Perturbation method in the theory of nonlinear oscillations

Asymptotic recurrence formulas for treating nonlinear oscillation problems are presented. These formulas are based on a Lie transform similar to that described by Deprit for Hamiltonian systems. It is shown that the basic formulas have essentially the same forms as those obtained by Deprit and by the present author in the Hamiltonian case.     

An Integrated Study of the Dynamics of Electromagnetic and Acoustic Regimes During Failure of Complex Macrosystems Using Rock Blocks

The development of the failure process in complex macrosystems using large rock samples subjected to biaxial compression has been studied by means of electromagnetic radiation (EMR) and acoustic emission (AE). In order to increase the stage of macrofailure development, a special procedure of rock loading was used to reveal regularities of nucleation and evolution of electromagnetic and acoustic structures. The synchronised measurements of EMR and AE allowed the control of the stress–strain state in the rocks and the structural developments of fracturing. Non-homogeneous distribution of the rock spatial crystalline structure subject to load leads to a mosaic distribution of EMR and AE characteristics. As a result, the crack scale effect may be observed in the EMR and AE structure behaviours. The EMR and AE following the failure at different levels behave differently according to the difference in the scale and type of cracks. Intense high-frequency EMR pulses were recorded during the initial stage of microcrack generation occurring prior to major failure of material. This was not the case for AE. The nucleation and development of the macroscopic progressive failure evolution caused an alternation in energetic and frequencial properties of electromagnetic and acoustic events. It has been detected that the tensile cracks were more efficient than shear cracks in capacity of EMR generation. The analysis of self potentials allowed reaching the maximum of registered anomalous variations in the stage of microcracking interaction. This stage showed an increase in the EMR activity, which implies the nucleation of microcracks in various regions of rock interfaces. The gradual accumulation of these defects led to weakening some parts of the rock along with a disintegration of electric anomalies, increase of AE and a significant fluctuation in the rate of EMR. When crack concentration attains its critical value, which results in the formation of dangerous macroscopic failure of higher level, AE shows an intense activity as well as an EMR lower frequency. The hierarchical development of rock failure using the ratio of the average crack size and the mean distance between cracks as a statistical concentration criterion is used to control the boundary of the transition from small dispersed cracks accumulation to gradual crack merger and the formation of the main macrofailure. These results could be transferred into larger scale levels to forecast dynamic events in the earth crust.     

Gypsum and dolomite biomineralization in endoevaporitic microbial niche,EMISAL, Fayium,Egypt

Biogenic gypsum in the form of microbialite and potential domal stromatolite as well as endoevaporitic dolomite are deposited in a perennial saline basin characterized by microbial bloom. Deposition environment, mode of occurrence, and microscopic investigation including SEM of these precipitates are discussed in conjunction with XRD, XRF, and FTIR data. Combined effects of salinity gradient and the wind action on the maturity of gypsum outcrop are evident. A characteristic multi-color vertical gypsum profile reflects steep gradient of oxi-anoxic microenvironments and encodes diverse seasonal microbial communities. Direct impact of microbial signature in gypsum crystal habit is conspicuous. Endoevaporitic authigenic dolomite is recorded in specific horizons in interstices of selenite layers.     

Recharge mode and mineralization of groundwater in a semi-arid region: Sidi Bouzid plain (central Tunisia)

Groundwater is the most important source of water supply in Sidi Bouzid plain located in central Tunisia. Proper understanding of the geochemical evolution of groundwater is important for sustainable development of water resources in this region. A hydrogeochemical survey was conducted on the Mio–Plio–Quaternary aquifer system using stable isotopes, radiocarbon, tritium and major elements, in order to evaluate the groundwater chemistry patterns and the main mineralization processes occurring in this system. The chemical data indicate that dissolution of evaporate minerals and evaporation are the main processes controlling groundwater mineralization. The isotopic data show that groundwater in the study area is a mixture of recent shallow waters located upstream and along Wadi Al Fakka bed and paleowaters located towards plain limits and discharge areas. Low ³H and ¹⁴C contents are observed in major part of the plain indicating that recharge of the aquifer occurs mainly through direct infiltration at Wadi Al Fakka while there is no evidence of significant recharge in major part of the plain and mountains piedmonts.     

Rotational excitation of protonated hydrogen cyanide (HCNH+) by He atom at low temperature

We report on ab initio coupled-cluster calculations of the interaction potential energy surface for the HCNH⁺–He complex. The aug-cc-pVTZ Gaussian basis, to which is added a set of bond functions placed at mid-distance between HCNH⁺ center of mass and He atom is used. The HCNH⁺ bonds length are set to their values at the equilibrium geometry, i.e., r _e [HC]=1.0780 Å, r _e [CN]=1.1339 Å and r _e [NH]=1.0126 Å. The interaction energy presents a global minimum located $266.9~\mathrm{cm^{-1}}$ below the HCNH⁺–He dissociation limit. Using the interaction potential obtained, we have computed rotational excitation cross sections in the close-coupling approach and downward rate coefficients at low temperature (T≤120 K). It is expected that the data worked out in this study may be beneficial for further astrophysical investigations as well as laboratory experiments.     

