We report high-precision K isotopes, apatite U–Pb ages, whole-rock elements and Sr–Nd isotopes for the Saima nephelite syenite in the North China Craton. Trace-element and Sr–Nd–Hf–O isotope data indicate the presence of subducting sediments in the source region, while K isotopic compositions show a narrow range between –0.54 ‰ and –0.28 ‰, with an average of –0.41 ± 0.06 ‰, identical to the value of the asthenosphere. The nearly identical K isotopic compositions are low probability events compared with the K isotopic compositions of island arc lavas reported previously (–1.55 ‰ to +0.2 ‰). Although crustal contamination is consistent with the Sr–Nd–K isotopic data, alternatively we propose that the isotopic data also reconcile with the interaction between cratonic roots and the underlying convective asthenosphere, if this interaction is over prolonged periods of time. Numerical simulations successfully reproduced the observed data, if the metasomatism of the lithospheric mantle root, the source of the Saima alkaline rocks, occurred 500 Ma ago. Our study reveals that the isotopic compositions of fast-diffusion components in a lithospheric mantle metasomatized by ancient subducting melts can be effectively homogenized by convective asthenosphere through diffusion over a long time interval.

This paper presents a geometrical alternative to estimate the accuracy of a deployable mechanism equipped on the Synthetic Aperture Radar (SAR) space satellite. The deployable mechanism is simplified into a planar mechanism, and the error space of the outer panel in its deployed state is modeled concerning multiple revolute joint clearances and link length tolerances. Compared with the existing methods, the advance of the proposed geometrical approach lies in that it gives expressions of the complete error mobility that the outer panel may have. After deducing the expressions, the final error space is visualized and evaluated numerically with discrete sampling points. Finally, based on the error space and the computed maximum errors, effects of tolerances on accuracy are studied and the optimal accuracy design of tolerances is obtained. The result reveals that, for the deployable mechanism discussed in this paper, effects of tolerances on the final accuracy can be eliminated without increasing the manufacturing cost.

Laboratory experiments have shown that thermal gradients in silicate melts can lead to isotopic fractionation; this is known as the Richter effect. However, it is perplexing that the Richter effect has not been documented in natural samples as thermal gradients commonly exist within natural igneous systems. To resolve this discrepancy, theoretical analysis and calculations were undertaken. We found that the Richter effect, commonly seen in experiments with wholly molten silicates, cannot be applied to natural systems because natural igneous samples are more likely to be formed out of partially molten magma and the presence of minerals adds complexity to the behaviour of the isotope. In this study, we consider two related diffusion-rate kinetic isotope effects that originate from chemical diffusion, which are absent from experiments with wholly molten samples. We performed detailed calculations for magnesium isotopes, and the results indicated that the Richter effect for magnesium isotopes is buffered by kinetic isotope effects and the total value of magnesium isotope fractionation can be zero or even undetectable. Our study provides a new understanding of isotopic behaviour during the processes of cooling and solidification in natural magmatic systems.

Porous TiAl3 intermetallics were synthesized by the thermal explosion (TE) reaction from TiH2–75 at.% Al elemental powders combining with carbamide as the space holder. The results showed that the space holder particles were removed completely by dissolving in water before sintering and the violent exothermic reaction occurred from the temperature of 672–1193 °C within a few seconds. After TE, TiAl3 was the dominant phase in sintered products and the open porosity of 60.8% was obtained without space holder, while the porosity considerably increased to 81.4% with the addition of 60 vol% carbamide particles. The pore-forming mechanism can be concluded as follows: the sphere large pores replicated from carbamide particles and the small pores generated by the TE reaction. Moreover, porous TiAl3 intermetallics possess the excellent oxidation resistance at 650 °C in air, which enabled them good candidate materials for improving the service life and the accuracy of filtration under special conditions.

The initiation and evolution of shear bands in Zr64.13Cu15.75Ni10.12Al10 bulk metallic glass tensile samples has been investigated in situ by scanning electron microscopy. The initial shear band originates from the highest stressed area, and does not propagate during further tension, which is attributed to the weakening of the stress field in front of the shear band tip, possibly caused by atomic rearrangement and local temperature rise. As a result, multiple shear bands occur in sequence with gradually increased length and offset. This result is due to the fact that the stress in front of the tip of the initial shear band does not concentrate again during further tension above the shear yield strength. Numerical analysis was carried out to investigate the stress distribution under tension, suggesting that the maximum pressure-dependent shear stress criterion overestimates the yield strength, while the shear plane criterion describes the conditions for the formation of shear bands well.

This paper presents a method for the inverse fractional matching problem. We show that the dual of this inverse problem can be transformed into the circulation flow problem on a directed bipartite graph which can be solved easily. We also give an algorithm to obtain the primal optimum solution of the inverse problem from its dual optimum solution by solving a shortest path problem. Furthermore, we generalize this method to solve the inverse symmetric transportation problem.