Lie transforms and the Hamiltonization of non-Hamiltonian systems

To develop the perturbation solution of the non-Hamiltonian system of differential equationsy=g(y, t; ), it is sufficient to obtain the perturbation solution of a Hamiltonian system represented by the HamiltonianK=Y·g(y, t; ) which is linear in the adjoint vectorY. This Hamiltonization allows the direct use of the perturbation methods already established for Hamiltonian systems. To demonstrate this fact, a Hamiltonian algorithm developed by this author and based on the Lie-Deprit transform is applied to the Hamiltonized system and is shown to be equivalent to the application of the non-Hamiltonian form of this same algorithm to the original non-Hamiltonian system.     

Third order uranus-neptune planetary theory

We calculate in this paper the secular and critical terms arising from the principal part of the classical planetary Hamiltonian. This is the first step to establish a third order canonical planetary theory of Uranus-Neptune through the Hori-Lie technique. We truncate our expansions at the second degree of eccentricity-inclination. Our planetary theory is expressed in terms of the canonical variables of H. Poincaré.     

Third-order Jupiter — Saturn planetary theory

The construction of a third order J-S theory is presented. The Hori theory of planetary perturbations is employed. No Critical J-S terms due to the 2:5 commensurabilities and its multiples exist, when we take into account the periodic terms of order 0, 1, 2 with respect to the eccentricity- inclination. In this case the Lie series transformation degenerates and is meaningless. The J-S equations of motion for secular perturbations are solved when we neglect in our treatment, the Poisson terms of degree > 2 in the Poincaré canonical variables H _u , K _u , P _u Q _u (u = 1, 2). The Jacobi-Radau referential is adopted, and the theory is expressed in terms of the canonical variables of H. Poincaré.Now at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, U.S.A.     

Role of Fracturing in the Organization of the Karst Features of Azrou Plateau (Middle Atlas,Morroco) Studied by Remote Sensing Imagery

Karst formation geometry can be controlled by fractures and faults, and by other lithologies. Here we show the organization of kastic collapse features related to structures and to extensive basaltic lava flows in the Middle Atlas of Morocco. A lineament map of major faults and fractures has been created for the Middle Atlas using Landsat 7 ETM⁺ satellite images. This shows a dominant NE–SW regional direction and less prominent NNW–SSE and ENE–WSE directions. All these directions coincide with the alignments of karstic depressions that have formed in the Liassic limestones. The basaltic flows covering these formations on the Middle Atlas limestone plateau, have allowed the generation of cryptokarst, geometrically organized a long these major lineament directions. Karst landforms probabaly existed before the eruption of the lavas, but there were partly invaded by intrusions and volcanism. The extensive basaltic flows allowed for increased infiltration, and subsurface water flow, increasing the rate of kast formation after eruptions. Some basins show evidence of increased subsidence after lava emplacement (Aguelmam Sidi Ali Lake) and some maar-like craters also have subsided after eruption, by karts formation. We lay out the structural and lithological controls on Karstic formation in an intraplate volcanic field based on limestones and evaporites.     

Station-keeping for a translunar communication station

A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10^?6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10^?8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day.     

Parsimonious wave‐equation travel‐time inversion for refraction waves

We present a parsimonious wave‐equation travel‐time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave‐equation travel‐time inversion. Numerical results show that the parsimonious wave‐equation travel‐time tomogram has about the same accuracy as the tomogram computed by standard wave‐equation travel‐time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.     

Hydrochemical and stable isotopic investigation of groundwater quality and its sustainability for irrigation in the Hammamet-Nabeul basin,northeastern Tunisia

