The effect of gravity on the stability of a line-tied coronal magnetohydrostatic equilibrium

Abstract

The magnetohydrodynamic stability of a class of magnetohydrostatic equilibria is investigated. The effect of gravity is included as well as the stabilising influence of the dense photospheric line-tying.

Although the two-dimensional equilibria exhibit a catastrophe point, when the ratio of plasma pressure to magnetic pressure exceeds a critical value, arcade structures, with both footpoints connected to the photosphere, become unstable to three-dimensional disturbances before the catastrophe point is reached.

Numerical results for field lines that are open into the solar corona suggest that they are completely stable. Although there is no definite proof of stability, this would allow the point of non-equilibrium to be reached.     

Soil‐pile interaction in the pile vertical vibration considering true three‐dimensional wave effect of soil

The dynamic response of an end bearing pile embedded in a linear visco‐elastic soil layer with hysteretic type damping is theoretically investigated when the pile is subjected to a time‐harmonic vertical loading at the pile top. The soil is modeled as a three‐dimensional axisymmetric continuum in which both its radial and vertical displacements are taken into account. The pile is assumed to be vertical, elastic and of uniform circular cross section. By using two potential functions to decompose the displacements of the soil layer and utilizing the separation of variables technique, the dynamic equilibrium equation is uncoupled and solved. At the interface of soil‐pile system, the boundary conditions of displacement continuity and force equilibrium are invoked to derive a closed‐form solution of the vertical dynamic response of the pile in frequency domain. The corresponding inverted solutions in time domain for the velocity response of a pile subjected to a semi‐sine excitation force applied at the pile top are obtained by means of inverse Fourier transform and the convolution theorem. A comparison with two other simplified solutions has been performed to verify the more rigorous solutions presented in this paper. Using the developed solutions, a parametric study has also been conducted to investigate the influence of the major parameters of the soil‐pile system on the vertical vibration characteristics of the pile. Copyright © 2013 John Wiley & Sons, Ltd.     

Isotope geochemistry and Re–Os geochronology of the Yanjiagou Mo deposit in the central North China Craton

The Yanjiagou deposit, located in the central North China Craton (NCC), is a newly found porphyry‐type Mo deposit. The Mo mineralization here is spatially associated with the Mapeng batholith. In this study, we identify four stages of ore formation in this deposit: pyrite phyllic stage (I), quartz–pyrite stage (II), quartz–pyrite–molybdenite stage (III), which is the main mineralization stage, and quartz–carbonate stage (IV). We present sulphur and lead isotope data on pyrite, and rhenium and osmium isotopes of molybdenite from the porphyry deposit and evaluate the timing and origin of ore formation. The δ³⁴S values of the pyrite range from ‐1.1‰ to −0.6‰, with an average of −0.875‰, suggesting origin from a mixture of magmatic/mantle sources and the basement rocks. The Pb isotope compositions of the pyrite show a range of 16.369 to 17.079 for ²⁰⁶Pb/²⁰⁴Pb, 15.201 to 15.355 for ²⁰⁷Pb/²⁰⁴Pb, and 36.696 to 37.380 for ²⁰⁸Pb/²⁰⁴Pb, indicating that the ore‐forming materials were derived from a mixture of lower crust (or basement rocks) and mantle. Rhenium contents in molybdenite samples from the main ore stage are between 74.73 to 254.43 ppm, with an average of 147.9 ppm, indicating a mixed crustal‐mantle source for the metal. Eight molybdenite separates yield model ages ranging from 124.17 to 130.80 Ma and a mean model age of 128.46 Ma. An isochron age of 126.7 ± 1.1 Ma (MSWD = 2.1, initial ¹⁸⁷Os = 0.0032 ± 0.0012 ppb) is computed, which reveals a close link between the Mo mineralization and the magmatism that generated the Mapeng batholith. The age is close to the zircon U–Pb age of ca. 130 Ma from the batholith reported in a recent study. The age is also consistent with the timing of mineralization in the Fuping ore cluster in the central NCC, as well as the peak time of lithosphere thinning and destruction of the NCC. We evaluate the spatio‐temporal distribution of the Mo deposits in the NCC and identify three important molybdenum provinces along the northern and southern margins of the craton formed during three distinct episodes: Middle to Late Triassic (240–220 Ma), Early Jurassic (190–175 Ma), and Late Jurassic to Early Cretaceous (150–125 Ma). The third period is considered to mark the most important metallogenic event, coinciding with the peak of lithosphere thinning and craton destruction in the NCC. Copyright © 2014 John Wiley & Sons, Ltd.     

A global assessment of the impact of climate change on water scarcity

This paper presents a global scale assessment of the impact of climate change on water scarcity. Patterns of climate change from 21 Global Climate Models (GCMs) under four SRES scenarios are applied to a global hydrological model to estimate water resources across 1339 watersheds. The Water Crowding Index (WCI) and the Water Stress Index (WSI) are used to calculate exposure to increases and decreases in global water scarcity due to climate change. 1.6 (WCI) and 2.4 (WSI) billion people are estimated to be currently living within watersheds exposed to water scarcity. Using the WCI, by 2050 under the A1B scenario, 0.5 to 3.1 billion people are exposed to an increase in water scarcity due to climate change (range across 21 GCMs). This represents a higher upper-estimate than previous assessments because scenarios are constructed from a wider range of GCMs. A substantial proportion of the uncertainty in the global-scale effect of climate change on water scarcity is due to uncertainty in the estimates for South Asia and East Asia. Sensitivity to the WCI and WSI thresholds that define water scarcity can be comparable to the sensitivity to climate change pattern. More of the world will see an increase in exposure to water scarcity than a decrease due to climate change but this is not consistent across all climate change patterns. Additionally, investigation of the effects of a set of prescribed global mean temperature change scenarios show rapid increases in water scarcity due to climate change across many regions of the globe, up to 2 °C, followed by stabilisation to 4 °C.     

Response of low‐angle dunes to variable flow

Current understanding of bedform dynamics is largely based on field and laboratory observations of bedforms in steady flow environments. There are relatively few investigations of bedforms in flows dominated by unsteadiness associated with rapidly changing flows or tides. As a consequence, the ability to predict bedform response to variable flow is rudimentary. Using high‐resolution multibeam bathymetric data, this study explores the dynamics of a dune field developed by tidally modulated, fluvially dominated flow in the Fraser River Estuary, British Columbia, Canada. The dunes were dominantly low lee angle features characteristic of large, deep river channels. Data were collected over a field ca 1·0 km long and 0·5 km wide through a complete diurnal tidal cycle during the rising limb of the hydrograph immediately prior to peak freshet, yielding the most comprehensive characterization of low‐angle dunes ever reported. The data show that bedform height and lee angle slope respond to variable flow by declining as the tide ebbs, then increasing as the tide rises and the flow velocities decrease. Bedform lengths do not appear to respond to the changes in velocity caused by the tides. Changes in the bedform height and lee angle have a counterclockwise hysteresis with mean flow velocity, indicating that changes in the bedform geometry lag changes in the flow. The data reveal that lee angle slope responds directly to suspended sediment concentration, supporting previous speculation that low‐angle dune morphology is maintained by erosion of the dune stoss and crest at high flow, and deposition of that material in the dune trough.