On some applications of invariant manifolds

Taking transfer orbits of a collinear libration point probe, a lunar probe and an interplanetary probe as examples, some applications of stable and unstable invariant manifolds of the restricted three-body problem are discussed. Research shows that transfer energy is not necessarily conserved when invariant manifolds are used. For the cases in which the transfer energy is conserved, the cost is a much longer transfer time.     

Formation flying in elliptic orbits with the J2 perturbation

Relative dynamics between the chief satellite and the deputy ones in formation flying is crucial to maintaining the formation. A good choice of the formation usually requires a lower control frequency or less control energy. For formation flying missions in highly elliptic orbits, the well-known C-W equation is not accurate enough. Instead, Lawden’s equation is often used. First, the solution to Lawden’s equation with a very simple form is deduced. Then the J2 perturbation is added. It is found that Lawden’s solution is not necessarily valid when the J2 perturbation is considered. Completely discarding Lawden’s solution and borrowing the idea of mean orbit elements, two rules to initialize the formation are proposed. The deviation speed is greatly reduced. Different from previous studies on the J2 perturbation, except for the relatively simple expression for the semi-major axis, the tedious formulae of the long period terms and the short period terms of other orbital elements are not used. In addition, the deviation speed is further reduced by compensation of the nonlinear effects. Finally, a loose control strategy of the formation is proposed. To test the robustness of this strategy, a third body perturbation is added in numerical simulations.     

Interpretation of combined infrared,submillimeter, and millimeter thermal flux data obtained during the Rosetta fly-by of Asteroid (21) Lutetia

The European Space Agency’s Rosetta spacecraft is the first Solar System mission to include instrumentation capable of measuring planetary thermal fluxes at both near-IR (VIRTIS) and submillimeter–millimeter (smm–mm, MIRO) wavelengths. Its primary mission is a 1 year reconnaissance of Comet 67P/Churyumov–Gerasimenko beginning in 2014. During a 2010 close fly-by of Asteroid 21 Lutetia, the VIRTIS and MIRO instruments provided complementary data that have been analyzed to produce a consistent model of Lutetia’s surface layer thermal and electrical properties, including a physical model of self-heating. VIRTIS dayside measurements provided highly resolved 1 K accuracy surface temperatures that required a low thermal inertia, I < 30 J/(K m² s^0.5). MIRO smm and mm measurements of polar night thermal fluxes produced constraints on Lutetia’s subsurface thermal properties to depths comparable to the seasonal thermal wave, yielding a model of I < 20 J/(K m² s^0.5) in the upper few centimeters, increasing with depth in a manner very similar to that of Earth’s Moon. Subsequent MIRO-based model predictions of the dayside surface temperatures reveal negative offsets of ～5–30 K from the higher VIRTIS-measurements. By adding surface roughness in the form of 50% fractional coverage of hemispherical mini-craters to the MIRO-based thermal model, sufficient self-heating is produced to largely remove the offsets relative to the VIRTIS measurements and also reproduce the thermal limb brightening features (relative to a smooth surface model) seen by VIRTIS. The Lutetia physical property constraints provided by the VIRTIS and MIRO data sets demonstrate the unique diagnostic capabilities of combined infrared and submillimeter/millimeter thermal flux measurements.     

Environmental dependence of stellar mass,SFR, and SSFR for the Luminous Red Galaxy (LRG) sample of the SDSS DR7

Using the Luminous Red Galaxy (LRG) sample of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), we investigate the environmental dependence of stellar mass, star formation rate (SFR) and specific star formation rate (SSFR) of LRGs. It is found that stellar mass of LRGs nearly is independent of local environments, and that the environmental dependence of SFR and SSFR in the LRG sample is much weaker than the one in the Main galaxy sample. One possible explanation is that galaxy color and morphology are a pair of galaxy properties most predictive of local environments, while LRGs are a group of galaxies that are likely to be luminous, red and of early types (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Volcanic hazards from Bezymianny- and Bandai-type eruptions

