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.     

Photometric distances to nine dark globules

Distances to nine dark globules are determined by a method using optical ( VRI ) and near-infrared (near-IR) ( JHK ) photometry of stars projected towards the field containing the globules. In this method, we compute intrinsic colour indices of stars projected towards the direction of the globule by dereddening the observed colour indices using various trial values of extinction   A _V   and a standard extinction law. These computed intrinsic colour indices for each star are then compared with the intrinsic colour indices of normal main-sequence stars and a spectral type is assigned to the star for which the computed colour indices best match with the standard intrinsic colour indices. Distances ( d ) to the stars are determined using the   A _V   and absolute magnitude  ( M_V )  corresponding to the spectral types thus obtained. A distance versus extinction plot is made and the distance at which   A _V   undergoes a sharp rise is taken to be the distance to the globule. All the clouds studied in this work are in the distance range 160–400 pc. The estimated distances to dark globules LDN 544, LDN 549, LDN 567, LDN 543, LDN 1113, LDN 1031, LDN 1225, LDN 1252 and LDN 1257 are  180 ± 35, 200 ± 40, 180 ± 35, 160 ± 30, 350 ± 70, 200 ± 40, 400 ± 80, 250 ± 50  and 250 ± 50 pc, respectively. Using the distances determined, we have estimated the masses of the globules and the far-IR luminosity of the IRAS sources associated with them. The mass of the clouds studied are in the range  10–200 M_⊙  .     

Excitation mechanism of atmospheric pressure waves from the 1980 Mount St Helens eruption

Summary. Atmospheric pressure waves from the Mount St Helens eruption 1980 May 18 have been clearly recorded by a sensitive microbarograph at Berkeley, California. The record shows three types of waves with different group velocities. The pressure waves can be interpreted in terms of direct waves A1, antipodean travelling waves A2 and circumnavigating waves A3, all of which are composed of several acoustic-gravity modes propagated in the lower atmosphere. Synthetic barograms appropriate to the Berkeley station have been calculated on the basis of the dynamic response of the lower atmospheric structure, together with various assumptions of source properties. Comparisons between synthetic and observed barograms provide estimates for ranges of the time history of upward particle velocity at the source, source dimensions and the velocity of the source spreading over the blast zone, as well as for the average dissipation effects over the circumferential path. The results suggest that two major compression pulses on the A1 record correlate with the arrival of pressure waves from the first (lateral) blast and second (vertical) blast, although the inferred interblast time interval is not consistent with that estimated from seismic observations.     

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.     

Deep-ocean piezometer probe technology for geotechnical investigations

Two single-sensor piezometer probes, 8 mm in diameter, were developed for deep-ocean geotechnical investigations. These probes were tested in a hyperbaric chamber pressurized to 55 MPa (8000 psi). Testing was performed for a period of five weeks under high hydrostatic pressure with the probes inserted in reconstituted illitic marine sediment. Small differential pore-water pressures were generated in response to both mechanically and thermally generated forcing functions. During deep-ocean simulated pressure tests, the sensors exhibited excellent sensitivity and stability. These developments in piezometer-probe technology provide a quantitative means of assessing important geotechnical parameters of fine-grained seabed deposits.     

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.     

Methods of array element localization for a towed underwateracoustic array

The location of the hydrophones on a towed underwater acoustic array as a function of time (array element localization) is needed for signal processing. Methods to perform this localization using least squares polynomial fitting to data from depth sensors, heading sensors, and sensors detecting a ping from a single source are discussed. Arc distance along the array is used as the independent parameter so that all solutions are constrained to be space curves. Examples of application to real data are presented, and techniques to discriminate against bad sensor data are discussed     

New developments in eclipsing binary light curve modeling

The light curve modeling of binary stars has continued to evolve since its founding by Henry Norris Russell (see Russell and Merrill 1952 and citations therein) nearly a century ago, accelerated in the 1950s by Kopal's introduction of Roche geometry into models and by the development of synthetic light curve computer code in the 1970's. Improved physics and the use of more kinds of observational input are providing another round of important advances that promise to enlarge our knowledge of both binary stars and ensembles containing them. Here we discuss the newer horizons of light curve modeling and the steps being taken toward them.     

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.