A simple model for lensing by black holes in galactic nuclei

The lensing properties of the Plummer model with a central point mass and external shear are derived, including the image multiplicities, critical curves and caustics. This provides a simple model for a flattened galaxy with a central supermassive black hole. For the Plummer model with black hole, the maximum number of images is four, provided the black hole mass is less than an upper bound which is calculated analytically. This introduces a method to constrain black hole masses by counting images, thus applicable at cosmological distance. With shear, the maximum number of images is six and we illustrate the occurrence of an astroid caustic and two metamorphoses.     

Infrared spectrophotometry of Comet IRAS-Araki-Alcock (1983d): a bare nucleus revealed?

Spectra of the central core and surrounding coma of Comet IRAS-Araki-Alcock (1983d) were obtained at 8–13 μm on 11 May and 2–4 μm on 12 May 1983. Spatially resolved measurements at 10 μm with a 4-arcsec beam showed that the central core was more than 100 times brighter than the inner coma only 8 arcsec away; for radially outflowing dust, the brightness ratio would be a factor of 8. The observations of the central core are consistent with direct detection of a nucleus having a radius of approximately 5 km. The temperature of the sunlit hemisphere was > 300 K. Spectra of the core are featureless, while spectra of the coma suggest weak silicate emission. The spectra show no evidence for icy grains. The dust producton rate on 11.4 May was ～ 10⁵ g/sec, assuming that the gas flux from the dust-producing areas on the nucleus was ～ 10^?5 g/cm²/sec.     

Numerical simulation of comet nuclei I. Water-ice comets

A one-dimensional simulation of pure water-ice cometary nuclei is presented, and the effect of the nucleus as a heat reservoir is considered. The phase transition from amorphous to crystalline ice is studied for two cases: (1) where the released latent heat goes entirely into heating adjacent layers and (2) where the released latent heat goes entirely into sublimation. For a Halley-like orbit it was found that for case 1 the phase boundary penetrates about 15 m on the first orbit and does not advance until sublimation brings the surface to some 10 m from the phase boundary. For case 2 the phase boundary penetrates about 1 m below the surface and remains at this depth as the surface sublimates. For an orbit like that of Schwassmann-Wachmann 1 the phase boundary penetrates about 50 m initially for case 1 and about 1 m for case 2. There is no further transformation until the entire comet is heated slowly to near the transition temperature, after which the entire nucleus is converted to crystalline ice. For an Encke-type orbit case 1 gives a nearly continuous transition of the entire nucleus to crystalline ice, while for case 2 the initial penetration is about 8 m and remains at this depth relative to the surface as sublimation decreases the cometary radius. Thus the entire comet is converted to crystalline ice just before it is completely dissipated.     

X-ray synchrotron emission from the oblique shock in the jet of the powerful radio galaxy 3C 346

We report the first detection, with Chandra , of X-ray emission from the jet of the powerful narrow-line radio galaxy 3C 346. X-rays are detected from the bright radio and optical knot at which the jet apparently bends by approximately 70°. The Chandra observation also reveals a bright galaxy-scale atmosphere within the previously known cluster and provides a good X-ray spectrum for the bright core of 3C 346. The X-ray emission from the knot is synchrotron radiation, as seen in lower-power sources. In common with these sources, there is evidence of morphological differences between the radio/optical and X-ray structures, and the spectrum is inconsistent with a one-component continuous-injection model. We suggest that the X-ray-bright knot is associated with a strong oblique shock in a moderately relativistic, light jet, at ∼ 20° to the line of sight, and that this shock is caused by the jet interacting with the wake in the cluster medium behind the companion galaxy of 3C 346. The general jet curvature can result from pressure gradients in the cluster atmosphere.     

CATASTROPHIC ECO-ENVIRONMENTAL CHANGE IN THE SONGNEN PLAIN, NORTHEASTERN CHINA SINCE 1900S

Although the Songnen Plain in the northeastern China was developed relatively late in the temperate zone of the world, its eco-environment has changed greatly. This paper analyzes the changes of land cover and the rates and trends ofdesertification during the past 100 years in the Songnen Plain. According to the macroscopic analysis, we find that the eco-environment in the plain has reached to the threshold of catastrophic change since the 1950s. The Thorn Needle Catastrophic Model was used to determine and validate this conclusion. Human activities, including large-scale construction projects, such as huge dams and dikes, and excessive grazing were the primary factors contributing to regional eco-environmental catastrophe. And irrational reclamation of the wilderness also affected the eco-environmental change. The results reveal the complex human-land interactions.     

Einsteins' gravity with massive gravitons

Graviton may, in principle, have a small non-zero mass. In this paper the relevant theory of the massive graviton with six polarisations is developed. The drastic impact of a non-zero mass of the graviton on cosmology is also illustrated.     

Generalized strain probing of constitutive models

Advanced material constitutive models are used to describe complex soil behaviour. These models are often used in the solution of boundary value problems under general loading conditions. Users and developers of constitutive models need to methodically investigate the represented soil response under a wide range of loading conditions. This paper presents a systematic procedure for probing constitutive models. A general incremental strain probe, 6D hyperspherical strain probe (HSP), is introduced to examine rate‐independent model response under all possible strain loading conditions. Two special cases of HSP, the true triaxial strain probe (TTSP) and the plane‐strain strain probe (PSSP), are used to generate 3‐D objects that represent model stress response to probing. The TTSP, PSSP and general HSP procedures are demonstrated using elasto‐plastic models. The objects resulting from the probing procedure readily highlight important model characteristics including anisotropy, yielding, hardening, softening and failure. The PSSP procedure is applied to a Neural Network (NN) based constitutive model. It shows that this probing is especially useful in understanding NN constitutive models, which do not contain explicit functions for yield surface, hardening, or anisotropy. Copyright © 2004 John Wiley & Sons, Ltd.     

Porous interstellar grains

Recent observations of stellar composition suggest that elements in the Sun are significantly more abundant than in other stars. The reduction in the available element budget implies a drastic revision in current models of interstellar dust. Theoretical models are therefore exploring fluffy, porous physical structure for the grain material. Since a detailed exact treatment of extinction cross-sections is mandatory for a correct understanding of the nature of interstellar dust, we present a technique based on the multipole expansions of the electromagnetic field, which has proven to be general, flexible and powerful in treating scattering of light by porous, composite, arbitrarily shaped particles. The results of this study speak in favour of core–mantle structures characterized by the presence of porosities.     

Theoretical accuracy of synthetic aperture sonar micronavigation using a displaced phase-center antenna

The Cramer-Rao lower bounds on the cross-track translation and rotation of a displaced phase-center antenna (DPCA) in the slant range plane between two successive pings (known as DPCA sway and yaw in what follows) are computed, assuming statistically homogeneous backscatter. These bounds are validated using experimental data from a 118-182-kHz sonar, showing an accuracy of the order of 20 microns on the ping-to-ping cross-track displacements. Next, the accuracy required on the DPCA sway and yaw in order to achieve a given synthetic aperture sonar (SAS) beampattern specification, specified by the expected SAS array gain, is computed as a function of the number P of pings in the SAS. Higher accuracy is required when P increases to counter the accumulation of errors during the integration of the elementary ping-to-ping estimates: the standard deviation must decrease as P/sup -1/2/ for the DPCA sway and P/sup -3/2/ for the yaw. Finally, by combining the above results, the lower bounds on DPCA micronavigation accuracy are established. These bounds set an upper limit to the SAS length achievable in practice. The maximum gain Q in cross-range resolution achievable by a DPCA micronavigated SAS is computed as a function of the key SAS parameters. These theoretical predictions are compared with simulations and experimental results.