Efficient Method for Computing with Certainty Periodic Orbits on a Surface of Section

We present an improved method for locating periodic orbits of a dynamical system of arbitrary dimension. The method first employs the characteristic bisection method (CBM) to roughly locate a periodic orbit, followed by the quadratically convergent Newton method to rapidly refine its position. The method is applied to the physically interesting example of the two degrees of freedom photogravitational problem, and shown to surpass the CBM algorithm and Newton's method alone.     

P–T modelling of the andalusite–kyanite–andalusite sequence and related assemblages in high-Al graphitic pelites. Prograde and retrograde paths in a late kyanite belt in the Variscan Iberia

The exceptional andalusite–kyanite–andalusite sequence occurs in Al‐rich graphitic slates in a narrow pelite belt on the hangingwall of a ductile normal fault in NW Variscan Iberia. Early chiastolite is replaced by Ky–Ms–Pg aggregates, which are overgrown by pleochroic andalusite near granites intruded along the fault. Slates plot in AKFM above the chloritoid‐chlorite tie‐line. Their P–T grids are modelled with Thermocalc v2.7 and the 1998 databases in the NaKFMASH and KFMASH systems. The univariant reaction Ctd + And/Ky = St + Chl + Qtz + H₂O ends at progressively lower pressure as F/FM increases and A/AFM decreases, shrinking the assemblage Cld–Ky–Chl, and opening a chlorite‐free Cld–Ky trivariant field on the low temperature reaction side. This modelling matches the observed absence of chlorite in high F/FM rocks, which is restricted to low pressure in the andalusite stability field. The P–T path deduced from modelling shows a first prograde event in the andalusite field followed by retrogression into the kyanite field, most likely coupled with a slight pressure increase. The final prograde evolution into the andalusite field can be explained by two different prograde paths. Granite intrusion caused the first prograde part of the path with andalusite growth. The subsequent thermal relaxation, together with a_H2O decrease, generated the retrograde andalusite–kyanite transformation, plus chlorite consumption and chloritoid growth. This transformation could have been related to folding in the beginning, and aided later by downthrowing due to normal faulting. Heat supplied by syntectonic granite intrusion explains the isobaric part of the path in the late stages of evolution, causing the prograde andalusite growth after the assemblage St–Ky–Chl. Near postectonic granites, a prograde path with pressure decrease originated the assemblage St–And–Chl.     

Statistical estimation of the apex of a sediment distribution system from paleocurrent data

Precise statistical models are proposed for the distribution of paleocurrent directions in distributary systems. These models are based on a von Mises distribution for directions of paleocurrents in a system. The method of maximum likelihood is used to obtain an estimated position and confidence regions for the apex of the system. Both axial data (where only the trend of the paleocurrent is known) and directional data (where the direction of paleoflow is known) can be used. These models have been applied to two fluvial distributary systems in flat-lying Miocene deposits in the Ebro Basin, northern Spain. The estimate of the position of the apex of one of these systems is in good agreement with the position at the basin margin predicted from sedimentary facies information. The estimate of the position of the apex of the second system lies outside of the sedimentary basin; this result is considered to indicate that the distributary system had several feeder points along the basin margin, a situation which is predicted also from facies distributions. This statistical procedure can be used successfully on small data sets of around a hundred paleocurrent readings provided that they are scattered evenly across the area or lie in a wide arc.     

First locking of the Virgo central area interferometer with suspension hierarchical control

Operation of the central portion of Virgo as a simple 6 m Michelson interferometer has given the first demonstration of the possibility to control an interferometer suspended from Virgo full scale multistage seismic attenuators using information derived from the interferometer locking signal. A special role in the control is played by the first stage of these suspensions, an inverted pendulum: besides its seismic preisolation action, this stage has positioning dynamics of several mm, and it allows to exert a very low frequency control at the upper level of the suspension using the interferometer fringe signal. The application of this feedback to the top-stage of the suspension allows corrections of drifts, such as tidal ones, at a stage of the suspension where a large dynamic range in displacements is available, without introducing noise at the level of the mirror, resulting in a significant reduction of the lock keeping force applied directly on the mirror at the lowest stage of the attenuator.     

The impact of parameter lumping and geometric simplification in modelling runoff and erosion in the shrublands of southeast Arizona

There have been many studies of hydrologic processes and scale. However, some researchers have found that predictions from hydrologic models may not be improved by attempting to incorporate the understanding of these processes into hydrologic models. This paper quantifies the effect of simplifying watershed geometry and averaging the parameter values on simulations generated using the KINEROS2 model. Furthermore, it examines how these changes in model input effect model output. The model was applied on a small semiarid rangeland watershed in which runoff is generated by the infiltration excess mechanism. The study concludes that averaging input parameter values has little effect on runoff volume and peak in simulating runoff. However, geometric simplification does have an effect on runoff peak and volume, but it is not statistically significant. In contrast, both averaging input parameter values and geometric simplification have an effect on model‐predicted sediment yield. Copyright © 2005 John Wiley & Sons, Ltd.     

Solute and gas geothermometry of geothermal wells: a geochemometrics study for evaluating the effectiveness of geothermometers to predict deep reservoir temperatures

Deep reservoir temperatures of 10 important geothermal systems of the world were estimated by applying 13 solute (Na/K) and 21 gas geothermometers. The predicted temperatures were comprehensively evaluated and compared with measured bottom-hole temperatures using geochemometric techniques. The present study reveals (1) high prediction performances in most of the Na/K geothermometers for the majority of the geothermal fields with liquid-dominated reservoirs, whereas low prediction performances were indicated for the geothermal fields with vapour-dominated and high-temperature reservoirs; (2) the gas geothermometers, in comparison to Na/K, are more successful in predicting the subsurface temperatures in high-temperature geothermal systems; (3) the geothermal systems for which Na/K geothermometers have indicated a high prediction performance, the gas geothermometers have specified a low prediction performances, and vice versa; (4) both Na/K and gas geothermometers, generally, overestimated the reservoir temperatures for the majority of the low-enthalpy geothermal fields and underestimated for the majority of the high-enthalpy geothermal fields; (5) the reservoir temperature predictions of gas geothermometers have more scatter than those temperatures inferred from Na/K geothermometers; and (6) in general, Na/K geothermometers seem to be a more successful geochemical tool in predicting reliable reservoir temperatures than gas geothermometers.