Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

Seismic hazard monitoring in Kamchatka and its applications to the M = 6.6 earthquake of 6 October 1987

The earthquake of 6 October 1987 (M = 6.6), which occurred near the Shipunsky Cape, Kamchatka, was the largest crustal event in the vicinity of the main city of Kamchatka — Petropavlovsk-Kamchatsky — during the last three decades. It was followed by numerous aftershocks. This earthquake allowed us to test the effectiveness of the seismic hazard monitoring in Kamchatka, including the seismological, geodetic and hydrogeochemical surveys. The seismic survey provided the location and source nature of the main shock and aftershocks and the seismic environment of the main shock. The geodetic and hydrogeochemical surveys have yielded data on the response to earthquakes of the Earth's surface deformations, water level, and chemical elements concentration in the underground water. As a result, the following data were obtained:

u

The earthquake of 6 October had a seismic moment 4–10 E18 Nm, thrust type of faulting and the source volume of 20 × 20 × 10 km³. The maximum intensity was VI–VII (MSK-64 scale) and maximum acceleration 88 cm/s².

Before this event, a relative increase in the number of the upper mantle (depth more than 100 km) moderate magnitude earthquakes during 5 years and a one-year period of seismic quiescence for small shallow earthquakes, were recognized. Significant anomalies in HCO₃ and H₃BO₃ concentrations in the underground waters were observed in the wells a week before the main shock.

     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Site effect on vulnerability of high-rise shear wall buildings under near and far field earthquakes

Worldwide experience repeatedly shows that damages in structures caused by earthquakes are highly dependent on site condition and epicentral distance. In this paper, a 21-storey shear wall-structure built in the 1960s in Hong Kong is selected as an example to investigate these two effects. Under various design earthquake intensities and for various site conditions, the fragility curves or damage probability matrix of such building is quantified in terms of the ductility factor, which is estimated from the ratio of storey yield shear to the inter-storey seismic shear. For high-rise buildings, a higher probability of damage is obtained for a softer site condition, and damage is more severe for far field earthquakes than for near field earthquakes. For earthquake intensity of VIII, the probability of complete collapse (P) increases from 1 to 24% for near field earthquakes and from 1 to 41% for far field earthquakes if the building is moved form a rock site to a site consisting a 80 m thick soft clay. For intensity IX, P increases from 6 to 69% for near field earthquake and from 14 to 79% for far field earthquake if the building is again moved form rock site to soft soil site. Therefore, site effect is very important and not to be neglected. Similar site and epicentral effects should also be expected for other types of high-rise structures.     

Searches for very high energy gamma rays from blazars with CANGAROO-III telescope in 2005-2009

We have searched for very high energy (VHE) gamma rays from four blazars using the CANGAROO-III imaging atmospheric Cherenkov telescope. We report the results of the observations of H 2356-309, PKS 2155-304, PKS 0537-441, and 3C 279, performed from 2005 to 2009, applying a new analysis to suppress the effects of the position dependence of Cherenkov images in the field of view. No significant VHE gamma ray emission was detected from any of the four blazars. The GeV gamma-ray spectra of these objects were obtained by analyzing Fermi/LAT archival data. Wide range (radio to VHE gamma-ray bands) spectral energy distributions (SEDs) including CANGAROO-III upper limits, GeV gamma-ray spectra, and archival data, even though they are non-simultaneous, are discussed using a one-zone synchrotron self-Compton (SSC) model in combination with a external Compton (EC) radiation. The HBLs (H 2356-309 and PKS 2155-304) can be explained by a simple SSC model, and PKS 0537-441 and 3C 279 are well modeled by a combination of SSC and EC model. We find a consistency with the blazar sequence in terms of strength of magnetic field and component size.     

Dust masses and abundances in planetary nebulae: likely strong elemental depletion in low-abundance sources

An analysis is undertaken of the relation between dust/gas mass ratios and elemental abundances within planetary nebulae (PNe). It is found that M _DUST/ M _GAS is broadly invariant with abundance, and similar to the values observed in asymptotic giant branch (AGB)-type stars. However, it is noted that the masses of dust observed in low-abundance PNe are similar to the masses of heavy elements observed in the gas phase. This is taken to imply that levels of elemental depletion must be particularly severe, and extend to many more species than have been identified so far. In particular, given that levels of C and O depletion are likely to be large, then this probably implies that species such as Fe, S, Si and Mg are depleted as well. There is already evidence for depletion of Fe, Si and Mg in individual PNe. It follows that whilst quoted abundances may accurately reflect gas-phase conditions, they are likely to be at variance with intrinsic abundances in low Z _N nebulae.
Finally, we note that there appears to be a variation in dust/gas mass ratios with galactocentric distance, with gradient similar to that observed for several elemental abundances. This may represent direct evidence for a correlation between dust/gas mass ratios and nebular abundances.