Genericity of the non-periodic solutions of the central force problem

We study the classical problem of two-dimensional motion of a particle in the field of a central force proportional to a real power of the distancer. for negative energy and (0, 2), each energy levelI _h is foliated by the invariant toriI _hc of constant angular momentumc and, by Liouville-Arnold's theorem, the flow on eachI _hc is conjugated to a linear flow of rotation number _h (c).A well-known result asserts that if we require _h (c) to be rational for every value ofh andc, the, must be equal to one (Kepler's problem). In this paper we prove that for almost every (0, 2) _h (c) is a non-constant continuous function ofc, for everyh<0. In particular, we deduce that motion under central potentials is generically non-periodic.Partially supported by CIRIT under grant No. EE88/2.     

Detection and evaluation of horizontal fractures in earth dams using the self-potential method

The self-potential method can be applied to evaluate the degree of water seepage into earth or rockfill dams. Spatial distribution of measured self-potential data can indicate possible anomalous water flow. Phenomena, such as piping, can be modelled as cylindrical bodies. Internal erosion can develop structures, which can be represented by a sphere or point source. Differential settlement in the dam structure occasionally creates horizontal fractures, which require equivalent geometrical body formula. An equation, which allows the calculation of a self-potential profile over a horizontal contact, was developed. This equation can also be applied to the inspection of water flow into horizontal drainage filters. When inverse interpretation returns bodies of relatively small amplitudes, then their probability can be tested statistically. A test, based on cross-correlation between a modelled curve and field data, can be used to evaluate their existence at a given probability level. An acceptance criterion is computed, using the concept of likelihood coefficient. The equation was applied to two case histories. The first is an example of water flow evaluation into a horizontal drainage filter. Several anomalous bodies were interpreted from residual self-potential data, i.e. from the difference between the theoretical response of the filter and the measured self-potential values, then, most of the interpreted bodies were statistically tested. The second case deals with detection and evaluation of a horizontal fissure. The interpreted parameters of the detected body corresponded well to a horizontal fracture found when the water level in the reservoir was lowered.     

Aftershocks series monitoring of the September 18, 2004 M = 4.6 earthquake at the western Pyrenees: A case of reservoir-triggered seismicity?

On September 18, 2004, a 4.6 mbLg earthquake was widely felt in the region around Pamplona, at the western Pyrenees. Preliminary locations reported an epicenter less than 20 km ESE of Pamplona and close to the Itoiz reservoir, which started impounding in January 2004. The area apparently lacks of significant seismic activity in recent times. After the main shock, which was preceded by series of foreshocks reaching magnitudes of 3.3 mbLg, a dense temporal network of 13 seismic stations was deployed there to monitor the aftershocks series and to constrain the hypocentral pattern. Aftershock determinations obtained with a double-difference algorithm define a narrow epicentral zone of less than 10 km², ESE–WNW oriented. The events are mainly concentrated between 3 and 9 km depth. Focal solutions were computed for the main event and 12 aftershocks including the highest secondary one of 3.8 mbLg. They show mainly normal faulting with some strike-slip component and one of the nodal planes oriented NW–SE and dipping to the NE. Cross-correlation techniques applied to detect and associate events with similar waveforms, provided up to 33 families relating the 67% of the 326 relocated aftershocks. Families show event clusters grouped by periods and migrating from NW to SE. Interestingly, the narrow epicentral zone inferred here is located less than 4 km away from the 111-m high Itoiz dam. These hypocentral results, and the correlation observed between fluctuations of the reservoir water level and the seismic activity, favour the explanation of this foreshock–aftershock series as a rapid response case of reservoir-triggered seismicity, burst by the first impoundment of the Itoiz reservoir. The region is folded and affected by shallow dipping thrusts, and the Itoiz reservoir is located on the hangingwall of a low angle southward verging thrust, which might be a case sensible to water level fluctuations. However, continued seismic monitoring in the coming years is mandatory in this area to infer more reliable seismotectonic and hazard assessments.     

Enregistrement de la variabilité hydroclimatique au cours des 6500 dernières années sur le littoral de Cabo Frio (Rio de Janeiro,Brésil)

This study concerns a core collected in Brejo do Espinho's lagoon from Cabo Frio littoral (Brazil) submitted to dry influence of local upwelling controlled by north-east trade winds from the South Atlantic and particularly strengthened during El Niño events. Diatoms study supported by sedimentological and isotopic analyses shows dry phases infrequent before 4000 yr, a highly variable climatic phase between 3600 and 2900 yr and from 2400 yr onward a dryness enhancement. To cite this article: B. Laslandes et al., C. R. Geoscience 338 (2006).     

Daily Air Temperature and Pressure Series for Stockholm (1756–1998)

Daily meteorological observations have been made at the old astronomical observatory in Stockholm since 1754. Complete daily mean series of air temperature and sea level pressure are reconstructed from the observational data for 1756–1998. The temperature and pressure series arereconstructed and homogenized with the aid of metadata, statistical tests and comparisons with data from other stations. Comparisons with independently reconstructed daily series for nearby Uppsala (1722–1998) show that the quality of thedaily Stockholm data is good, although the reliability is lower before the mid-19th century. The daily temperature data show that the colder winter mean temperatures of the late 18th to early 19th centuries were connected with a particularly high frequency of very cold winter days. The warmer summers of the same period are more connected with a general shift of the temperature distribution towards higher temperatures than in the late 20th century.     