A determination of secular terms in first-order planetary theory

The secular terms of the first-order planetary Hamiltonian is determined, by two methods, in terms of the variables of H. Poincaré, neglecting powers higher than the second in the eccentricity-inclination.     

The construction of a third order secular analytical J-S-U-N theory by Hori-Lie technique

We construct the outline of a third order secular theory for the four major planets. We apply the Hori-Lie technique to solve the problem. We take into consideration both parts of the perturbing function. Our canonical variables are those of H. Poincaré. Our periodic terms are the only 2:5 and 1:2 critical terms of J-S and U-N respectively. Terms of degree higher than the second in the Poincaré canonical variables H, K, P, Q are neglected.     

Application des outils chimiques et isotopiques à l'étude de la relation hydrodynamique entre les aquifères profonds de Sfax et de la Djeffara de Gabès Nord (Sud-Est tunisien)

Résumé

L'étude des bassins côtiers de Sfax et de la Djeffara de Gabès Nord, basée sur l'interprétation des données hydrochimiques (éléments majeurs) et isotopiques (¹⁸O, ²H et ¹⁴C), a permis une meilleure compréhension du fonctionnement hydrodynamique de l'aquifère Miocène le long de la frange côtière. En effet, d'après les données géochimiques, apparaît la présence de deux types de faciès chimiques: chloruré sodique dans le bassin de Sfax et mixte à chloruré sodique dans le bassin de Gabès Nord. Cette transition d'un faciès à un autre souligne la variabilité des origines de minéralisation des eaux. L'utilisation des outils isotopiques a permis l'identification d'une eau relativement ancienne à l'exception de quelques poches de recharge récente matérialisées à partir du relief de Zemlet El Beida en amont du bassin de Gabès Nord. Ceci a été vérifié par les fortes activités en¹⁴C des eaux dans cette région. Par conséquent, on peut noter que le passage du Sud au Nord le long de la côte est marqué par une grande variation latérale de lithologie et d'épaisseur de la formation aquifère, soulignant ainsi l'indépendance de chacun des deux réservoirs de Sfax et de la Djeffara de Gabès en absence de toute continuité hydrodynamique entre les deux bassins.

Editeur Z.W. Kundzewicz; Editeur associé S. Faye

Citation Ben Cheikh, N., Zouari, K., et Abidi, B., 2012. Application des outils chimiques et isotopiques à l'étude de la relation hydrodynamique entre les aquifères profonds de Sfax et de la Djeffara de Gabès Nord (Sud-Est tunisien). Hydrological Sciences Journal, 57 (8), 1662–1671.     

Probabilistic model to forecast earthquakes in the Zemmouri (Algeria) seismoactive area on the basis of moment magnitude scale distribution functions

Based on the moment magnitude scale, a probabilistic model was developed to predict the occurrences of strong earthquakes in the seismoactive area of Zemmouri, Algeria. Firstly, the distributions of earthquake magnitudes M _i were described using the distribution function F ₀(m), which adjusts the magnitudes considered as independent random variables. Secondly, the obtained result, i.e., the distribution function F ₀(m) of the variables M _i was used to deduce the distribution functions G(x) and H(y) of the variables Y _i = Log M _0,i and Z _i = M _0,i , where (Y _i ) _i and (Z _i ) _i are independent. Thirdly, some forecast for moments of the future earthquakes in the studied area is given.     

Determination of the interstitial velocity field in the swash zone by Ultrasonic Doppler Velocimetry (UDV)

The experimental study of the hydrodynamics of the sediments and the physical analysis of the process of exchange at the water-sediment interface in a zone of swash are essential for the understanding of the sedimentary transport processes in coastal environments, in particular to control and forecast the evolution of the coastline. The objective of this study was to exploit the technique of Ultrasonic Doppler Velocimetry (UDV) to examine the evolution of the velocity field at the water-sediment interface in a zone of swash in various conditions of incidental regular waves in a wave flume. The velocities were measured in different conditions of the swash within the sediment bed, and in the fluid vein at the swash edge. These measurements show: an exponential distribution of velocities inside the sediment bed; a difference in the velocity gradient at the water-sediment interface, between the velocity in the water vein at the swash edge and the interstitial flow in the swash. The measurements obtained in the wave flume made it possible to observe an evolution of the velocity profiles according to the phases of the swash, which are characterized by a phase shift between the free flow at the swash edge and the interstitial flow during the two phases of the swash: uprush and backwash.