Irregular behaviour and eccentricity increase in the trajectories of a dynamical system modelling asteroidal motions

Many trajectories of the third body are integrated numerically in a modified elliptical restricted three body problem (ERTBP), in which the eccentricity, e, of the orbit of the second primary varies sinusoidally with time. It is found that, in the case of the 2:1 resonance, the introduction of the time variability of e modifies significantly the behaviour of the trajectories of the third body. In particular their osculating eccentricity e, present the following two notable features: (a) In all cases it shows a definite chaotic variation, which appears at significantly shorter time-scales than the one found by Wisdom in the e = constant case. (b) In many cases it shows a significant increase, up and beyond the (critical) value e _crit = 0.52. As a result the third body approaches the first primary at distances smaller than 0.29 (where by we denote the semi-major axis of the trajectory of the second primary around the first), which in the actual Sun-Jupiter-asteroid problem corresponds to the semi-major axis of Mars. Our result might be of interest in the context of explaining the Kirkwood gaps at the resonances where the osculating eccentricity of asteroid trajectories calculated in the classical (e = constant) ERTBP does not reach Mars crosser values.     

Multi-decadal synthesis of benthic–pelagic coupling in the western arctic: Role of cross-shelf advective processes

Using geographic information systems (GIS) software and geostatistical techniques, we utilized three decades of water-column chlorophyll a data to examine the relative importance of autochthonous versus allochthonous sources of reduced carbon to benthic communities that occur from the northern Bering to the eastern Beaufort Sea shelf. Spatial trend analyses revealed areas of high benthic biomass (>300 g m⁻²) and chlorophyll (>150 mg m⁻²) on both the southern and northern Chukchi shelf; both areas are known as depositional centers for reduced organic matter that originates on the Bering Sea shelf and is advected northward in Anadyr and Bering shelf water masses. We found a significant correlation between biomass and chlorophyll a in the Chukchi Sea, reflective of the strong benthic–pelagic coupling in a system that is utilized heavily by benthic-feeding marine mammals. In contrast, there was no significant correlation between biomass and chlorophyll in the Beaufort Sea, which by comparison, is considerably less productive (biomass and chlorophyll, <75 g m⁻² and <50 mg m⁻², respectively). One notable exception is an area of relatively high biomass (50–100 g m⁻²) and chlorophyll (80 mg m⁻²) near Barter Island in the eastern Beaufort Sea. Compared to other adjacent areas in the Beaufort Sea, the chlorophyll values in the vicinity of Barter Island were considerably higher and likely reflect a long-hypothesized upwelling in that area and close coupling between the benthos and autochthonous production. In the Bering Sea, a drop in benthic biomass in 1994 compared with previous measurements (1974–1993) may support earlier observations that document a decline in biomass that began between the 1980s and 1990s in the Chirikov Basin and south of St. Lawrence Island. The results of this study indicate that the benthos is an excellent long-term indicator of both local and physical advective processes. In addition, this work provides further evidence that secondary production on arctic shelves can be significantly augmented by reduced carbon advected from highly productive adjacent shelves.     

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.     

Simulations of deep pencil-beam redshift surveys

We create mock pencil-beam redshift surveys from very large cosmological N -body simulations of two cold dark matter (CDM) cosmogonies, an Einstein–de Sitter model ( τ CDM) and a flat model with Ω₀=0.3 and a cosmological constant (ΛCDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. Simulation particles are tagged as 'galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our τ CDM (ΛCDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no 'preferred' period over our many realizations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a τ CDM (ΛCDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the regularity on a scale of ∼130  h ⁻¹ Mpc observed by Broadhurst et al. has a priori probability well below 10⁻³.     

Ellipticity of Nearby Elliptical Galaxies Identified with Extended Extragalactic Radio Sources

The dependence of the ellipticity of nearby optical galaxies associated with extragalactic radio sources on the type of radio galaxy is considered. It is shown that elliptical galaxies identified with radio galaxies of the FRI type and with radio sources having a radio image with a small elongation have a smaller ellipticity, on the average, than those associated with radio galaxies of the FRII type and with radio sources with greater elongation. As one possible explanation for this phenomenon, one can assume that the optical galaxies associated with radio galaxies of type FRI and with radio sources of small elongation are oriented in space so that they are observed edge-on relatively rarely.     

Laboratory study of deep-water breaking waves

In an attempt to elucidate the mechanics of deep-water wave breaking, a variety of breaking waves, including spilling and plunging waves, of different length scales and geometries was studied. The waves were generated through wave-wave interactions using wave packets with constant-steepness components, constant-amplitude components, and also components following the Pierson-Moskowitz distribution. Wave steepening prior to breaking were found to cause an increase in the high frequency spectral slope of the wave spectrum. The slopes were correlated to the type of breaking and the intensity of the breaking. The energy loss through breaking varied with the spectral characteristics of the wave packet. On the other hand, it was also noted that, irrespective of the wave packet, the losses were from the higher frequency end of the first harmonics.     