A Re–Os study of sulfide minerals from the Bagdad porphyry Cu–Mo deposit, northern Arizona, USA

Rhenium and osmium isotopes in sulfide minerals from the Bagdad porphyry Cu–Mo deposit have been used to determine timing of mineralization and the source of osmium and, by inference, ore metals. Molybdenite, chalcopyrite and pyrite were analyzed mainly from the quartz monzonite and porphyritic quartz monzonite units, which are characterized by moderate to strong potassic alteration (secondary biotite and K-feldspar). Rhenium concentrations in molybdenite are between 330 and 642 ppm. Four Re–Os analyses of two molybdenite samples from the quartz monzonite and porphyritic quartz monzonite yield a weighted average age of 71.8±0.2 Ma (2s). Analyses of a third sample from a molybdenite vein in Precambrian rocks, outside of the main ore zone, yield a weighted average age of 75.9±0.2 Ma (2s), and provide evidence of two separate mineralization episodes. Chalcopyrite samples contain 6 to 12 ppt Os and 1.7 to 4.1 ppb Re; ¹⁸⁷Os/ ¹⁸⁸Os initial ratios are between 0.1 and 0.8. Pyrite samples have osmium and rhenium concentrations varying in the range 8–17 ppt and 3.9–6.8 ppb, respectively. Analyses from these pyrite samples yield an eight-point isochron with an age of 77±15 Ma (2s) and an initial ¹⁸⁷Os/ ¹⁸⁸Os ratio of 2.1±0.8 (MSWD=0.90). The results presented here add to the growing body of work indicating that porphyry-type mineralization is produced by long-term, multiple episodes of magmatism and associated mineralization. The data also support the hypothesis that a significant part of the metals and magmas may have a crustal source, as has been suggested for other copper deposits and districts in Arizona.     

Establishment of a Non-Permanent GPS Network to Monitor the Recent NE-SW Deformation in the Granada Basin (Betic Cordillera,Southern Spain)

The Granada Basin (Central Betic Cordillera), one of the most seismically active areas of the Iberian Peninsula, is currently subjected to NW-SE compression and NE-SW extension. The present day extension is accommodated by normal faults with various orientations but particularly with a NW-SE strike. At the surface, these active NW-SE normal faults are mainly concentrated on the NE part of the Basin. In this part we have selected a 15-km long segment where several active normal faults crop out. Using the marine Tortonian rocks as a reference, we have calculated a minimum extensional rate of 0.15-0.30 mm/year. The observed block rotation, the listric geometry of faults at depth and the distribution of seismicity over the whole Basin, indicate that this rate is a minimum value. In the framework of an interdisciplinary research project a non-permanent GPS-network has been established in the central sector of Betic Cordillera to monitor the crustal deformations. The first two observation campaigns were done in 1999 and 2000.     

Inelastic displacement ratios for evaluation of existing structures

Results of a detailed statistical study of constant relative strength inelastic displacement ratios to estimate maximum lateral inelastic displacement demands on existing structures from maximum lateral elastic displacement demands are presented. These ratios were computed for single‐degree‐of‐freedom systems with different levels of lateral strength normalized to the strength required to remain elastic when subjected to a relatively large ensemble of recorded earthquake ground motions. Three groups of soil conditions with shear wave velocities higher than 180m/s are considered. The influence of period of vibration, level of lateral yielding strength, site conditions, earthquake magnitude, distance to the source, and strain‐hardening ratio are evaluated and discussed. Mean inelastic displacement ratios and those associated with various percentiles are presented. A special emphasis is given to the dispersion of these ratios. It is concluded that distance to the source has a negligible influence on constant relative strength inelastic displacement ratios. However, for periods smaller than 1s earthquake magnitude and soil conditions have a moderate influence on these ratios. Strain hardening decreases maximum inelastic displacement at a fairly constant rate depending on the level of relative strength for periods of vibration longer than about 1.0s while it decreases maximum inelastic displacement non‐linearly as the period of vibration shortens and as the relative‐strength ratio increases for periods of vibration shorter than 1.0s. Finally, results from non‐linear regression analyses are presented that provide a simplified expression to be used to approximate mean inelastic displacement ratios during the evaluation of existing structures built on firm sites. Copyright © 2003 John Wiley & Sons, Ltd.     

Tree growth response to the 1913 eruption of Volcán de Fuego de Colima, Mexico

The impact of volcanic eruptions on forest ecosystems can be investigated using dendrochronological records. While long-range effects are usually mediated by decreased air temperatures, resulting in frost rings or reduced maximum latewood density, local effects include abrupt suppression of radial growth, occasionally followed by greater than normal growth rates. Annual rings in Mexican mountain pine (Pinus hartwegii Lindl.) on Nevado de Colima, at the western end of the Mexican Neovolcanic Belt, indicate extremely low growth in 1913 and 1914, following the January 1913 Plinian eruption of Volcán de Fuego, 7.7 km to the south. That event, which is listed among the largest explosive eruptions since A.D. 1500, produced ashflow deposits up to 40 m thick and blanketed our study area on Nevado de Colima with a tephra fallout 15–30 cm deep. Radial growth reduction in 1913–14 was ≥30% in 73% of the sampled trees. We geostatistically investigated the ecological impact of the eruption by mapping the decrease in xylem increment and found no evidence of a spatial structure in growth reduction. Little information has been available to date on forest species as biological archives of past environments in the North American tropics, yet this historical case study suggests that treeline tropical sites hold valuable records of prehistoric phenomena, including volcanic eruptions.