The octagon, the hendecagon and the approximation of pi: the geometric design of the clypeus in the enclosure of Imperial cult in Tarraco

The ancient temple dedicated to the Roman Emperor Augustus on the hilltop of Tarraco (today’s Tarragona), was the main element of the sacred precinct of the Imperial cult. It was a two hectare square, bordered by a portico with an attic decorated with a sequence of clypeus (i.e. monumental shields) made with marble plates from the Luni-Carrara’s quarries. This contribution presents the results of the analysis of a three-dimensional photogrammetric survey of one of these clipeus, partially restored and exhibited at the National Archaeological Museum of Tarragona. The perimeter ring was bounded by a sequence of meanders inscribed in a polygon of 11 sides, a hendecagon. Moreover, a closer geometric analysis suggests that the relationship between the outer meander rim and the oval pearl ring that delimited the divinity of Jupiter Ammon can be accurately determined by the diagonals of an octagon inscribed in the perimeter of the clypeus. This double evidence suggests a combined layout, in the same design, of an octagon and a hendecagon. Hypothetically, this could be achieved by combining the octagon with the approximation to Pi used in antiquity: 22/7 of the circle’s diameter. This method allows the drawing of a hendecagon with a clearly higher precision than with other ancient methods. Even the modelling of the motifs that separate the different decorative stripes corroborates the geometric scheme that we propose.

The effect of skewness and kurtosis on the Kenward-Roger approximation when group distributions differ

This study examined the independent effect of skewness and kurtosis on the robustness of the linear mixed model (LMM), with the Kenward-Roger (KR) procedure, when group distributions are different, sample sizes are small, and sphericity cannot be assumed. Methods: A Monte Carlo simulation study considering a split-plot design involving three groups and four repeated measures was performed. Results: The results showed that when group distributions are different, the effect of skewness on KR robustness is greater than that of kurtosis for the corresponding values. Furthermore, the pairings of skewness and kurtosis with group size were found to be relevant variables when applying this procedure. Conclusions: With sample sizes of 45 and 60, KR is a suitable option for analyzing data when the distributions are: (a) mesokurtic and not highly or extremely skewed, and (b) symmetric with different degrees of kurtosis. With total sample sizes of 30, it is adequate when group sizes are equal and the distributions are: (a) mesokurtic and slightly or moderately skewed, and sphericity is assumed; and (b) symmetric with a moderate or high/extreme violation of kurtosis. Alternative analyses should be considered when the distributions are highly or extremely skewed and samples sizes are small.

A test of Suchey-Brooks (pubic symphysis) and Buckberry-Chamberlain (auricular surface) methods on an identified Spanish sample: paleodemographic implications

Forensic Anthropology and Bioarchaeology studies depend critically on the accuracy and reliability of age-estimation techniques. In this study we have evaluated two age-estimation methods for adults based on the pubic symphysis (Suchey-Brooks) and the auricular surface (Buckberry-Chamberlain) in a current sample of 139 individuals (67 women and 72 men) from Madrid in order to verify the accuracy of both methods applied to a sample of innominate bones from the central Iberian Peninsula. Based on the overall results of this study, the Buckberry-Chamberlain method seems to be the method that provides better estimates in terms of accuracy (percentage of hits) and absolute difference to the chronological age taking into account the total sample. The percentage of hits and mean absolute difference of the Buckberry-Chamberlain and Suchey-Brooks methods are 97.3% and 11.24 years, and 85.7% and 14.38 years, respectively. However, this apparently greater applicability of the Buckberry-Chamberlain method is mainly due to the broad age ranges provided. Results indicated that Suchey-Brooks method is more appropriate for populations with a majority of young individuals, whereas Buckberry-Chamberlain method is recommended for populations with a higher percentage of individuals in the range 60-70 years. These different age estimation methodologies significantly influence the resulting demographic profile, consequently affecting the biological characteristics reconstruction of the samples in which they are applied.

