Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

A dynamo theory of solar flares

It is proposed that the solar flare phenomenon can be understood as a manifestation of the electrodynamic coupling process of the photosphere-chromosphere-corona system as a whole. The system is coupled by electric currents, flowing along (both upward and downward) and across the magnetic field lines, powered by the dynamo process driven by the neutral wind in the photosphere and the lower chromosphere. A self-consistent formulation of the proposed coupling system is given. It is shown in particular that the coupling system can generate and dissipate the power of 10²⁹ erg s^#X2212;1 and the total energy of 10³² erg during a typical life time (10³ s) of solar flares. The energy consumptions include Joule heat production, acceleration of current-carrying particles along field lines, magnetic energy storage and kinetic energy of plasma convection. The particle acceleration arises from the development of field-aligned potential drops of 10–150 kV due to the loss-cone constriction effect along the upward field-aligned currents, causing optical, X-ray and radio emissions. The total number of precipitating electrons during a flare is shown to be of order 10³⁷–10³⁸.     

Is the ‘superhot’ hard x-ray component in solar flares consistent with a thermal source?

It has been shown by Brown and Emslie (1988) that any optically thin thermal bremsstrahlung source must emit an energy spectrumL () (keV s^–1 keV^–1) which has the property that higher derivatives alternate in sign, i.e., (–) ^j L(^j)() > 0 for allj. In this short note, we apply this test to the superhot component discussed by Linet al. (1981) in order to determine whether a strictly thermal interpretation of this component is valid. We find that all statistically significant higher derivatives do indeed have the correct sign; this strengthens the identification of this component as due to a thermal source.Presidential Young Investigator.     

A model of an exploding,radiating star in general relativity

In a previous paper Adams, Cary and Cohen (1994) presented a model of a supernova. In that paper the equations of General Relativity describing the evolution of a spherically symmetric, radiating star were solved analytically. The evolution of the star was determined by the application of boundary conditions at the center and at the edge. Due to lmitations in the presupernova model, only the very slow inward motion of an unstable, degenerate core could be considered. The solution was also limited by the need to exclude a runaway term, one that increased exponentially with time. Without the exclusion of the runaway, the luminosity would have increased without bound and the mass would have become negative.This paper presents a completely analytic solution to the equations of General Relativity describing the evolution of a Type II supernova. Professor S.E. Woosley kindly gave us data on the physical variables of a 12M ₀ presupernova star. In our model the core collapses within 1 s, leaving a 1.3M ₀ remnant. Shortly afterward 10.6M ₀ is ejected to infinity, and 0.17M ₀ is radiated away in the form of neutrinos. The distance of the edge from the center increases proportionally to the two-thirds power of the time. The luminosity decreases proportionally to the inverse four-thirds power.Although the runaway solution was modified by the exploding rather than a static envelope, it must still be excluded by adjusting initial conditions. Its character is changed from an exponential to a very large power (55) of time. The removal of a degree of freedom by this exclusion leads to physically non-sensical results such as negative luminosity. The inclusion of a term describing motion of the mantle due to neutrino interactions provides the additional degree of freedom necessary for physically reasonable results.     

White-light enhancements and small-scale chromospheric activities in an active region

A microflare or a group of Ellerman bombs was found to be associated with several points of white-light enhancements. These points had similar sizes as facular points (d 0.3 arc sec). Temporal evolution of these activities is described. Origins of these activities are discussed to be deeply seated excess heating in chromospheric and photospheric levels.     

On solving Kepler's equation for nearly parabolic orbits

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these points on a scientific vest-pocket calculator. Moreover, srtarting with these points in the Newton's method we can calculate a root of Kepler's equation with an accuracy greater than 0.001 in 0–2 iterations. This accuracy holds for the true anomaly || 135° and |e – 1| 0.01. We explain the reason for this effect also.Dedicated to the memory of Professor G.N. Duboshin (1903–1986).     

Origin of the hydrocarbon component of carbonaceous chondrites: the star-meteorite connection

We report the results of an experiment that produced a residue which closely matches the hydrocarbon component of the Murchison carbonaceous chondrite. This experiment suggests that the parent material of the meteoritic component originated as polycyclic aromatic hydrocarbon species in carbon stars during their later stages of evolution. The experiments also indicate that the pathway from those formation sites to eventual incorporation into the meteorite parent body involved hydrogenation in a plasma in the solar nebula or in H II regions prior to the solar nebula. This model is consistent with what is known about the meteoritic hydrocarbon component including deuterium abundance, the observation of cosmic infrared emission bands best attributed to polycyclic aromatic hydrocarbon molecules, and the inherent stability of these molecules that allows their formation in stars and subsequent survival in the interstellar medium.     

Upper limits to trace constituents in Jupiter's atmosphere from an analysis of its 5-μm spectrum

A high-resolution (0.6 cm^?1) spectrum of Jupiter at 5 μm recorded at the Kuiper Airborne Observatory is used to determine upper limits to the column density of 19 molecules. The upper limits to the mixing ratios of SiH₄, H₂S, HCN, and simple hydrocarbons are discussed with respect to current models of Jupiter's atmosphere. These upper limits are compared to expectations based upon the solar abundance of the elements. This analysis permits upper limit measurements (SiH₄), or actual detections (GeH₄), of molecules with mixing ratios with hydrogen as low as 10^?9. In future observations at 5 μm the sensitivity of remote spectroscopic analyses should permit the study of constituents with mixing ratios as low as 10^?10, which would include the hydrides of such elements as Sn and As as well as numerous organic molecules.