Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

Geochronology of anthropogenic pollutants in riparian wetland sediments of the Lippe River (Germany)

Anthropogenic pollutants were determined in a dated sediment core, collected from a riparian wetland of the Lippe River (Ruhr district, Germany). The historical trend in heavy metals, polycyclic aromatic hydrocarbons, organochlorines, polychlorinated biphenyls and linear alkylbenzenes as well as more recent contaminants such as industrial additives, organotins, synthetic musks, methyltriclosan and some other compounds were determined for the time period between 1930 and 1986. Emission sources, information on technical production and usage, as well as on the individual pollution pathways, with appropriate environmental stability, were considered in the interpretation of the sediment contamination over the past 50 years.Contaminants were analysed and interpreted according to two different criteria: (a) the origin of the main contaminants as related to mining and industrial activities as well as municipal sewage and agricultural effluents and (b) the pollution history. Due to a significant appearance of formerly missing contaminants in sediments deposited since 1970, we suggest classifying contaminants as either common (predating 1970) or modern (postdating 1970).In summary, the study provided a comprehensive reconstruction of the pollution history of the Lippe River system.     

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

The complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is verified through comparison with known semi‐analytical and numerical solutions that involve interaction between a circular opening and specific systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole. Copyright © 2000 John Wiley & Sons, Ltd.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Rockfall Hazard Analysis From Discrete Fracture Network Modelling with Finite Persistence Discontinuities

Developing an accurate representation of the rock mass fabric is a key element in rock fall hazard analysis. The orientation, persistence and density of fractures control the volume and shape of unstable blocks or compartments. In this study, the discrete fracture modelling technique and digital photogrammetry were used to accurately depict the fabric. A volume distribution of unstable blocks was derived combining polyhedral modelling and kinematic analyses. For each block size, probabilities of failure and probabilities of propagation were calculated. A complete energy distribution was obtained by considering, for each block size, its occurrence in the rock mass, its probability of falling, its probability to reach a given location, and the resulting distribution of energies at each location. This distribution was then used with an energy–frequency diagram to assess the hazard.     

Resolving mechanisms of toxicity while pursuing ecotoxicological relevance?

In this age of modern biology, aquatic toxicological research has pursued mechanisms of action of toxicants. This has provided potential tools for ecotoxicologic investigations. However, problems of biocomplexity and issues at higher levels of biological organization remain a challenge. In the 1980s and 1990s and continuing to a lesser extent today, organisms residing in highly contaminated field sites or exposed in the laboratory to calibrated concentrations of individual compounds were carefully analyzed for their responses to priority pollutants. Correlation of biochemical and structural analyses in cultured cells and tissues, as well as the in vivo exposures led to the production and application of biomarkers of exposure and effect and to our awareness of genotoxicity and its chronic manifestations, such as neoplasms, in wild fishes. To gain acceptance of these findings in the greater environmental toxicology community, “validation of the model” versus other, better-established often rodent models, was necessary and became a major focus. Resultant biomarkers were applied to heavily contaminated and reference field sites as part of effects assessment and with investigations following large-scale disasters such as oil spills or industrial accidents.

Over the past 15 years, in the laboratory, small aquarium fish models such as medaka (Oryzias latipes), zebrafish (Danio rerio), platyfish (Xiphophorus species), fathead minnow (Pimephales promelas), and sheepshead minnow (Cyprinodon variegatus) were increasingly used establishing mechanisms of toxicants. Today, the same organisms provide reliable information at higher levels of biological organization relevant to ecotoxicology. We review studies resolving mechanisms of toxicity and discuss ways to address biocomplexity, mixtures of contaminants, and the need to relate individual level responses to populations and communities.