Ocean surface winds drive dynamics of transoceanic aerial movements

Global wind patterns influence dispersal and migration processes of aerial organisms, propagules and particles, which ultimately could determine the dynamics of colonizations, invasions or spread of pathogens. However, studying how wind-mediated movements actually happen has been hampered so far by the lack of high resolution global wind data as well as the impossibility to track aerial movements. Using concurrent data on winds and actual pathways of a tracked seabird, here we show that oceanic winds define spatiotemporal pathways and barriers for large-scale aerial movements. We obtained wind data from NASA SeaWinds scatterometer to calculate wind cost (impedance) models reflecting the resistance to the aerial movement near the ocean surface. We also tracked the movements of a model organism, the Cory's shearwater (Calonectris diomedea), a pelagic bird known to perform long distance migrations. Cost models revealed that distant areas can be connected through"wind highways" that do not match the shortest great circle routes. Bird routes closely followed the low-cost"wind-highways" linking breeding and wintering areas. In addition, we found that a potential barrier, the near surface westerlies in the Atlantic sector of the Intertropical Convergence Zone (ITCZ), temporally hindered meridional trans-equatorial movements. Once the westerlies vanished, birds crossed the ITCZ to their winter quarters. This study provides a novel approach to investigate wind-mediated movements in oceanic environments and shows that large-scale migration and dispersal processes over the oceans can be largely driven by spatiotemporal wind patterns.

Molecular Physics of Elementary Processes relevant to Hypersonics: atom-molecule, molecule-molecule and atom-surface processes.

In the present chapter some prototype gas and gas-surface processes occurring within the hypersonic flow layer surrounding spacecrafts at planetary entry are discussed. The discussion is based on microscopic dynamical calculations of the detailed cross sections and rate coefficients performed using classical mechanics treatments for atoms, molecules and surfaces. Such treatment allows the evaluation of the efficiency of thermal processes (both at equilibrium and nonequilibrium distributions) based on state-to-state and state specific calculations properly averaged over the population of the initial states. The dependence of the efficiency of the considered processes on the initial partitioning of energy among the various degrees of freedom is discussed.

The role of surface vertical mixing in phytoplankton distribution in a stratified reservoir

We investigated convection caused by surface cooling and mixing attributable to wind shear stress and their roles as agents for the transport of phytoplankton cells in the water column by carrying out two daily surveys during the stratified period of the Sau reservoir. Green algae, diatoms, and cryptophyceae were the dominant phytoplankton communities during the surveys carried out in the middle (July) and end (September) of the stratified period. We show that a system with a linear stratification and that is subject to weak surface forcing, with weak winds , < 4 m S (-1) and low energy dissipation rate values of the order of 1028 m2 s23 or lower, enables the formation of thin phytoplankton layers. These layers quickly disappear when water parcels mix because there is a medium external forcing (convection) induced by the night surface cooling, which is characterized by energy dissipation rates on the order of , 5x10(-8)m2s(-3). During both surveys the wind generated internal waves during the entire diurnal cycle. During the day, and because of the weak winds, phytoplankton layers rise in the water column up to a depth determined by both solar heating and internal waves. In contrast, during the night phytoplankton mixes down to a depth determined by both convection and internal waves. These internal waves, together with the wind-driven current generated at the surface, seem to be the agents responsible for the horizontal transport of phytoplankton across the reservoir.

Discrepancies over the onset of surfactant monomer aggregation interpreted by fluorescence, conductivity and surface tension methods

Molecular probe techniques have made important contributions to the determination of microstructure of surfactant assemblies such as size, stability, micropolarity and conformation. Conductivity and surface tension were used to determine the critical aggregation concentration (cac) of polymer-surfactant complexes and the critical micellar concentration (cmc) of aqueous micellar aggregates. The results are compared with those of fluorescent techniques. Several surfactant systems were examined, 1-butanol-sodium dodecylsulfate (SDS) mixtures, solutions containing poly(ethylene oxide)-SDS, poly(vinylpyrrolidone)-SDS and poly(acrylic acid)-alkyltrimethylammonium bromide complexes. We found differences between the cac and cmc values obtained by conductivity or surface tension and those obtained by techniques which use hydrophobic probe.

Degradation of the surface of a metasilicate glass due to atmosphere moisture

Glasses with low silica content are very susceptible to suffer pronounced degradation when exposed to room atmosphere during short times. In this work the results of the degradation of the surface of a metasilicate glass with composition 2Na2O.1CaO.3SiO2 are presented. Optical and scanning electron microscopy observations, X-ray diffraction, infrared and Raman microprobe spectroscopic measurements of the modified surface of this glass show strong evidences that it is formed essentially by a crystalline carbonate layer.