39Ar‐40Ar ages of eucrites and thermal history of asteroid 4 Vesta

Abstract— Eucrite meteorites are igneous rocks that derived from a large asteroid, probably 4 Vesta. Past studies have shown that after most eucrites formed, they underwent metamorphism in temperatures up to ≥800°C. Much later, many were brecciated and heated by large impacts into the parent body surface. The less common basaltic, unbrecciated eucrites also formed near the surface but, presumably, escaped later brecciation, while the cumulate eucrites formed at depths where metamorphism may have persisted for a considerable period. To further understand the complex HED parent body thermal history, we determined new ³⁹Ar‐⁴⁰Ar ages for 9 eucrites classified as basaltic but unbrecciated, 6 eucrites classified as cumulate, and several basaltic‐brecciated eucrites. Precise Ar‐Ar ages of 2 cumulate eucrites (Moama and EET 87520) and 4 unbrecciated eucrites give a tight cluster at 4.48 ± 0.02 Gyr (not including any uncertainties in the flux monitor age). Ar‐Ar ages of 6 additional unbrecciated eucrites are consistent with this age within their relatively larger age uncertainties. By contrast, available literature data on Pb‐Pb isochron ages of 4 cumulate eucrites and 1 unbrecciated eucrite vary over 4.4–4.515 Gyr, and ¹⁴⁷Sm‐¹⁴³Nd isochron ages of 4 cumulate and 3 unbrecciated eucrites vary over 4.41–4.55 Gyr. Similar Ar‐Ar ages for cumulate and unbrecciated eucrites imply that cumulate eucrites do not have a younger formation age than basaltic eucrites, as was previously proposed. We suggest that these cumulate and unbrecciated eucrites resided at a depth where parent body temperatures were sufficiently high to cause the K‐Ar and some other chronometers to remain as open diffusion systems. From the strong clustering of Ar‐Ar ages at ?4.48 Gyr, we propose that these meteorites were excavated from depth in a single large impact event ?4.48 Gyr ago, which quickly cooled the samples and started the K‐Ar chronometer. A large (?460 km) crater postulated to exist on Vesta may be the source of these eucrites and of many smaller asteroids thought to be spectrally or physically associated with Vesta. Some Pb‐Pb and Sm‐Nd ages of cumulate and unbrecciated eucrites are consistent with the Ar‐Ar age of 4.48 Gyr, and the few older Pb‐Pb and Sm‐Nd ages may reflect an isotopic closure before the large cratering event. One cumulate eucrite gives an Ar‐Ar age of 4.25 Gyr; 3 additional cumulate eucrites give Ar‐Ar ages of 3.4–3.7 Gyr; and 2 unbrecciated eucrites give Ar‐Ar ages of ?3.55 Gyr. We attribute these younger ages to a later impact heating. Furthermore, the Ar‐Ar impact‐reset ages of several brecciated eucrites and eucritic clasts in howardites fall within the range of 3.5–4.1 Gyr. Among these, Piplia Kalan, the first eucrite to show evidence for extinct ²⁶Al, was strongly impact heated ?3.5 Gyr ago. When these data are combined with eucrite Ar‐Ar ages in the literature, they confirm that several large impact heating events occurred on Vesta between ?4.1–3.4 Gyr ago. The onset of major impact heating may have occurred at similar times for both Vesta and the moon, but impact heating appears to have persisted for a somewhat later time on Vesta.     

Invasions in Marine Communities: Contrasting Species Richness and Community Composition Across Habitats and Salinity

While many studies of non-native species have examined either soft-bottom or hard-bottom marine communities, including artificial structures at docks and marinas, formal comparisons across these habitat types are rare. The number of non-indigenous species (NIS) may differ among habitats, due to differences in species delivery (trade history) and susceptibility to invasions. In this study, we quantitatively compared NIS to native species richness and distribution and examined community similarity across hard-bottom and soft-sediment habitats in San Francisco Bay, California (USA). Benthic invertebrates were sampled using settlement panels (hard-bottom habitats) and sediment grabs (soft-bottom habitats) in 13 paired sites, including eight in higher salinity areas and five in lower salinity areas during 2 years. Mean NIS richness was greatest in hard-bottom habitat at high salinity, being significantly higher than each (a) native species at high salinity and (b) NIS richness at low salinity. In contrast, mean NIS richness in soft-bottom communities was not significantly different from native species richness in either high- or low-salinity waters, nor was there a difference in NIS richness between salinities. For hard-bottom communities, NIS represented an average of 79% of total species richness per sample at high salinity and 78% at low salinity, whereas the comparable values for soft bottom were 46 and 60%, respectively. On average, NIS occurred at a significantly higher frequency (percent of samples) than native species for hard-bottom habitats at both salinities, but this was not the case for soft-bottom habitats. Finally, NIS contributed significantly to the existing community structure (dissimilarity) across habitat types and salinities. Our results show that NIS richness and occurrence frequency is highest in hard-bottom and high-salinity habitat for this Bay but also that NIS contribute strongly to species richness and community structure across each habitat evaluated.     

Magnetic properties of the Lower Old Red Sandstone lavas in the Midland Valley,Scotland; palaeomagnetic and tectonic considerations

Thermal demagnetization studies of lavas in the Strathmore area of the Midland Valley, Scotland, support overall palaeomagnetic data found in previous studies of these rocks. Reduced directional scatter as compared to some earlier studies, is attributed to more effective demagnetization, resolving some of the directional complexity of previous studies. Combined magnetic fabric and directional analysis suggest that at least some deviating directions may be explained by local tectonism. The existence of almost antiparallel directional groups and field tests give supporting evidence for a “primary” (deuteric) origin of the main magnetization of these rocks. Additionally, a second remanence component having shallow reverse directions of magnetization, is attributed to later remagnetization in Old Red Sandstone time. The Midland Valley results are seen in conjunction with other Palaeozoic palaeomagnetic results and possible geodynamic implications are discussed.