The tidal stripping of satellites

We present an improved analytic calculation for the tidal radius of satellites and test our results against N -body simulations.
The tidal radius in general depends upon four factors: the potential of the host galaxy, the potential of the satellite, the orbit of the satellite and the orbit of the star within the satellite . We demonstrate that this last point is critical and suggest using three tidal radii to cover the range of orbits of stars within the satellite. In this way we show explicitly that prograde star orbits will be more easily stripped than radial orbits; while radial orbits are more easily stripped than retrograde ones. This result has previously been established by several authors numerically, but can now be understood analytically. For point mass, power-law (which includes the isothermal sphere), and a restricted class of split power-law potentials our solution is fully analytic. For more general potentials, we provide an equation which may be rapidly solved numerically.
Over short times (≲1–2 Gyr ∼1 satellite orbit), we find excellent agreement between our analytic and numerical models. Over longer times, star orbits within the satellite are transformed by the tidal field of the host galaxy. In a Hubble time, this causes a convergence of the three limiting tidal radii towards the prograde stripping radius. Beyond the prograde stripping radius, the velocity dispersion will be tangentially anisotropic.     

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.     

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.     

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.     

A sapphirine–phlogopite–cordierite paragenesis in a low-P amphibolite facies terrain, Arunta Inlier, Australia

Summary Silica-undersaturated phlogopite schists from the Cackleberry Metamorphics, Arunta Inlier, central Australia, preserve relatively low-temperature sapphirine-bearing parageneses that developed during low-pressure upper amphibolite facies metamorphism. Peak metamorphic phlogopite–cordierite–sapphirine assemblages are interpreted to have formed during the same event recorded in nearby metapelites, at c.3 kbar and 650–700 °C. Initial cooling of the terrain resulted in the breakdown of sapphirine to corundum–chlorite–phlogopite and corundum–spinel–chlorite assemblages. Further retrogression at greenschist facies conditions resulted in the replacement of sapphirine by diaspore–chlorite intergrowths. The reaction textures are consistent with a near-isobaric heating-cooling path at low-pressure, and provide evidence for the stability of sapphirine at c.700 °C at low pressures in rocks of an appropriate Mg- and Fe³⁺-rich bulk composition. Received August 15, 2001 accepted December 27, 2001