The elimination of short-periodic terms in a Uranus-Neptune general planetary theory by von Zeipel's method

We eliminate by the method of von Zeipel the short-period terms in a first order-with respect to planetary masses—general planetary Uranus-Neptune theory. We exclude in the expansion terms of eccentricities and sines of inclinations higher than the third power.Our variables are the Poincaré canonical variables. We use the Jacobi-Radau set of origins, and we refer the planes of the osculating ellipses to a common fixed plane, the longitudes to a common origin. The short-periodic terms arising from the indirect and principal parts of the disturbing functions, are eliminated separately. The Fourier series of the principal part of the disturbing function, is reduced to the sum of only the first three terms.     

Placing Venus in an orbit similar to that of the Earth

Motivated by the recent proposals of A. Abian, we introduce the physical and dynamical considerations for producing a second Earth-like planet on which life sustaining conditions may exist, and hence we acquire multiplication of the cosmic resources of the human race. We investigate the perturbations in our solar system after alteration, through a third order Hamiltonian planetary theory for the eight principal planets. The Hori-Lie theorem, the Jacobi-Radau coordinates, and the canonical variables of H. Poincaré are adopted.     

Expansion formulae in canonical transformations depending on a small parameter

The theory of perturbation based on Lie transforms is considered. Deprit's equation is reduced to a form which enables us to generate simplified general recursion formulae. These expansions are then modified to speed up the implementation of such perturbation theory in the computerized symbolic manipulation.     

A note on the Hori-Lie perturbation technique

In this paper we describe how to avoid the introduction of Hori's pseudo time in general planetary theory in the case of two planets.     

Expansion of the mutual distance between two planets raised to any negative power

An expression for ^–s in terms of the Poincaré variablesL, , H, K, P. Q has been evaluated. The inclinations of the two planets are referred to a common fixed plane. We neglect in the final formula powers higher than the third of the Poincaré variables.     

Analysis, in a free surface steady flow, of the interstitial velocity field inside a sedimentary bed

The objective of our study is to exploit ultrasonic Doppler velocimetry (UDV) to analyze the velocity field within a steady flow on a porous sedimentary bottom. Velocities are measured for several sedimentary beds, as well within the fluid vein as within the sediment. Our results highlight an exponential distribution of the velocities inside the sediment and a discontinuity of the velocity at the interface water–sediment, between the velocity in the free flow and the velocity within the sediment. These results highlight the need to base the analysis of sedimentary transport on the reality of the physical processes at the interface water–sediment.     

Some Probabilistic and Statistical Properties of the Seismic Regime of Zemmouri (Algeria) Seismoactive Zone

Statistical tests have been used to adjust the Zemmouri seismic data using a distribution function. The Pareto law has been used and the probabilities of various expected earthquakes were computed. A mathematical expression giving the quantiles was established. The extreme values limiting law confirmed the accuracy of the adjustment method. Using the moment magnitude scale, a probabilistic model was made to predict the occurrences of strong earthquakes. The seismic structure has been characterized by the slope of the recurrence plot γ, fractal dimension D, concentration parameter K_sr, Hurst exponents H_r and H_t. The values of D, γ, K_sr, H_r, and H_t diminished many months before the principal seismic shock (M = 6.9) of the studied seismoactive zone has occurred. Three stages of the deformation of the geophysical medium are manifested in the variation of the coefficient G% of the clustering of minor seismic events.     

Effect of temperature on the physical precursors of rock block failure

The influence of temperature (25–400 °C) on the variations of mechanical, acoustic, electric and electromagnetic precursors of rock failure has been shown experimentally. The most significant variations were detected in the principal parameters of the acoustic and electromagnetic emissions whose impulse energy underwent a fast growth. However, the general character of hierarchical evolution stages of micro and macrofailure was practically unchanged. This has been confirmed by the so-called concentration parameter of rupture, which is theoretically calculated and checked in experiments; its space-time variations preceding the occurrence and progression of macrofailure are slightly depending on the rock temperature effect. This has been shown through the convolution of some physical precursors in a complex parameter whose variation showed an approaching of macrofailure, which remains slightly influenced by changes in temperature. Our results are interpreted in relation to physics of superficial earthquakes and precursors.     

Incorporation of a Non-linear Image Filtering Technique for Noise Reduction in Seismic Data

Seismic noise is a fundamental part of seismic data which cannot be avoided when conducting any seismic survey. It consists of coherent and random noise. Noise removal or filtering is one of the major concerns in the field of seismic processing. In this paper, we introduce an image filtering technique based on a detection-estimation algorithm for Gaussian and random noise removal in seismic data, namely the trilateral filter, based on a statistic called rank-ordered absolute differences. The non-linear and adaptive behaviour of this filter makes it very robust in the presence of random and coherent noise, in addition to its computational simplicity and its ability to automatically identify noise in data. We have modified the strategy of trilateral filtering by adapting the rank-ordered absolute differences formula in order to extract the signal component. We have successfully used this filter for the removal of surface waves and random spiky noise from synthetic and field data. Results are very encouraging and show the superiority of this filter compared with other filters, particularly when used recursively.     

Probabilistic stability assessment using adaptive limit analysis and random fields

For deterministic scenarios, adaptive finite element limit analysis has been successfully employed to achieve tight bounds on the ultimate load of a geotechnical structure in a much more efficient manner than a dense uniform mesh. However, no probabilistic studies have so far considered finite element limit analysis with adaptive remeshing. Therefore, this research explores the benefits of combining adaptive mesh refinement with finite element limit analysis for probabilistic applications. The outcomes indicate that in order to achieve tight bounds on probabilistic results (such as the probability of failure), the ultimate load in each individual simulation (e.g. factor of safety or bearing capacity) has to be estimated with a very high level of accuracy and this can be achieved more economically using adaptive mesh refinement. The benefits, assessed here for undrained conditions, are expected to be much more pronounced in the case of frictional soils and complex geometries.