The response of an elastic half‐space under a momentary shear line impulse

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Can gas dynamics in centres of galaxies reveal orbiting massive black holes?

If supermassive black holes in centres of galaxies form by merging of black hole remnants of massive Population III stars, then there should be a few black holes of mass one or two orders of magnitude smaller than that of the central ones, orbiting around the centre of a typical galaxy. These black holes constitute a weak perturbation in the gravitational potential, which can generate wave phenomena in gas within a disc close to the centre of the galaxy. Here, we show that a single orbiting black hole generates a three-arm spiral pattern in the central gaseous disc. The density excess in the spiral arms in the disc reaches values of 3–12 per cent when the orbiting black hole is about 10 times less massive than the central black hole. Therefore, the observed density pattern in gas can be used as a signature in detecting the most massive orbiting black holes.     

Virtual Huanghe River System： Framework and Technology

1 Introduction Huanghe (Yellow) River basin is located in 32°–42°N, 96°–119°E. The area of the catchment is more than 752,000km2. The river is 5464km long with a drop in elevation of 4830m. Among the whole area, the moun- tainous and stone area accounts for 29%, loess and hills area 46%, sandy area 11% and plain area 14%, respec- tively. Different natural landscapes exist in this area. The Huanghe River flows through the Loess Plateau, where the soil is eroded seriously (Wang, 2002;…     

The plane of the Edgeworth-Kuiper belt

We examine possible locations for the primordial disk of the Edgeworth-Kuiper Belt (EKB), using several subsets of the known objects as markers of the total mass distribution. Using a secular perturbation theory, we find that the primordial plane of the EKB could have remained thin enough to escape detection only if it is clustered very closely about the invariable plane of the Solar System.     

The efficiency of the spiral-in of a black hole to the Galactic Centre

We study the efficiency at which a black hole or dense star cluster spirals in to the Galactic Centre. This process takes place on a dynamical friction time-scale, which depends on the value of the Coulomb logarithm (ln Λ). We determine the accurate value of this parameter using the direct N -body method, a tree algorithm and a particle-mesh technique with up to two million plus one particles. The three different techniques are in excellent agreement. Our measurement for the Coulomb logarithm appears to be independent of the number of particles. We conclude that  ln Λ= 6.6 ± 0.6  for a massive point particle in the inner few parsec of the Galactic bulge. For an extended object, such as a dense star cluster, ln Λ is smaller, with a value of the logarithm argument Λ inversely proportional to the object size.     

Dynamical implications of Jupiter's tropospheric ammonia abundance

Groundbased radio observations indicate that Jupiter's ammonia is globally depleted from 0.6 bars to at least 4-6 bars relative to the deep abundance of ∼3 times solar, a fact that has so far defied explanation. The observations also indicate that (i) the depletion is greater in belts than zones, and (ii) the greatest depletion occurs within Jupiter's local 5-μm hot spots, which have recently been detected at radio wavelengths. Here, we first show that both the global depletion and its belt-zone variation can be explained by a simple model for the interaction of moist convection with Jupiter's cloud-layer circulation. If the global depletion is dynamical in origin, then important endmember models for the belt-zone circulation can be ruled out. Next, we show that the radio observations of Jupiter's 5-μm hot spots imply that the equatorial wave inferred to cause hot spots induces vertical parcel oscillation of a factor of ∼2 in pressure near the 2-bar level, which places important constraints on hot-spot dynamics. Finally, using spatially resolved radio maps, we demonstrate that low-latitude features exceeding ∼4000 km diameter, such as the equatorial plumes and large vortices, are also depleted in ammonia from 0.6 bars to at least 2 bars relative to the deep abundance of 3 times solar. If any low-latitude features exist that contain 3-times-solar ammonia up to the 0.6-bar ammonia condensation level, they must have diameters less than ∼4000 km.     

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.     

Damage identification method using harmonic excitation force considering both modelling and measurement errors

A method of structural damage identification using harmonic excitation force is presented. It considers the effects of both measurement and modelling errors in the baseline finite element model. Damage that accompanies changes in structural parameters can be estimated for a damaged structure from the change between measured vibration responses and ones calculated from the analytical model of the intact structure. In practice, modelling errors exist in the analytical model due to material and geometric uncertainties and a reduction in the degrees of freedom as well as measurement errors, making identification difficult. To surmount these problems, bootstrap hypothesis testing, which enables statistical judgment without information about these errors, was introduced. The method was validated by numerical simulation using a three‐dimensional frame structure and real vibration data for a three‐storey steel frame structure. Copyright © 2005 John Wiley & Sons, Ltd.     

A high resolution,multiproxy Late‐glacial record of climate change and intrasystem responses in northwest England

A lacustrine carbonate sequence from Hawes Water, Lancashire, UK, has been studied using stable isotopic, lithological, pollen and mineral magnetic analysis. The data reveal four abrupt climatic oscillations in the Late‐glacial Interstadial leading up to the onset of the Loch Lomond Stadial. The data also point to climatic warming relatively early within the stadial, ca. 12 500 GRIP yr, prior to the onset of the Holocene. The oxygen isotope record is taken as a signature of climate forcing against which the response of the lake‐system can be monitored. By adopting this approach it is revealed that the response of the biological system to the rapid climatic oscillations is non‐linear and primarily a function of the antecedent conditions. A significant end‐Devensian isotopic excursion (A) is matched by only minor changes in the cold‐adapted floras and faunas. During the warmer interstadial, the response of the biological ecosystem (events B–D) is clearly influenced by thresholds: major changes in the catchment vegetation associated with relatively minor oscillations in the isotopic signature. The stratigraphical patterns reveal significant lag effects between the onset of climate deterioration and resulting changes in vegetation. Copyright © 2002 John Wiley & Sons, Ltd.