The reduced modulus in the analysis of sharp instrumented indentation tests

In the analysis of instrumented indentation data, it is common practice to incorporate the combined moduli of the indenter (E-i) and the specimen (E) in the so-called reduced modulus (E-r) to account for indenter deformation. Although indenter systems with rigid or elastic tips are considered as equivalent if E-r is the same, the validity of this practice has been questioned over the years. The present work uses systematic finite element simulations to examine the role of the elastic deformation of the indenter tip in instrumented indentation measurements and the validity of the concept of the reduced modulus in conical and pyramidal (Berkovich) indentations. It is found that the apical angle increases as a result of the indenter deformation, which influences in the analysis of the results. Based upon the inaccuracies introduced by the reduced modulus approximation in the analysis of the unloading segment of instrumented indentation applied load (P)-penetration depth (delta) curves, a detailed examination is then conducted on the role of indenter deformation upon the dimensionless functions describing the loading stages of such curves. Consequences of the present results in the extraction of the uniaxial stress-strain characteristics of the indented material through such dimensional analyses are finally illustrated. It is found that large overestimations in the assessment of the strain hardening behavior result by neglecting tip compliance. Guidelines are given in the paper to reduce such overestimations.

Habitat use by Sharp-tailed Tyrant (Culicivora caudacuta), and Cock-tailed Tyrant (Alectrurus tricolor) in the Cerrado of Southeastern Brazil

Habitat use by Sharp-tailed Tyrant (Culicivora caudacuta), and Cock-tailed Tyrant (Alectrurus tricolor) in the Cerrado of Southeastern Brazil. Obligatory grassland birds are dependent on a limited set of native habitats that are disappearing almost everywhere. We examined the use of macrohabitat and microhabitat by two threatened species of flycatchers, the Sharp-tailed Tyrant, Culicivora caudacuta and the Cock-tailed Tyrant, Alectrurus tricolor in a preserved area of cerrado. We generated logistic regression models to explain the presence of these species through variables of microhabitat. Both flycatchers occurred mainly in grassland areas and favored areas with a low density of palms (Attalea geraensis) and trees. The Sharp-tailed Tyrant also favored areas with a high density of low shrubs (< 1 m) and less exposed soil. The positive relationship found between the presence of Sharp-tailed Tyrant and soil cover may indicate the importance of litter and understory vegetation for shelter and food. The conservation of both flycatcher species in the study area should benefit from controlling palm density and the maintenance of grasslands with low shrubs.

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.