Stability criteria in many-body systems

The analytical stability criterion applicable to coplanar hierarchical three-body systems described in the first paper of this series, Walkeret al. (1980), is modified to give an exact representation ofHill-type stability in all such cases. The dependence of the stability on all orbital parameters (in the coplanar case) is taken into account. The criterion for stability is now dependant upon the participating masses, the elements of the initial osculating Keplerian orbits of the system (viz. the orbits ofm ₂ aboutm ₁ andm ₃ about the mass-centre of the (m ₁,m ₂) system) and the positions within these orbits.The behaviour of the stability of such systems is demonstrated (both analytically and numerically) with respect to certain of the parameters involved to consider effects not dealt with in the above-mentioned paper. In particular two interesting real cases of triple systems in the Solar System are discussed, namely Sun-Jupiter-Saturn and Earth-Moon-Sun. The results of the present paper are compared with those of past authors who considered the same systems.Finally some general features arising out of our analysis are discussed.     

Distribution, habitat use and ecology of deepwater Anemones (Actiniaria) in the Gulf of Mexico

The distribution of deepwater Actiniaria is poorly known. Rarely are these organisms identified to family, as this requires both well-preserved specimens and taxonomic expertise. Ecological information is similarly lacking. From the results of a comprehensive surveying program in the deep Gulf of Mexico, we report the occurrence of nine species of Actiniaria. For the most abundant four of these, we plot distributions and discuss habitat use, morphological variation, and feeding strategies. Actiniaria in the Gulf appear to have broad, basin-wide distributions with little depth preference. Faunal biomass is highest in the NE Gulf within submarine canyons or at the base of slope escarpments. Attachment mode is mostly opportunistic on various types of hard substrata, including trash. Sediment-dwelling forms are very abundant at an organically rich site within a large submarine canyon.     

Water use patterns of mule deer (Odocoileus hemionus) and the effects of human disturbance

To aid the effectiveness of water developments, patterns of deer visiting water sources and the responses of deer to disturbance were examined. Deer visited water sources day and night, but not all deer at water sources drank. Thus, the assumption that radio-telemetry locations within arbitrary distances of water indicate drinking events may lead to overestimates of watering frequency. Human disturbance did not preclude or seriously impede use of water by deer. Deer reacted by adjusting the amount of time spent at water sources, moving away from water to return later and/or increasing the frequency with which they drank.     

Stability criteria in many-body systems

An expansion of the force function ofn-body dynamical systems, where the equations of motion are expressed in the Jacobian coordinate system, is shown to give rise naturally to a set of (n–1) (n–2) dimensionless parameters ^ki _li {i = 2,...,n;k = 2,...,i – 1 (i 3);l =i + 1,...,n (i n – 1)}, representative of the size of the disturbances on the Keplerian orbits of the various bodies. The expansion is particularized to the casen=3 which involves the consideration of only two parameters ²³ and ₃₂. Further, the work of Szebehely and Zare (1977) is reviewed briefly with reference to a sufficient condition for the stability of corotational coplanar three-body systems, in which two of the bodies form a binary system. This condition is sufficient in the sense that it precludes any possibility of an exchange of bodies, i.e. Hill type stability, however, it is not a necessary condition. These two approaches are then combined to yield regions of stability or instability in terms of the parameters ²³ and ₃₂ for any system of given masses and orbital characteristics (neglecting eccentricities and inclinations) with the following result: that there is a readily applicable rule to assess the likelihood of stability or instability of any given triple system in terms of ²³ and ₃₂.Treating a system ofn bodies as a set of disturbed three-body systems we use existing data from the solar system, known triple systems and numerical experiments in the many-body problem to plot a large number of triple systems in the ²³, ₃₂ plane and show the results agree well with the ²³, ₃₂ analysis above (eccentricities and inclinations as appropriate to most real systems being negligible). We further deal briefly with the extension of the criteria to many-body systems wheren>4, and discuss several interesting cases of dynamical systems.     

Comparative biomass structure and estimated carbon flow in food webs in the deep Gulf of Mexico

A budget of the standing stocks and cycling of organic carbon associated with the sea floor has been generated for seven sites across a 3-km depth gradient in the NE Gulf of Mexico, based on a series of reports by co-authors on specific biotic groups or processes. The standing stocks measured at each site were bacteria, Foraminifera, metazoan meiofauna, macrofauna, invertebrate megafauna, and demersal fishes. Sediment community oxygen consumption (SCOC) by the sediment-dwelling organisms was measured at each site using a remotely deployed benthic lander, profiles of oxygen concentration in the sediment pore water of recovered cores and ship-board core incubations. The long-term incorporation and burial of organic carbon into the sediments has been estimated using profiles of a combination of stable and radiocarbon isotopes. The total stock estimates, carbon burial, and the SCOC allowed estimates of living and detrital carbon residence time within the sediments, illustrating that the total biota turns over on time scales of months on the upper continental slope but this is extended to years on the abyssal plain at 3.6 km depth. The detrital carbon turnover is many times longer, however, over the same depths. A composite carbon budget illustrates that total carbon biomass and associated fluxes declined precipitously with increasing depth. Imbalances in the carbon budgets suggest that organic detritus is exported from the upper continental slope to greater depths offshore.The respiration of each individual “size” or functional group within the community has been estimated from allometric models, supplemented by direct measurements in the laboratory. The respiration and standing stocks were incorporated into budgets of carbon flow through and between the different size groups in hypothetical food webs. The decline in stocks and respiration with depth were more abrupt in the larger forms (fishes and megafauna), resulting in an increase in the relative predominance of smaller sizes (bacteria and meiofauna) at depth. Rates and stocks in the deep northern GoM appeared to be comparable to other continental margins where similar comparisons have been made.     

Post-settlement alteration of spatial patterns of soft shell clam (<Emphasis Type="Italic">Mya arenaria</Emphasis>) recruits

To examine the roles of settlement and early post-settlement processes in patterns of recruitment of the soft shell clamMya arenaria, abundance of juvenileMya at three intertidal sites in Barnstable Harbor, Massachusetts, was monitored over two settlement seasons. Two peaks of settlement occurred in 1998 (July and September) and one peak was recorded in June 1999, indicating that a late season settlement event is not a consistent feature at this site. Abundance of recent settlers (i.e., early recruits, < 1 week past settlement) varied significantly among the tidal flats (sites) that were separated by hundreds of meters to kilometers, but not among plots meters apart. Differences in abundance of settlers likely resulted in these differences in early-recruit abundance among sites. Settlement was greatest at the site with the greatest variability in flow speed. Sites also differed to some extent in their sediment characteristics and macrofaunal assemblages, which may influence larval substrate choice. Between-site differences in abundance ofMya decreased after settlement. The rate of decline of abundance varied among cohorts and sites. Comparison of abundance of recent settlers (up to 145,000 m⁻²) to that of juveniles > 3-mm shell length at the end of the settlement season (up to 60 m⁻²) indicated large losses of individuals during the early post-settlement period. This study demonstrates that spatial patterns inMya abundance can change substantially during the early post-settlement period, and that high mortality rates can result in cohorts contributing little to the population size even when rates of settlement are high.