Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.     

Cancelling magnetic feature and filament activation

We report in this paper the analysis of the evolution of a magnetic fragment observed in NOAA 9445 on 5 May, 2001. This magnetic fragment emerged laterally to a filament which later split into two parts. The bifurcation site coincided with the magnetic fragment location and the part of the filament which split was later destabilized and a flare occurred. The magnetic flux variations in the magnetic fragment and in the surrounding area were analyzed and, considering their trends and other observational signatures (Hα brightenings and associated plasma motions), we could infer that it was a cancelling magnetic feature (CMF).We determined some geometrical and physical parameters of the CMF (area, magnetic flux variation, cancellation speed and flux cancellation rate) using high resolution magnetograms taken by BBSO. We compared the observed parameters of the CMF with the parameters of low‐lying reconnection current sheets given in the model proposed by Litvinenko (1999) and found good agreement between observed and theoretical values. Therefore, we conclude that a low‐lying magnetic reconnection process might be the cause of the filament activation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray absorption study of Ti-bearing silicate glasses

Ti K-edge XANES spectra have been collected on a series of Ti-bearing silicate glasses with metasilicate and tetrasilicate compositions. The intensity of the preedge feature in these spectra has been found to change with glass composition and varies from 29 to 58% (normalized intensity) suggesting a variation in structural environent around the absorbing atom. The pre-edge peak intensity increases for the alkali titanium tetrasilicate glasses from 35% to 58% in the order Li < Na < K < Rb, Cs whereas for the metasilicate compositions there is a maximum for the K-bearing glass. The pre-edge peak intensity remains constant for the alkaline earth titanium metasilicate glasses, Ca and Sr (34%) but increases slightly for Ba (41%). As the intensity of this feature is inversely correlated with coordination number, a comparison of the pre-edge intensity data for the investigated glasses with those of materials of known coordination number leads us to establish a regression equation and to infer that the average coordination number of Ti in these glasses ranges from 4.8 to 5.8. Large alkali cations appear to stabilize a relatively low average coordination number for Ti in silicate melts. The Ti structural environment results appear also to vary as a function of SiO₂ content within the K₂O-TiO₂-SiO₂ system. A number of physical properties of the melts from which these glasses were quenched and of other Ti-bearing silicate melts, have been determined in recent years. Clear evidence of a variable coordination number of Ti, consistent with the interpretation of the present XANES data is available from density measurements. These and other property determinations are compared with the present spectroscopic observations in an attempt to relate structure and properties in these melts which contain a major component with variable coordination number.     

High temperature structural and thermoelastic behaviour of mantle orthopyroxene: an in situ neutron powder diffraction study

The temperature induced structural evolution and thermoelastic behaviour of a natural (Pbca) orthopyroxene (Opx), with chemical formula ^M2(Mg_0.856Ca_0.025Fe²⁺ _0.119) ^M1(Mg_0.957Fe²⁺ _0.011Fe³⁺ _0.016Cr_0.011Al_0.005)Al_0.032Si_1.968O₆, from a suite of high pressure ultramafic nodules of mantle origin, have been investigated by in-situ neutron powder diffraction at several temperatures starting from 1,200°C down to 150°C. Unit-cell parameter variations as a function of T show no phase transition within this temperature range. The volume thermal expansion coefficient, α = V ⁻¹(∂V/∂T) _P0, varies linearly with T. The axial thermal expansion coefficients, α_j = l _j⁻¹(∂l _j/∂T)_P0, increase non-linearly with T. The principal Lagrangian unit-strain coefficients (ɛ//a, ɛ//b, ɛ//c), increase continuously with T. However, the orientation of the unit-strain ellipsoid appears to change with T. With decreasing T, the values of the unit-strain coefficients along the b and c axes tend to converge. The orientation at ΔT = 1,080°C is maintained down to the lowest temperature (150°C). The two non-equivalent tetrahedral chains, TA _n OA_3n and TB _n OB_3n , are kinked differently. At room-T, the TB _n OB_3n chain is more strongly kinked by about 23° than the TA _n OA_3n chain. With increasing T, the difference decreases by 3° for the TB _n OB_3n chain. The intersite cation exchange reaction between M1 and M2 (Mg²⁺ and Fe²⁺) shows a slight residual order at 1,200°C followed by reordering with decreasing temperature although seemingly not with a definite progressive trend. At the lowest temperature reached (150°C), reordering has occurred with the same value of partitioning coefficient K _D as that before heating. The absence of the expected phase transition is most likely due to the presence of minor amounts of Fe³⁺, Al, Ca and Cr which must play a crucial role on the thermoelastic behaviour and phase stability fields in natural Opx, with consequent important petrologic and geological implications.     

