The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.     

Late Quaternary vegetation changes around Lake Rutundu,Mount Kenya,East Africa: evidence from grass cuticles,pollen and stable carbon isotopes

Woody, subalpine shrubs and grasses currently surround Lake Rutundu, Mount Kenya. Multiple proxies, including carbon isotopes, pollen and grass cuticles, from a 755‐cm‐long core were used to reconstruct the vegetation over the past 38 300 calendar years. Stable carbon‐isotope ratios of total organic carbon and terrestrial biomarkers from the lake sediments imply that the proportion of terrestrial plants using the C₄ photosynthetic pathway was greater during the Late Pleistocene than in the Holocene. Pollen data show that grasses were a major constituent of the vegetation throughout the Late Pleistocene and Holocene. The proportion of grass pollen relative to the pollen from other plants was greatest at the last glacial maximum (LGM). Grass cuticles confirm evidence that C₄ grass taxa were present at the LGM and that the majority followed the cold‐tolerant NADP‐MEC₄ subpathway. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional calculations of high- and low-mass planets embedded in protoplanetary discs

We analyse the non-linear, three-dimensional response of a gaseous, viscous protoplanetary disc to the presence of a planet of mass ranging from 1 Earth mass (1 M_⊕) to 1 Jupiter mass (1 M_J) by using the zeus hydrodynamics code. We determine the gas flow pattern, and the accretion and migration rates of the planet. The planet is assumed to be in a fixed circular orbit about the central star. It is also assumed to be able to accrete gas without expansion on the scale of its Roche radius. Only planets with masses   M _p≳ 0.1 M_J  produce significant perturbations in the surface density of the disc. The flow within the Roche lobe of the planet is fully three-dimensional. Gas streams generally enter the Roche lobe close to the disc mid-plane, but produce much weaker shocks than the streams in two-dimensional models. The streams supply material to a circumplanetary disc that rotates in the same sense as the orbit of the planet. Much of the mass supply to the circumplanetary disc comes from non-coplanar flow. The accretion rate peaks with a planet mass of approximately 0.1 M_J and is highly efficient, occurring at the local viscous rate. The migration time-scales for planets of mass less than 0.1 M_J, based on torques from disc material outside the Roche lobes of the planets, are in excellent agreement with the linear theory of type I (non-gap) migration for three-dimensional discs. The transition from type I to type II (gap) migration is smooth, with changes in migration times of about a factor of 2. Starting with a core which can undergo runaway growth, a planet can gain up to a few M_J with little migration. Planets with final masses of the order of 10 M_J would undergo large migration, which makes formation and survival difficult.     

VLA and MERLIN observations of RZ Cassiopeiae

We present radio interferometric observations of the Algol-type binary system RZ Cassiopeiae made with the VLA and MERLIN arrays at 6 cm over an incomplete orbital cycle of the system (1.195 d). We detected RZ Cas with both instruments. The images were unresolved in both cases, with angular extents comparable to the synthesized beams. The peak flux density in the VLA image was 1.14 mJy beam⁻¹ and in the MERLIN image it was 0.93 mJy beam⁻¹. The derived brightness temperatures are  4.02 × 10⁸  and  4.35 × 10⁸ K  and the effective electron energies are 0.347 and 0.346 MeV for the MERLIN and VLA data respectively. The radio light curve shows an interesting modulation centred close to the primary eclipse which seems to correlate with ASCA SIS observations of the system. The results can be interpreted as an emitting region on the outer hemisphere of the cool component aligned along the centroid axis of the binary system.     

Generation of reactive oxygen species in different fractions of the coelomocytes of holothurian Eupentacta fraudatrix in response to the thermostable toxin of Yersinia pseudotuberculosis in vitro

Pure fraction (92%–95%) of phagocytes (FP) and a mixture of amoebocytes (62%) and morula cells (38%)-FPMC- of the holothurianEupentacta fraudatrix' (Holothuroidea, Dendrochirota) were obtained by using ficoll-verographine step gradient. Basal production of reactive oxygen species (ROS) in FP quantified by using reduction of nitroblue tetrazolium (NBT) was more than twice that in FPMC. Thermostable toxin ofYersinia pseudotuberculosis (TST) at different concentrations (0.2; 0.5; 2.5 μg/ml, but not 0.1 μg/ml) stimulated NBT reduction in FPMC after 24 h incubation. In FP, TST at concentrations of 0.1 and 0.2 μg/ml inhibited and at concentrations of 0.5 and 2.5 μg/ml stimulated NBT reduction after 24 h incubation. Maximal effect was observed in FP and FPMC at TST concentrations of 0.5 and 0.2 μg/ml, respectively. Addition of catalase (0.7 μg/ml) to the cells treated with TST (2.5 μg/ml) was followed by a decrease in NBT reduction compared to that under toxin treatment alone. TST stimulated superoxide dismutase activity in concentration-dependent manner (maximum at 0.5 μg/ml concentration in FP) after 24 h treatment, and this stimulation was prevented by a commercial catalase. Plant lectin concanavalin A stimulated NBT reduction more than 5-fold in FPMC compared to the control. With addition of TST, lectin stimulated ROS to lesser extent than that with lectin alone. When catalase, TST, and lectin were added into the FPMC simultaneously, ROS increase was similar to that under lectin treatment alone. On the whole, data obtained indicated that ROS generation in holothurian coelomocytes especially occurs in both stimulated and not stimulated phagocytes, and that changes in ROS production by these cells may be one of the mechanisms of antibacterial protection of holothurians. This work was financially supported by the Russian Foundation for Fundamental Research Grant (No. 00-04-48949).     

Bianchi VI0 cosmological model in Saez and Ballester theory

The problem of perfect fluid distribution in spatially homogeneous and anisotropic Bianchi type VI₀ space-time is considered in a scalar tensor theory of gravitation proposed by Saez and Ballester (1985). Exact solutions of the field equations are derived when the metric potentials are functions of cosmic time only. Some physical and geometrical properties of the solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.