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.     

Particulate organic matter in the coastal and estuarine waters of Goa and its relationship with phytoplankton production

In the coastal and estuarine waters of Goa, particulate organic carbon (POC) varied from 0.52 to 2.51 mg l^?1 and from 0.28 to 5.24 mg l^?1 and particulate phosphorus (PP) varied from 0.71 to 5.18 μg l^?1 and from 0.78 to 20.34 μg l^?1, respectively. The mean values of chlorophyll and primary productivity were 1.94 mg m^?3 and 938.1 mg C m^?2 day^?1 in the coastal waters and 4.3 mg m^?3 and 636.5 mg C m^?1 day^?1 in the estuarine waters, respectively.$\text{POC}\text{chl}$ ratios were low in June and October even when POC values were quite high. The POC in surface waters was linearly correlated with the chlorophyll content. Also PP increased when chlorophyll and primary productivity remained high. The results suggest that the phytoplankton was sharply increasing and contributed to POC and PP content. The percentage of detritus calculated from the intercept values of chlorophyll on POC varied from 46 to 76% depending on season. Results indicate that the major portion of POC and PP during postmonsoon (October–January) is derived from phytoplankton production while the allochthonous matter predominate during monsoon (June–September).     

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.     

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     

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.     

Metamorphism in Archaean greenstone belts: calculated fluid compositions and implications for gold mineralization

An inescapable consequence of the metamorphism of greenstone belt sequences is the release of a large volume of metamorphic fluid of low salinity with chemical characteristics controlled by the mineral assemblages involved in the devolatilization reactions. For mafic and ultramafic sequences, the composition of fluids released at upper greenschist to lower amphibolite facies conditions for the necessary relatively hot geotherm corresponds to those inferred for greenstone gold deposits (X_CO2= 0.2–0.3). This result follows from the calculation of mineral equilibria in the model system CaO–MgO–FeO–Al₂O₃–SiO₂–H₂O–CO₂, using a new, expanded, internally consistent dataset. Greenstone metamorphism cannot have involved much crustal over-thickening, because very shallow levels of greenstone belts are preserved. Such orogeny can be accounted for if compressive deformation of the crust is accompanied by thinning of the mantle lithosphere. In this case, the observed metamorphism, which was contemporaneous with deformation, is of the low-P high-T type. For this type of metamorphism, the metamorphic peak should have occurred earlier at deeper levels in the crust; i.e. the piezothermal array should be of the ‘deeper-earlier’type. However, at shallow crustal levels, the piezothermal array is likely to have been of ‘deeper-later’type, as a consequence of erosion. Thus, while the lower crust reached maximum temperatures, and partially melted to produce the observed granites, mid-crustal levels were releasing fluids prograde into shallow crustal levels that were already retrograde. We propose that these fluids are responsible for the gold mineralization. Thus, the contemporaneity of igneous activity and gold mineralization is a natural consequence of the thermal evolution, and does not mean that the mineralization has to be a consequence of igneous processes. Upward migration of metamorphic fluid, via appropriate structurally controlled pathways, will bring the fluid into contact with mineral assemblages that have equilibrated with a fluid with significantly lower X_CO2. These assemblages are therefore grossly out of equilibrium with the fluid. In the case of infiltrated metabasic rocks, intense carbonation and sulphidation is predicted. If, as seems reasonable, gold is mobilized by the fluid generated by devolatilization, then the combination of processes proposed, most of which are an inevitable consequence of the metamorphism, leads to the formation of greenstone gold deposits predominantly from metamorphic fluids.     

Dissolution and depletion of ferromagnesian minerals from Holocene tephra layers in an acid bog,New Zealand,and implications for tephra correlation

This study examines the depletion of ferromagnesian silicate minerals from a sequence of thin, distal, mainly rhyolitic tephra layers of Holocene age preserved in an acid peat bog (Kopouatai), North Island, New Zealand. The rate of such depletion has been fast, as indicated by the complete loss of biotite from one tephra layer (Kaharoa Tephra), in which it is normally dominant, in only ca. 770 yr. Chemical dissolution is advocated as the likely cause for the depletion, with amphiboles and other mineral grains commonly showing etch pits, microcaves, and other characteristic surface solution features. Theoretical thermodynamic and kinetic models show a marked increase in the rate of dissolution of all ferromagnesian minerals under conditions of low pH (< 4), but that where silica concentrations in solution are high the relative proportions of minerals remaining are unaffected. However, where concentrations of dissolved silica are low, as in most bog environments, the relative proportions of ferromagnesian minerals are affected as well as absolute amounts being decreased. Amphiboles are depleted relative to pyroxenes, consistent with kinetic studies. The results show that the identification and correlation of tephras on the basis of relative abundances of ferromagnesian minerals alone may be unreliable, and emphasise the need to use multiple criteria in such studies.     

Response of circular footings and anchor plates in non-homogeneous elastic soils

The axisymmetric elastic response of circular footings and anchor plates in a linearly non-homogeneous elastic soil is analysed. It is assumed that footings/anchors are flexible and subjected to axisymmetric vertical loads. The response of the footing/anchor is modelled by using the classical Poisson–Kirchhoff thin plate theory. A variational technique is used to analyse the interaction problem. A representation for the contact stress is established by using a fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the non-homogeneous soil. The fundamental solution can be derived by using rigorous analytical procedures. The influence of the footing flexibility and the degree of soil non-homogeneity on the displacements, bending moments and contact stresses of a surface footing is examined over a wide range of governing parameters. In the case of anchor plates the influence of depth of embedment, degree of soil non-homogeneity and anchor flexibility on the anchor displacement is investigated.     

Double starbursts triggered by mergers in hierarchical clustering scenarios

We use cosmological smooth particle hydrodynamical (SPH) simulations to study the effects of mergers in the star formation history of galactic objects in hierarchical clustering scenarios. We find that during some merger events, gaseous discs can experience two starbursts: the first one during the orbital decay phase, owing to gas inflows driven as the satellite approaches, and the second one when the two baryonic clumps collide. A trend for these first induced starbursts to be more efficient at transforming the gas into stars is also found. We detect that systems that do not experience early gas inflows have well-formed stellar bulges and more concentrated potential wells, which seem to be responsible for preventing further gas inward transport triggered by tidal forces. The potential wells concentrate owing to the accumulation of baryons in the central regions and of dark matter as the result of the pulling in by baryons. The coupled evolution of the dark matter and baryons would lead to an evolutionary sequence during which systems with shallower total potential wells suffer early gas inflows during the orbital decay phase that help to feed their central mass concentration, pulling in dark matter and contributing to build up more stable systems. Within this scenario, starbursts triggered by early gas inflows are more likely to occur at early stages of evolution of the systems and to be an important contributor to the formation of stellar bulges. Our results constitute the first proof that bulges can form as the product of collapse, collisions and secular evolution in a cosmological framework, and they are consistent with a rejuvenation of the stellar population in bulges at intermediate z with, at least, 50 per cent of the stars (in SCDM) being formed at high z .