Effects of the geometry of two‐dimensional fractures on their hydraulic aperture and on the validity of the local cubic law

Flow through rough fractures is investigated numerically in order to assess the validity of the local cubic law for different fracture geometries. Two‐dimensional channels with sinusoidal walls having different geometrical properties defined by the aperture, the amplitude, and the wavelength of the walls' corrugations, the corrugations asymmetry, and the phase shift between the two walls are considered to represent different fracture geometries. First, it is analytically shown that the hydraulic aperture clearly deviates from the mean aperture when the walls' roughness, the phase shift, and/or the asymmetry between the fracture walls are relatively high. The continuity and the Navier–Stokes equations are then solved by means of the finite element method and the numerical solutions compared to the theoretical predictions of the local cubic law. Reynolds numbers ranging from 0.066 to 66.66 are investigated so as to focus more particularly on the effect of flow inertial effects on the validity of the local cubic law. For low Reynolds number, typically less than 15, the local cubic law properly describes the fracture flow, especially when the fracture walls have small corrugation amplitudes. For Reynolds numbers higher than 15, the local cubic law is valid under the conditions that the fracture presents a low aspect ratio, small corrugation amplitudes, and a moderate phase lag between its walls.     

Is dark matter created in the gravitation field of galaxies?

Using the heuristic arguments of quantum physics we describe a new mechanism of the creation of short-living particles from the virtual ones in a stationary gravitation field. The mass of these particles is a function of the intensity of gravitation field. We suppose that the particles created in the gravitation field form a part of the non-baryonic dark matter. Having the intensity of gravitation field in a galaxy we can calculate the density of dark matter created in it by the vacuum quantum fluctuation. We calculate the distribution of this dark matter in a model galaxy and show that its total mass is comparable with the visible mass of the galaxy.     

Terminal Outflow Velocities from the Mass-Losing AGB Stars

We have calculated terminal gas outflow velocities from the circumstellar shells of the AGB stars. Our results confirm that, in case of the stationary dust driven winds, the dynamics of the outflow is governed essentially by the dust properties and stellar luminosities, while only marginally by other stellar parameters. Although being far from comprehensive, our calculations also indicate that the dust driven winds may only occur in cool, luminous, low mass objects. This revised version was published online in September 2006 with corrections to the Cover Date.     

Radar observations of the Geminid meteoroid stream

Continuous radio-wave monitoring of the Geminid activity in December 1992 and 1993 by using a forward scatter (FS) bistatic radar over the Bologna-Lecce baseline (700 km) in Italy, reveals peculiar structural aspects of the stream in terms of signal amplitude-rate and duration-rate dependence. The observational results of the Geminid display obtained in the two consecutive years with differentiated peak levels of transmitted power, exhibit different time distributions of underdense meteors against the signal received power. Both sets of the data relative to the peak activity in December 12–14, show reflection properties of Geminids which are atypical if compared with echoes from cometary-type showers, with really high echo counts at mid-upper levels of the peak received power. An assymmetric curve of activity of the Geminids complex is evidenced, with the peak flux of smaller particles occurring earlier than that of larger ones.     

Interactions and the Evolution of Cluster Galaxies

We have developed model predictions for the morphological distribution of cluster galaxies as a function of the cluster-centric distance and the local galaxy density, using a semi-analytical code. This code allows us to obtain magnitudes and colours for cluster galaxies at different redshifts, and thus to study in detail the evolution of the colour–magnitude relation of specific distant clusters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Prediction of Stellar Atmospheric Parameters using Instance-Based Machine Learning and Genetic Algorithms

In this article we present a method for the automated prediction of stellar atmospheric parameters from spectral indices. This method uses a genetic algorithm (GA) for the selection of relevant spectral indices and prototypical stars and predicts their properties, using the k-nearest neighbors method (KNN). We have applied the method to predict the effective temperature, surface gravity, metallicity, luminosity class and spectral class of stars from spectral indices. Our experimental results show that the feature selection performed by the genetic algorithm reduces the running time of KNN up to 92%, and the predictive accuracy error up to 35%. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fracture energy release and size effect in borehole breakout

The paper presents a simple approximate analytical solution of the remote stresses that cause the collapse of a borehole or other circular cylindrical cavity in an infinite elastic space. Regions of parallel equidistant splitting cracks are assumed to form on the sides of the cavity. Their boundary is assumed to be an ellipse of a growing horizontal axis, the other axis remaining equal to the borehole diameter. The slabs of rock between the splitting cracks are assumed to buckle as slender columns, and their post-critical stress is considered as the residual stress in the cracked rock. The buckling of these slab columns is assumed to be resisted not only by their elastic bending stiffness but also shear stresses produced on rough crack faces by relative shear displacements. The energy release from the infinite medium caused by the growth of the elliptical cracking region is evaluated according to Eschelby's theorem. This release is set equal to the energy dissipated by the formation of all the splitting cracks, which is calculated under the assumption of constant fracture energy. This yields the collapse stress as a function of the elastic moduli, fracture energy, ratio of the remote principal stresses, crack shear resistance characteristic and borehole diameter. The collapse stress as a function of crack spacing is found to have a minimum, and the correct crack spacing is determined from this minimum. For small enough diameters, the crack spacing increases as the (4/5)-power of the borehole diameter, while for large enough diameters a constant spacing is approached. In contrast to plastic solutions, the breakout stress exhibits a size effect, such that for small enough diameters the breakout stress decreases as the (? 2/5)-power of the borehole diameter, while for large enough diameters a constant limiting value is approached. Finally, some numerical estimates are given and the validity of various simplifying assumptions made is discussed.     

Interplanetary dust particles and solar radiation

The problem of the action of the solar radiation on the motion of interplanetary dust particle is discussed. Differences between the action of electromagnetic solar radiation and that of the solar wind are explained not only from the point of view of the physical nature of these phenomena but also from the point of view of dust particle's orbital evolution. As for the electromagnetic solar radiation, general equation of motion for the particle is written and the most important consequences are: (i) the process of inspiralling toward the Sun is not the only possible motion - even spiralling from the Sun is also possible, and, (ii) the orbital plane of the particle (its inclination) may change in time. As for the solar wind, the effect corresponding to the fact that solar wind particles spread out from the Sun in nonradial direction causes that the process of inspiralling toward the Sun is in more than 50% less effective than for radial spread out; in the region of the asteroid belt (long period orbits) the process of inspiralling is changed into offspiralling. Also shift in the perihelion of dust particle's orbit exists.