Major slope failures are a significant degradational process at volcanoes. Slope failures and associated explosive eruptions have resulted in more than 20 000 fatalities in the past 400 years; the historic record provides evidence for at least six of these events in the past century. Several historic debris avalanches exceed 1 km³ in volume. Holocene avalanches an order of magnitude larger have traveled 50–100 km from the source volcano and affected areas of 500–1500 km². Historic eruptions associated with major slope failures include those with a magmatic component (Bezymianny type) and those solely phreatic (Bandai type). The associated gravitational failures remove major segments of the volcanoes, creating massive horseshoe-shaped depressions commonly of caldera size. The paroxysmal phase of a Bezymianny-type eruption may include powerful lateral explosions and pumiceous pyroclastic flows; it is often followed by construction of lava dome or pyroclastic cone in the new crater. Bandai-type eruptions begin and end with the paroxysmal phase, during which slope failure removes a portion of the edifice. Massive volcanic landslides can also occur without related explosive eruptions, as at the Unzen volcano in 1792.The main potential hazards from these events derive from lateral blasts, the debris avalanche itself, and avalanche-induced tsunamis. Lateral blasts produced by sudden decompression of hydrothermal and/or magmatic systems can devastate areas in excess of 500km² at velocities exceeding 100 m s^–1. The ratio of area covered to distance traveled for the Mount St. Helens and Bezymianny lateral blasts exceeds that of many pyroclastic flows or surges of comparable volume. The potential for large-scale lateral blasts is likely related to the location of magma at the time of slope failure and appears highest when magma has intruded into the upper edifice, as at Mount St. Helens and Bezymianny.Debris avalanches can move faster than 100 ms^–1 and travel tens of kilometers. When not confined by valley walls, avalanches can affect wide areas beyond the volcano's flanks. Tsunamis from debris avalanches at coastal volcanoes have caused more fatalities than have the landslides themselves or associated eruptions. The probable travel distance (L) of avalanches can be estimated by considering the potential vertical drop (H). Data from a catalog of around 200 debris avalanches indicates that the H/L rations for avalanches with volumes of 0.1–1 km³ average 0.13 and range 0.09–0.18; for avalanches exceeding 1 km³, H/L ratios average 0.09 and range 0.5–0.13.Large-scale deformation of the volcanic edefice and intense local seismicity precede many slope failures and can indicate the likely failure direction and orientation of potential lateral blasts. The nature and duration of precursory activity vary widely, and the timing of slope faliure greatly affects the type of associated eruption. Bandai-type eruptions are particularly difficult to anticipate because they typically climax suddenly without precursory eruptions and may be preceded by only short periods of seismicity.     

Effect of reproductive state and sex on movement and food consumption of western rock lobster (Panulirus cygnus) in a tank environment

The catchability of western rock lobsters (Panulirus cygnus) during the spawning season (October and November) may be affected by their reproductive state. In this study, movement and food consumption of males and females of different reproductive states held in laboratory tanks were measured as proxies for catchability. Density of lobsters was found to influence both movement and food consumption. Solitary animals and, to a lesser extent, two lobsters per tank, were more sedentary and consumed significantly less food than animals at a density of three or four specimens per tank. Tests using three animals per tank confirmed that mature, unmated, and ovigerous females carrying early stage eggs moved more frequently away from their shelters than males or females carrying late stage eggs (P < 0.0001, d.f. = 3). Further, unmated females and females with early stage eggs recorded significantly higher food consumption (P < 0.0061, d.f. = 3) compared with males or females carrying late stage eggs. The greater time spent away from shelter and also food consumption make unmated females and females with early stage eggs likely to be more catchable than males or females with late stage eggs. As catchability is commonly used to obtain population estimates from survey data, these results have implications for surveys which use catch rates of breeding animals as indicators of egg production.     

