defect mechanism of amorphous (a‐) indium zinc oxide (IZO) was probed through in situ electrical characterization of sputtered a‐IZO thin films in response to changes in oxygen partial pressure (pO) at 300C. The results yielded a power law dependence of conductivity (σ) versus pO of ～?1/6. This experimental method, known as Brouwer analysis, confirms doubly‐charged oxygen vacancies as the dominant defect species in a‐IZO. The success of this study suggests that Brouwer analysis is a viable method for studying the defect mechanisms of amorphous oxides.     

Self-cleaning and colour-preserving efficiency of photocatalytic concrete: case study of the Jubilee Church in Rome

ABSTRACT

The Jubilee Church in the south-eastern outskirts of Rome is one of the first buildings constructed with super white reinforced concrete with self-cleaning photocatalytic cement. However, 16 years after the opening of the building, the self-cleaning and colour-preserving properties arising from the titania particles (TiO2) within the concrete mix are not meeting the design requirements and the concrete is showing premature evidence of decay. While the form of the decay is affecting the appearance of the building and not its structural soundness, the ageing pattern of the building's components is resulting in a high maintenance cost, one not easily affordable within the ordinary budget supported by a small parish. This study comprises the first comprehensive step in understanding the causes of the accelerated ageing pattern of the concrete, highlighting methods to improve the long-term durability of the concrete and therefore reduce the cost of its maintenance. Moreover, this research offered the opportunity to test the durability and the effectiveness of the TiO₂ in the real conditions on an actual building featuring non-standard geometries. The findings highlight how the ageing pattern directly connects with the geometry of the building and inadequate consideration of the local weathering at the design stage.