Infill sampling criteria to locate extremes

Three problem-dependent meanings for engineering extremes are motivated, established, and translated into formal geostatistical (model-based) criteria for designing infill sample networks. (1) Locate an area within the domain of interest where a specified threshold is exceeded, if such areas exist. (2) Locate the maximum value in the domain of interest. (3) Minimize the chance of areas where values are significantly different from predicted values. An example application on a simulated dataset demonstrates how such purposive design criteria might affect practice.     

An analytical solution for stresses induced by a post-tensioned anchor in rocks containing two perpendicular joint sets

A new analytical approach for the analysis of stress around a post-tensioned anchor in rock with two perpendicular joint sets is presented. The solution considers nonlinear shear stresses developed along the anchor bond length as well as debonding at the tendon–grout interface. The bearing plate effects are also considered in the analyses. The following assumptions are made: (1) homogeneous and orthotropic elastic rock; (2) half-space rock mass with plane strain conditions; (3) trilinear bond-slip model for the behavior of the tendon–grout interface; (4) an elastic anchor. The employed methodology is to decompose the anchor problem into two problems of simpler loadings: stresses produced under a rigid bearing plate and stresses induced by interfacial shear stresses mobilized along the bond length. Based on the proposed solution, an illustrative example is given and the results show that a large compressive region is formed around the anchor free length. Tensile stress concentrations are also observed around the bond length and near the rock surface outside the bearing plate. A parametric study is also conducted to investigate the effects of joint properties on the induced stresses. The results show that as the number of joints intersecting the anchor axis increases, the magnitude of compressive stresses in the free zone decreases, while the size of compression zone around the anchor increases. To verify the results of the analytical approach, a comparison is made with numerical results obtained by using the finite element method. The analytical solutions compare very well with the results obtained by numerical method.     

The RbSr age dating of some Carboniferous shales

The RbSr age dating method has been applied to a sequence of Carboniferous shales for which some geochemical information was already available. In the marine shales, the Rb/Sr ratio is higher than in the non-marine and brackish water shales. Although the range of values can be attributed to depositional processes, the range of Rb/Sr values is too small to give a depositional isochron, and thus the age of deposition can not be determined. If samples with a variable mineralogy had been selected for the isotope study, the range of Rb/Sr could have been extended. Only by chance, however, would the depositional age have been obtained.A comparison of the RbSr isotope values in the Carboniferous shales with those in probable source rocks shows that a reduction in the Sr⁸⁷/Sr⁸⁶ ratio relative to the Rb⁸⁷/Sr⁸⁶ ratio may have taken place. Such a reduction could have occurred on the Carboniferous land-mass during the formation of the clay minerals.     

On Broucke's velocity-related series expansions in the two-body problem

This short article supplements a recent paper by Dr R. Broucke on velocity-related series expansions in the two-body problem. The derivations of the Fourier and Legendre expansions of the functionsF(v), \(\sqrt {F(\upsilon )} \) and \(\sqrt {{1 \mathord{\left/ {\vphantom {1 {F(\upsilon )}}} \right. \kern-0em} {F(\upsilon )}}} \) are given, where $$F(\upsilon ) = (1 - e^2 )/(1 + 2e\cos \upsilon + e^2 ), e< 1$$ In the two-body problem,v is identified with the true anomaly,e the eccentricity andF(v) equals (an/V)². Some interesting relations involving Legendre polynomials are also noted.     

A faint object spectrometer for the infrared

A cryogenic astronomical spectrometer for the NASA Infrared Telescope Facility is described. This spectrometer will employ an array of at least 20 detectors and provide a resolving power of 100 to 1500 at 1–5 m. The resolving power will be adjustable by changing gratings.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.