Depth of settlement of two mussel species on suspended collectors in Marlborough Sounds,New Zealand (Note)

The preferred depth of settlement and settlement period of two species of mussel spat were monitored at Yncyca Bay (NZMS1 S15 220460) and Wet Inlet (NZMS1 S16 265432) in the Marlborough Sounds on collectors suspended in 0–4 m of water between 20 October 1975 and 4 April 1976. Peak settlement of Mytilus edulis aoteanus was between 20 October 1975 and 4 January 1976, and decreased with increasing depth. Peak settlement of Perna canaliculus was between 16 February 1976 and 12 April 1976, and showed no preferred depth of settlement.

Capture of wild stocks of Mytilus edulis aoteanus and Perna canaliculus spat for use in aquaculture has become more reliable through accurate forecasting of peak settlement periods, and knowledge of preferred depth of settlement of the two species.

Preferred depth of settlement of spat may affect the shore zonation of mussels.     

Cadmium,lead, copper,and zinc in Elminius modestus Darwin (Crustacea,Cirripedia) from Waitemata and Manukau Harbours,Auckland, New Zealand

Abstract

Concentrations of cadmium (Cd), lead (Pb), copper (Cu), and zinc (Zn) were measured in adult barnacles (Elminius modestus Darwin) from Waitemata and Manukau Harbours in the Auckland area, New Zealand. As in studies on sediments reported in the literature, it was possible to identify areas of likely anthropogenic influence, e.g., around the Auckland Harbour Bridge for Pb, Cu, and Zn. Groups of individuals with highest concentrations for these metals showed 19.8–23.8 mg Pb kg^?1, 198–266 mg Cu kg^?1, and 4460–6530 mg Zn kg^?1 (95% confidence limits, dry weight basis). Cd concentrations found for all barnacles from the Auckland area ranged from 0.8 to 3.1 mg kg^?1. Two samples from Omaha Beach, 60 km north of Auckland, were used as a reference. Accordingly, groups of individuals with lowest concentrations for Pb, Cu, and Zn could be allocated to this site using the Student‐Newman‐Keuls Multiple Range Test (0.5–1.3 mg Pb kg^?1, 8–10 mg Cu kg^?1, and 144–214 mg Zn kg^?1 ; 95% confidence limits). Only Cd concentrations were highest at Omaha Beach (8.6–12.1 mg Cd kg^?1 ). This result may have arisen from “naturally” increased bio‐availabilities of certain metals in mangrove systems which are reported in the literature. Generally, metal concentrations in barnacles from the Auckland Harbour area and from Omaha Beach were within the wider range for E. modestus as well as other barnacle species reported in the international literature.     

Behavior of soil plugs in open‐ended model piles driven into sands

Calibration chamber tests were conducted on open‐ended model piles driven into dried siliceous sands with different soil conditions in order to clarify the effect of soil conditions on load transfer mechanism in the soil plug. The model pile used in the test series was devised so that the bearing capacity of an open‐ended pile could be measured as three components: outside shaft resistance, plug resistance, and tip resistance. Under the assumption that the unit shaft resistance due to pile‐soil plug interaction varies linearly near the pile tip, the plug resistance was estimated. The plug capacity, which was defined as the plug resistance at ultimate condition, is mainly dependent on the ambient lateral pressure and relative density. The length of wedged plug that transfers the load decreases with the decrease of relative density, but it is independent of the ambient pressure and penetration depth. Under several assumptions, the value of earth pressure coefficient in the soil plug can be calculated. It gradually reduces with increase in the longitudinal distance from the pile tip. At the bottom of the soil plug, it tends to decrease with increase in the penetration depth and relative density, and to increase with the increase of ambient pressure. This may be attributed to (1) the decrease of friction angle as a result of increase in the effective vertical stress, (2) the difference in the dilation degree of the soil plug during driving with ambient pressures, and (3) the difference in compaction degree of soil plug during driving with relative densities. Based on the test results, an empirical equation was suggested to compute the earth pressure coefficient to be used in the calculation of plug capacity using one‐dimensional analysis, and it produces proper plug capacities for all soil conditions.