Structures in the phase space of a four dimensional symplectic map

We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.     

The “Shiva Hypothesis”: Impacts, mass extinctions, and the galaxy

The “Shiva Hypothesis”, in which recurrent, cyclical mass extinctions of life on Earth result from impacts of comets or asteroids, provides a possible unification of important processes in astrophysics, planetary geology, and the history of life. Collisions with Earth-crossing asteroids and comets ≥ a few km in diameter are calculated to produce widespread environmental disasters (dust clouds, wildfires), and occur with the proper frequency to account for the record of five major mass extinctions (from ≥ 10⁸ Mt TNT impacts) and ~ 20 minor mass extinctions (from 10⁷–10⁸ Mt impacts) recorded in the past 540 million years. Recent studies of a number of extinctions show evidence of severe environmental disturbances and mass mortality consistent with the expected after-effects (dust clouds, wildfires) of catastrophic impacts. At least six cases of features generally considered diagnostic of large impacts (e.g., large impact craters, layers with high platinum-group elements, shock-related minerals, and/or microtektites) are known at or close to extinction-event boundaries. Six additional cases of elevated iridium levels at or near extinction boundaries are of the amplitude that might be expected from collision of relatively low-Ir objects such as comets. The records of cratering and mass extinction show a correlation, and might be explained by a combination of periodic and stochastic impactors. The mass extinction record shows evidence for a periodic component of about 26 to 30 Myr, and an ~ 30 Myr periodic component has been detected in impact craters by some workers, with recent pulses of impacts in the last 2–3 million years, and at ~ 35, 65, and 95 million years ago. A cyclical astronomical pacemaker for such pulses of impacts may involve the motions of the Earth through the Milky Way Galaxy. As the Solar System revolves around the galactic center, it also oscillates up and down through the plane of the disk-shaped galaxy with a half-cycle ~ 30±3 Myr. This cycle should lead to quasi-periodic encounters with interstellar clouds, and periodic variations in the galactic tidal force with maxima at times of plane crossing. This “galactic carrousel” effect may provide a viable perturber of the Oort Cloud comets, producing periodic showers of comets in the inner Solar System. These impact pulses, along with stochastic impactors, may represent the major punctuations in earth history.     

On the aging of comets

This study is based primarily on the calculations of comet orbits over ~ 10⁶ years for 160 short-period comets by Harold F. Levison and Martin J. Duncan from which there are calculated “ablation AGES”. There are positive statistical correlations (having many deviations) with radial nongravitational forces, comet activity measures, and dust-to-gas ratios in the spectra, in the sense that comets of greater “AGES” tend to be less active and to show less dust in their spectra than comets of lesser “AGES”.     

Wooden Panel Deterioration by Tropical Marine Wood Borers

Wood destruction in test panels ofShorea leprosulawas related to the percentage of fouling, types of wood borers and the number of wood borers. The natural durability ofShorea leprosulapanels was estimated to be 4–5 months in Malaysian marine waters. A higher fouling cover resulted in lower rates of wooden panel deterioration. Larger numbers of wood borers brought about greater panel deterioration. Primary wood destruction was caused by bivalve wood borers, mainlyMartesia striata, Lyrodus pedicellatus, Bankia campanellata, Teredo furciferaandTeredo bartschi. Martesia striatawas the important wood destroying agent in the intertidal zone and, together with the shipworms, was also responsible for panel destruction in the subtidal zone.     

Simulations of a giant hybrid air shower detector

We have used Monte Carlo simulations to investigate the capabilities of a giant air shower observatory designed to detect showers initiated by cosmic rays with energies exceeding 10¹⁹ eV. The observatory is to consist of an array of detectors that will characterise the air shower at ground level, and optical detectors to measure the fluorescence light emitted by the shower in the atmosphere. Using these detectors together in a ‘hybrid’ configuration, we find that precise geometrical reconstruction of the shower axis is possible, leading to excellent resolution in energy. The technique is also shown to provide very good reconstruction below 10¹⁹ eV, at energies where the ground array is not fully efficient.     

Derivation of frequency-dependentX- andY-functions for a non-coherent scattering problem

The equation of transfer for the case of non-coherent scattering (Hummer, 1968; Ivanov, 1973; McCormick and Siewert, 1970) has been considered. The correspondingX- andY-functions have been derived by a combination of eigenfunction method developed by Case, and from the principle of invariance as developed by Chandrasekhar (1960).     

A stepwise method for determining the number of component distributions in a mixture

This paper considers the problem of estimatingm, the number of components in a finite mixture of distributions from a parametric family. A step-up procedure using the bootstrap method is proposed. Some properties of the procedure are illustrated with simulation studies. An example of the method, applied to orientation of beach clasts, is given.