TheH-functions of radiative transfer in an active amplifying medium

We obtain two explicit closed form representations of Chandrasekhar'sH-functionsH(z) characterising transfer of radiation in an active amplifying medium corresponding to the dispersion function $$T(z) = 1 - 2z^2 \int\limits_0^1 {Y(x)dx/(z^2 - x^2 ), Y(x)< 0 on [0, 1]} .$$ Their basic properties are derived and the values of theH-functionH(z, ω) whenY(x)=ω/2, are approximately computed for values of ω in the range (?10^?12)–(?10²) and for values ofzε[0, 1].     

A comparison of different magnetic methods for determining the relative grain size of magnetite in natural materials: Some results from lake sediments

A new rapid method for identifying relative grain size variations in magnetic involves the parameter anhysteretic susceptibility (χ_ARM, i.e. specific ARM obtained in a 1 Oe steady field), which is particularly sensitive to the single domain (SD) and small pseudo-single domain (PSD) grains of the finer magnetite fraction. A second parameter, low-field susceptibility (χ), is relatively more sensitive to the coarser magnetite fraction (larger PSD and smaller multidomain (MD) grains). We can then obtain a measure of the ratio of coarse- to fine-grain magnetite for large numbers of samples by plotting χ_ARversusχ. A simple idealized model based on sized magnetite samples is proposed to explain the use of the χ_ARMversusχ plot for detecting relative grain-size changes in the magnetic content of natural materials. The sediments of three lakes that contain magnetite or a similar magnetic carrier and have a wide range of values of χ_ARM and χ are used to test the model.The model is used to interpret the magnetic variations observed, and the interpretations are supported by high-field hysteresis measurements of the same sediments. The combination of the high-field hysteresis method of Day et al. [1] and the χ_ARM vs. χ method is a powerful technique allowing the rapid identification of both the relative grain size and domain state for large numbers of samples containing magnetite. The χ_ARMvs.χ method should be used as an intial means of identifying distinct groups of samples.The high-field hysteresis method should then be applied to a few representative samples from each group to confirm the initial interpretation.     

A new approach to the determination of methane content of coal seams

Summary An approach to the determination of methane content of coal seams is proposed. The method utilizes the transformed Airey's empirical equation on desorption of methane from coals. The methane content values estimated by this method correspond well with actual values from laboratory experiments. In the case of Indian coals, the applicability of the relationship for the calculation of the gas lost from coal lumps during long periods of time loss appears to be limited due to poor agreement with the experimental values.     

The geochemistry of beryllium and fluorine in the gem fields of Sri Lanka

A study of the abundance of Be in the gem sediments of Sri Lanka shows that Be is found in the range of 1–13 ppm. Be shows an irregular distribution among sediments. It occurs in the silicate form and due to the proximity to the beryllium bearing rocks, namely granites and pegmatites of the Highland and Southwest Groups of Sri Lanka, very little decomposition of the Be-bearing minerals had taken place. This is further aided by the high resistance to weathering of the beryllium minerals, particularly beryl and chrysoberyl.The beryllian granites and pegmatites of the Precambrian of Sri Lanka are presumed to have been formed due to the magmatic activity associated and related to charnockitic rocks abundant in the main gem bearing areas of Sri Lanka.Fluorine is found in the range of 400–2,000 ppm and the F/Be ratios for all the areas studied show a range of 54–441. The analysis of the averages of these ratios do not show any particular anomaly in any of the areas studied. The narrow ranges of the F/Be ratios indicate the similar conditions under which weathering and geochemical transportation had taken place in the gem fields of Sri Lanka.     

Transient elastodynamic analysis of three-dimensional problems by boundary element method

An advanced implementation of the direct boundary element method applicable to transient problems involving three-dimensional solids of arbitrary shape and connectivity is presented. The work first focuses on the formulation of the method, followed by a discussion of the fundamental singular solutions. Subsequently, a family of isoparametric boundary elements is introduced, along with the necessary numerical integration techniques as well as the solution algorithm. Numerical examples are presented, which demonstrate the unconditional stability and high accuracy of this dynamic analysis technique.     

Numerical hysteresis model for intermittent studies in unsaturated soils

In the present study, the use of one of the recent dependent domain models of capillary hysteresis in the numerical analysis of intermittent infiltration and redistribution of water in two types of soils (a sand and Rubicon Sandy Loam) has been shown. The numerical results for both the soils have been presented in terms of pressure head depth, moisture content depth and the pressure head-moisture content relationships. The capillary hysteresis model has been found to be very useful for the prediction of both wetting and drying scanning curves of various orders.     

Dynamic analysis of piles and pile groups embedded in homogeneous soils

A boundary element formulation for the dynamic analysis of axially and laterally loaded single piles and pile groups is presented. The piles are represented by compressible beam-column elements and the soil as a hysteretic elastic half-space. The governing equations of motion for the pile domain have been solved exactly for distributed periodic loading intensities. These solutions are then coupled with a numerical solution for the motion of the soil domain by satisfying equilibrium and compatibility at the pile-soil interface. The results obtained from the analysis compare favourably with those from alternative analyses, e.g. finite element, but at greatly reduced computational costs.     

Combining paleointensity methods: A dual-valued determination on lunar sample 10017,135

A single-heating procedure is presented which makes possible the determination of two partially independent values of paleofield intensity for a given sample, one serving as a check to the other. The approach combines data required for Shaw-type and “ARM-method” determinations and in so doing furnishes a value of the ratio of TRM to ARM acquisition efficiency (f′) corrected for any physicochemical alteration to the magnetic carriers which may have occurred during laboratory heating.

Applicability of the Shaw-method to Fe-bearing samples is favorably demonstrated through simulated paleointensity determinations conducted on synthetic samples containing multi-domain grains. Moreover, coercivity spectra corresponding to anhysteretic remanent magnetization (ARM) are found to be considerably more sensitive to thermally induced alteration when compared with those corresponding to thermoremanent magnetization (TRM).

The combined Shaw-ARM procedure was successfully applied to lunar basalt sample 10017,135 rendering a paleointensity of 0.82 ± 0.11 Oe. The Thellier-Thellier method, however, was not able to provide a meaningful determination on the neighboring chip (number 136). These apparently conflicting findings may be explained by one or more of the following possible interpretations: (1) multiple step-wise heatings cause considerably more damage to the carriers of remanence than does a single-heating procedure; (2) the rock possesses extreme variability in magnetic properties from one sub-sample to the other; (3) the natural remanent magnetization in this lunar basalt is not a simple TRM.