The major ion hydrochemistry, sodium absorption ratio (SAR), sodium percentage, and isotopic signatures of Hammamet-Nabeul groundwaters were used to identify the processes that control the mineralization, irrigation suitability, and origin of different water bodies. This investigation highlights that groundwater mineralization is mainly influenced by water-rock interaction and pollution by the return flow of irrigation water. The comparison of groundwater quality with irrigation suitability standards proves that most parts of groundwater are unacceptable for irrigation and this long-term practice may result in a significant increase of the salinity and alkalinity in the soils. Based on isotopic signatures, the shallow aquifer groundwater samples were classified into (i) waters with depleted δ¹⁸O and δ²H contents, highlighting recharge by modern precipitation, and (ii) waters with enriched stable isotope contents, reflecting the significance of recharge by contaminated water derived from the return flow of evaporated irrigation waters. The deep-aquifer groundwater samples were also classified into (i) waters with relatively enriched isotope contents derived from modern recharge and mixed with shallow-aquifer groundwater and (ii) waters with depleted stable isotope contents reflecting a paleoclimatic origin. Tritium data permit to identify three origins of recharge, i.e., contemporaneous, post-nuclear, and pre-nuclear. Carbon-14 activities demonstrate the existence of old paleoclimatic recharge related to the Holocene and Late Pleistocene humid periods.     

Control of sea-water intrusion by salt-water pumping: Coast of Oman

A shallow alluvial coastal aquifer in the Batinah area of Oman, with sea-water intrusion that extends several kilometres inland, has been studied experimentally, analytically and numerically. The water table is proved to have a trough caused by intensive pumping from a fresh groundwater zone and evaporation from the saline phreatic surface. Resistivity traverses perpendicular to the shoreline indicated no fresh groundwater recharge into the sea. Using an analytical Dupuit-Forchheimer model, developed for the plain part of the catchment, explicit expressions for the water table, sharp interface location and stored volume of fresh water are obtained. It is shown that by the pumping of salt water from the intruded part of the aquifer, this intrusion can be mitigated. Different catchment sizes, intensities of fresh groundwater pumping, evaporation rates, water densities, sea level, incident fresh water level in the mountains and hydraulic conductivity are considered. SUTRA code is applied to a hypothetical case of a leaky aquifer with line sinks modeling fresh water withdrawal and evaporation. The numerical code also shows that pumping of saline water can pull the dispersion zone back to the shoreline.     

Impact of lateral force-resisting system and design/construction practices on seismic performance and cost of tall buildings in Dubai, UAE

The local design and construction practices in the United Arab Emirates(UAE),together with Dubai’s unique rate of development,warrant special attention to the selection of Lateral Force-Resisting Systems(LFRS).This research proposes four different feasible solutions for the selection of the LFRS for tall buildings and quantifies the impact of these selections on seismic performance and cost.The systems considered are: Steel Special Moment-Resisting Frame(SMRF),Concrete SMRF,Steel Dual System(SMRF with Special Steel Plates Shear Wall,SPSW),and Concrete Dual System(SMRF with Special Concrete Shear Wall,SCSW).The LFRS selection is driven by seismic setup as well as the adopted design and construction practices in Dubai.It is found that the concrete design alternatives are consistently less expensive than their steel counterparts.The steel dual system is expected to have the least damage based on its relatively lesser interstory drifts.However,this preferred performance comes at a higher initial construction cost.Conversely,the steel SMRF system is expected to have the most damage and associated repair cost due to its excessive flexibility.The two concrete alternatives are expected to have relatively moderate damage and repair costs in addition to their lesser initial construction cost.     

Groundwater salinization processes in shallow coastal aquifer of Djeffara plain of Medenine, Southeastern Tunisia

Urban and industrial development and the expansion of irrigated agriculture have led to a drastic increase in the exploitation of groundwater resources. The over-exploitation of coastal aquifers has caused a seawater intrusion and has seriously degraded groundwater quality. The shallow coastal aquifer of the Djeffara plain, southeastern Tunisia constitutes an example of water resource suffering an intensive and uncontrolled pumping for irrigation. Intensive exploitation of the aquifer and climate aridity caused a decrease in piezometric level and an increase in salinity. According to the hydrochemical data (Cl⁻, SO₄ ²⁻, NO₃ ⁻, HCO₃ ⁻, Br⁻, Ca²⁺, Mg²⁺, Na⁺, K⁺) and the stable isotope composition (oxygen-18 and deuterium content), groundwater salinization in the investigated system is caused by three main processes: (i) salts dissolution especially in the central part of Jerba and around Medenine plain; (ii) evaporation process; and (iii) seawater intrusion which caused the increase in salinity in the peninsula of El Jorf, in Jerba and in the North of Ben Gardane.