Kelvin-Helmholtz instability in an Alfvén resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfvén driving amplitude and inversely proportional to the width of the Alfvén resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Evaluating Natural Attentuation with Spreadsheet Analytical Fate and Transport Models

Superposition techniques can extend the capabilities of relatively simple analytical fate and transport models. Complex source geometries, simple aquifer boundaries, and electron acceptor limited biodegradation can be simulated by using superposition techniques in computer spreadsheets. Spreadsheet models are an easily used tool for interpreting sampling results and for estimating attenuation and degradation rates in relatively homogeneous aquifers. Analytical spreadsheet models are based on the Domenico analytical model and can provide results that are in close agreement with the numerical model UIOPLUMH II.     

High-resolution garnet chronometry and the rates of metamorphic processes

Garnets in an amphibolite-facies metasediment from Sulitjelma, North Norway yield precise and concordant SmNd, UPb and RbSr ages that relate directly to the pressure (P) and temperature (T) conditions of mineral growth. Differential mineral reaction between graphitic and non-graphitic layers within this sample preserves a record of theP-T and time (t) history experienced during Barrovian regional metamorphism. Garnets in graphitic layers grew during prograde metamorphism at462 ± 16°C and5.2 ± 0.5 kbar under conditions of lowaH₂O, and yield indistinguishable¹⁴⁷Sm¹⁴³Nd and²³⁸U²⁰⁶Pb ages of434.1 ± 1.2 Ma and433.9 ± 1.0 Ma, respectively. In contrast, garnet growth in adjacent graphite-free layers did not occur untilP-T conditions of540 ± 18°C and8.0 ± 1.0 kbar were attained, with continued growth in response to minor heating and decompression with final matrix equilibration at544 ± 16°C and7.0 ± 1.0 kbar. The inclusion-free garnet rims in this assemblage record indistinguishable¹⁴⁷Sm¹⁴³Nd and²³⁸U²⁰⁶Pb ages of424.6 ± 1.2 Ma and423.4± 1.7 Ma, respectively. These results provide precise estimates for average heating and burial rates during prograde metamorphism of 8.6_−4.4^+7.5°C Ma⁻¹ and 0.8_−0.5^+0.9 km Ma⁻¹, respectively. Rb and Sr exchange between coexisting silicates in the graphite-free assemblage continued for some 37 Ma after the “peak” of metamorphism, and require an average cooling rate of about 4.0°C Ma⁻¹ during uplift. These results illustrate a clear relationship between reaction history and the timing of mineral growth and provide definitive constraints on the rates of thermal and tectonic processes accompanying regional metamorphism.     

Chemical weathering associated with tafoni at Papago Park,central Arizona

Papago Park, Arizona, is a pediment-inselberg complex that hosts a variety of well developed tafoni and alveolar weathering forms. The purpose of this paper is to analyse the nature of chemical weathering associated with the tafoni using backscatter electron microscopy (BSE) and quantitative wavelength dispersive X-ray analysis (WDS). Calcium-rich and iron-rich coatings occur on the outer shells of the tafoni. Calcium carbonate precipitation within mineral microfractures occurs on the underside of the tafoni. Chemical weathering of primary mineral grains provides a source of material found in the coatings. The WDS analyses show a near-complete lack of salt-forming elements. Copyright © 1999 John Wiley & Sons, Ltd.     

MIGRATION IN THE PRESENCE OF NOISE*

It is shown that the so-called Kirchhoff-summation operator is of a very wide-band nature and even contains an evanescent part. As a consequence, discretization may cause serious aliasing errors, particularly for small extrapolation steps. It is proposed to use in all practical cases band-limited versions of the summation operator, the spatial cut-off frequency being determined by the spatial Fourier spectrum of the coherent noise.