Consistent tangent operators for constitutive rate equations

A general approach for obtaining the consistent tangent operator for constitutive rate equations is presented. The rate equations can be solved numerically by the user's favourite time integrator. In order to obtain reliable results, the substepping in integration should be based on a control of the local error. The main ingredient of the consistent tangent operator, namely the derivative of the stress with respect to the strain increment must be computed simultaneously with the same integrator, applied to a numerical approximation of the variational equations. This information enables finite‐element packages to assemble a consistent tangent operator and thus guarantees quadratic convergence of the equilibrium iterations. Several numerical examples with a hypoplastic constitutive law are given. As numerical integrator we used a second‐order extrapolated Euler method. Quadratic convergence of the equilibrium iteration is shown. Copyright © 2002 John Wiley & Sons, Ltd.     

The Galileo star scanner observations at Amalthea

In November of 2002, the Galileo spacecraft passed within 250 km of Jupiter's moon Amalthea. An onboard telescope, the star scanner, observed a series of bright flashes near the moon. It is believed that these flashes represent sunlight reflected from 7 to 9 small moonlets located within about 3000 km of Amalthea. From star scanner geometry considerations and other arguments, we can constrain the diameter of the observed bodies to be between 0.5 m to several tens of kilometers. In September of 2003, while crossing Amalthea's orbit just prior to Galileo's destruction in the jovian atmosphere, a single additional body seems to have been observed. It is suspected that these bodies are part of a discrete rocky ring embedded within Jupiter's Gossamer ring system.     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

The infrared luminosity of the torus and the visibility of scattered broad line emission in Seyfert 2 galaxies

A number of studies have shown that the visibility of scattered broad emission lines in Seyfert 2 galaxies is strongly dependent on the IRAS     flux ratio, where those Seyfert 2 galaxies with 'warm' IRAS colours show polarized broad line emission. It is now clear that this effect is owing to the increasing dominance of the galactic rather than the active galactic nucleus (AGN) emission at 60 μm in less-luminous 'cool' Seyfert 2 galaxies. However, we present evidence that the 25-μm emission is a good measure of the AGN luminosity for most Seyfert 2 galaxies. Using this result, we show that the visibility of scattered broad line emission has a dependence on the AGN luminosity. The observations can be interpreted self-consistently if the scaleheight of the scattering zone varies with central source luminosity whilst the scaleheight of the obscuring torus is approximately constant.     

Extended dust emission in NGC 7465

We present SCUBA 850-μm, JCMT  CO( J =2→1)  , B -band imaging and VLA H  i observations of the NGC 7465/4/3 group of galaxies. The 850-μm emission associated with NGC 7465 extends to at least ∼2 R ₂₅ and is well correlated with the H  i . We investigate a range of possible mechanisms by which dust beyond R ₂₅ may be heated to give the observed extended submillimetre emission. By modelling the dust heating by stars in two extreme geometries, we fail to find any reasonable star formation scenario that is consistent with both the 850-μm and optical data. Furthermore, we do not detect any  CO( J =2→1)  emission coincident with the extended dust and atomic gas as would be expected if significant star formation were occurring. We show that shock-heating of dust via cloud–cloud collisions in the stripped interstellar medium of NGC 7465 could be sufficient to explain the extended 850-μm emission and lack of optical emission in the stripped gas, and suggest that cloud–cloud collisions may be an important dust heating mechanism in gas-rich systems.     

The role of Fischer‐Tropsch catalysis in solar nebula chemistry

Abstract— Fischer‐Tropsch catalysis, the iron/nickel catalyzed conversion of CO and H₂ to hydrocarbons, would have been the only thermally‐driven pathway available in the solar nebula to convert CO into other forms of carbon. A major issue in meteoritics is to determine the origin of meteoritic organics: are they mainly formed from CO in the solar nebula via a process such as Fischer‐Tropsch, or are they derived from interstellar organics? In order to determine the role that Fischer‐Tropsch catalysis may have played in the organic chemical evolution of the solar nebula, we have developed a kinetic model for this process. Our model results agree well with experimental data from several existing laboratory studies. In contrast, empirical rate equations, which have been derived from experimental rate data for a limited temperature (T) and pressure (P) range, are inconsistent with experimental rate data for higher T and lower P. We have applied our model to pressure and temperature profiles for the solar nebula, during the epoch in which meteorite parent bodies condensed and agglomerated. We find that, under nebular conditions, the conversion rate of CO to CH₄ does not simply increase with temperature as the empirically‐derived equations suggest. Instead, our model results show that this process would have been most efficient in a fairly narrow region that coincides with the present position of the asteroid belt. Our results support the hypothesis that Fischer‐Tropsch catalysis may have played a role in solar nebula chemistry by converting CO into less volatile materials that can be much more readily processed in the nebula and in parent bodies.