Planetary Stability Zones in Hierarchical Triple Star Systems

A symplectic integrator algorithm suitable for hierarchical triple systems is formulated and tested. The positions of the stars are followed in hierarchical Jacobi coordinates, whilst the planets are referenced purely to their primary. The algorithm is fast, accurate and easily generalised to incorporate collisions. There are five distinct cases -- circumtriple orbits, circumbinary orbits and circumstellar orbits around each of the stars in the hierarchical triple -- which require a different formulation of the symplectic integration algorithm. As an application, a survey of the stability zones for planets in hierarchical triples is presented, with the case of a single planet orbiting the inner binary considered in detail. Fits to the inner and outer edges of the stability zone are computed. Considering the hierarchical triple as two decoupled binary systems, the earlier work of Holman & Wiegert on binaries is shown to be applicable to triples, except in the cases of high eccentricities and close or massive stars. Application to triple stars with good data in the multiple star catalogue suggests that more than 50 per cent are unable to support circumbinary planets, as the stable zone is almost non-existent.Comment: 16 pages, MNRAS, in pres

A New Superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r potential with three barrier terms preventing the particle crossing the principal planes. In 3 degrees of freedom, there are 5 functionally independent integrals of motion, and all bound, classical trajectories are closed and strictly periodic. The generalisation of the Laplace-Runge-Lenz vector is identified and shown to provide functionally independent isolating integrals. They are quartic in the momenta and do not arise from separability of the Hamilton-Jacobi equation. A formulation of the system in action-angle variables is presented.Comment: 11 pages, 4 figures, submitted to The Journal of Mathematical Physic

Formation of rings in galactic discs by infalling small companions

We use N-body simulations to study the formation of rings in a disc galaxy by the impact of a small spherical companion. Both barred and nonbarred target discs are considered. We discuss the effect of the properties of the target disc (distribution of mass in the disc, velocity dispersion, etc.) as well as of the mass and orbit of the companion on the properties of the rings, such as their amplitude, width, shape, expansion velocity and lifetime. In particular the amplitude, width, lifetime and expansion velocity of the first ring increase considerably with companion mass, and so does the expansion velocity of the particles in it and the total extent of the disc after the interaction. We also discuss the formation and evolution of spokes and show that they can be caused by companions of relatively small mass. In our three examples of oblique impacts on barred target galaxies we note important transient displacements of the bar, as well as changes of its pattern speed and size. An asymmetric pseudoring is formed in each case, and during the first stages of its evolution the bar forms part of it.Comment: 21 pages Latex, 22 figures, of which 7 as separate gif-files. Requires mn.sty, accepted for publication in MNRAS. High resolution version at http://www-obs.cnrs-mrs.fr/dynamique/pap/ring.htm

HD 98800: A most unusual debris disc

The dynamics of planetesimals in the circumbinary debris disc of the quadruple star system HD 98800 are investigated. Evolving a spherical shell of test particles from a million years ago to the present day indicates that both coplanar and retrograde warped discs could exist, as well as a high inclination halo of material. Significant gaps are seen in the discs, as well as unexpected regions of stability due to the retrograde nature of the stellar orbits. Despite a viewing angle almost perpendicular to the direction of the warp of the planetesimal disc it is still intersected by the line of sight for eccentricities of the outer orbit of 0.5 or less.Comment: MNRAS, in pres

High Inclination Planets in Multistellar Systems

The Kozai mechanism often destabilises high inclination orbits. It couples changes in the eccentricity and inclination, and drives high inclination, circular orbits to low inclination, eccentric orbits. In a recent study of the dynamics of planetesimals in the quadruple star system HD98800 (Verrier & Evans 2008), there were significant numbers of stable particles in circumbinary polar orbits about the inner binary pair which are apparently able to evade the Kozai instability. Here, we isolate this feature and investigate the dynamics through numerical and analytical models. The results show that the Kozai mechanism of the outer star is disrupted by a nodal libration induced by the inner binary pair on a shorter timescale. By empirically modelling the period of the libration, a criteria for determining the high inclination stability limits in general triple systems is derived. The nodal libration feature is interesting and, although effecting inclination and node only, shows many parallels to the Kozai mechanism. This raises the possibility that high inclination planets and asteroids may be able to survive in multistellar systems.Comment: MNRAS, submitte

Impact of the use of cryobank samples in a selected cattle breed: a simulation study

<p>Abstract</p> <p>Background</p> <p>High selection pressure on domestic cattle has led to an undesirable increase in inbreeding, as well as to the deterioration of some functional traits which are indirectly selected. Semen stored in a cryobank may be a useful way to redirect selection or limit the loss of genetic diversity in a selected breed. The purpose of this study was to analyse the efficiency of current cryobank sampling methods, by investigating the benefits of using cryopreserved semen in a selection scheme several generations after the semen was collected.</p> <p>Methods</p> <p>The theoretical impact of using cryopreserved semen in a selection scheme of a dairy cattle breed was investigated by simulating various scenarios involving two negatively correlated traits and a change in genetic variability of the breed.</p> <p>Results</p> <p>Our results indicate that using cryopreserved semen to redirect selection will have an impact on negatively selected traits only if it is combined with major changes in selection objectives or practices. If the purpose is to increase genetic diversity in the breed, it can be a viable option.</p> <p>Conclusions</p> <p>Using cryopreserved semen to redirect selection or to improve genetic diversity should be carried out with caution, by considering the pros and cons of prospective changes in genetic diversity and the value of the selected traits. However, the use of genomic information should lead to more interesting perspectives to choose which animals to store in a cryobank and to increase the value of cryobank collections for selected breeds.</p

Crack Detectability in Vertical Axis Cooling Pumps During Operation

The problem which is faced in this paper is the analysis of the effects of a transverse propagating crack on the vibrational behaviour of a vertical axis cooling pump. The crack is assumed to develop in a section between the impeller and a seal, which prevents the hot water to flow upwards along the rotor shaft. The pressurized seal is fed with an injection of cold water. Crack initiation may be due to a thermal striping phenomenon. Afterwards, crack growth could be driven by a combination of thermal and mechanical loads, causing alternate cyclic stress in the shaft. Cracking instances of this type have been reported worldwide in several machines of similar design. In this paper, the fact is emphasized that the crack behavior is likely to be influenced by the thermal field and by the water pressure in the cracked area. A dynamical lineshaft model, integrated by an original representation of the crack, has been developed to investigate the possible vibratory symptoms related to a crack propagation. The vibrations are generally measured in correspondence of a rigid coupling which connects the motor shaft to the pump shaft, in position which is rather far away from crack. 1x rev., 2x rev and 3x rev. vibration components, which are generally displayed by the machine condition monitoring system and are the most significative symptoms of the presence of a transverse crack in a rotating shaft, are calculated