Numerical efficiency assessment of energy dissipators for seismic protection of buildings

This paper presents a two-dimensional numerical study on the nonlinear seismic response of buildings equipped with two types of energy dissipators: Constant Friction Slip Braces (CFSB) and Adding Damping and Stiffness (ADAS). Three types of reinforced concrete buildings with 3, 7 and 15 storeys, representatives of the short-medium- and long-period ranges, are considered. Dissipators are placed in steel diagonal braces in all the floors. The sliding threshold (or yielding) forces for each mechanism are selected using two different criteria: (i) they are taken as 50, 75 and 100 per cent of those generated by the equivalent static lateral forces recommended by the UBC-91 for a ductile moment resisting frame and (ii) they are constant in the whole building (this constant value is chosen equal to the maximum forces obtained with the previous criterion). The input consists of ten recorded earthquakes (normalized with respect to their Housner intensity) corresponding to medium and stiff local soil conditions. Average values on the ten registers are given for the maximum horizontal displacement, the base shear, the energy dissipated and the interstorey drift. The possibility of failure in some devices has been numerically simulated to assess the robustness of the system. The obtained results show that both devices are useful to reduce the response compared to the bare frame and that CFSB is more efficient than ADAS; for 7- and 15-storey frames the lateral displacement with CFSB is even smaller than the one for the braced frame (rigid connections instead of dissipators). The conclusions are expected to provide simple design guidelines. © 1998 John Wiley & Sons, Ltd.     

Mechanical behavior of buildings subjected to impulsive motions

This article analyses the response of steel-moment resisting frames subjected to near-field ground motions. In near-field areas high damage and a relevant number of collapsed steel buildings arose even when both design and detailing had been performed in perfect accordance with the code provisions. These circumstances are related to the characteristics of the motion that in such areas shows large-amplitude pulses along the fault-normal component. The response of two steel moment resisting frames characterized by different stiffness levels and subjected to seven different accelerograms recorded in stations located in near-field areas is discussed in the following. The frames have been also analyzed by modelling the real behavior of semi-rigid joints between beams and columns and taking into account the presence of passive dampers (shear link devices). The non-linear dynamic analysis has been performed with the aim of acquiring a quantitative knowledge on the effects of near-field ground motions on frame buildings and on their damage.     

Stellar velocity dispersion in narrow-line Seyfert 1 galaxies

Several authors have recently explored, for narrow-line Seyfert 1 galaxies (NLS1s), the relationship between black hole mass ( M _BH) and stellar velocity dispersion (σ_*). Their results are more or less in agreement and seem to indicate that NLS1s fill the region below the fit obtained by Tremaine et al., showing a range of σ_* similar to that of Seyfert 1 galaxies, and a lower M _BH. Until now, the [O  iii ] width has been used in place of the stellar velocity dispersion, but some indications have begun to arise against the effectiveness of the gaseous kinematics in representing the bulge potential, at least in NLS1s. Bian & Zhao have stressed the urgency of producing true σ_* measurements. Here, we present new stellar velocity dispersions obtained through direct measurements of the Ca  ii absorption triplet (∼8550 Å) in the nuclei of eight NLS1 galaxies. The resulting σ_* values and a comparison with σ_[O III] confirm our suspicion that [O  iii ] typically overestimates the stellar velocity dispersion. We demonstrate that NLS1s follow the   M _BH–σ_*  relation as Seyfert 1, quasars and non-active galaxies.     

Space weathering of silicates simulated by nanosecond pulse UV excimer laser

Laser irradiation experiments have been performed on powdered silicates (othopyroxene, clinopyroxene, and olivine) using a nanosecond pulse UV excimer laser (193 and 248 nm) to simulate the effects of space weathering induced on minor bodies of the Solar System by micrometeorite bombardment. We have used different fluences (from 0.05 to 2 J/cm²) to weather the samples, experimenting below and above the ablation threshold. All the irradiated materials have shown reddening and darkening of their UV-vis-NIR reflectance spectra. In addition we have found that: (1) below ablation threshold, weathering effects increase with increasing number of laser pulses, and with increasing fluence, confirming that a thermal process is active; (2) above ablation threshold, weathering is much stronger and efficient than in the previous case, and is independent on the number of pulses. We show that astrophysical time-scales, i.e. times necessary to obtain similar effects on planetary objects, are of about 10⁸ yr for both olivine and pyroxene in the case of ablation. The time grows up to 10¹⁰ yr in the case of thermal effects. We infer that micrometeorite bombardment can be rightly simulated by laser irradiation only considering congruent laser ablation.