Dynamics of Kepler problem with linear drag

We study the dynamics of Kepler problem with linear drag. We prove that motions with nonzero angular momentum have no collisions and travel from infinity to the singularity. In the process, the energy takes all real values and the angular velocity becomes unbounded. We also prove that there are two types of linear motions: capture–collision and ejection–collision. The behaviour of solutions at collisions is the same as in the conservative case. Proofs are obtained using the geometric theory of ordinary differential equations and two regularizations for the singularity of Kepler problem equation. The first, already considered in Diacu (Celest Mech Dyn Astron 75:1–15, 1999), is mainly used for the study of the linear motions. The second, the well known Levi-Civita transformation, allows to complete the study of the asymptotic values of the energy and to prove the existence of collision solutions with arbitrary energy.     

Changes in sub-fossil chironomid assemblages in two Northern Patagonian lake systems associated with the occurrence of historical fires

Patagonia is commonly seen as an exceptionally pristine area because of its wildlife and practically unpolluted waters. However, during the twentieth century the burning of natural forests was one of the most important human activities in Northern Chilean Patagonia. Some estimations indicate that three million hectares were burned during the first three decades of the century. Hence the objective of this study was to evaluate the impacts of the historical fires in Lake Burgos (45º42′S) and Lake Thompson (45º38′S) in Chilean Patagonia. The impact was measured by evaluating chironomid assemblage since they are sensitive enough to be used as an indicator of aquatic ecosystem health. Fires have a direct and drastic effect on a lake watershed but also indirectly affect a lake ecosystem, changing sedimentation patterns or increasing nutrient inputs. In the studied lakes the periods with higher prevalence of fires were identified by charcoal analysis, while organic matter and magnetic susceptibility allowed the confirmation of pre-fire and post-fire periods. The chironomid composition was evaluated through a PCA and an analysis of similarity (ANOSIM) to test the significance among periods while a Detrended Correspondence Analysis was applied to the chironomid assemblage downcore to assess compositional structure and taxa turnover. In Lake Burgos the ANOSIM test indicated significant differences between the pre-fire and fire periods (p < 0.05), while in Lake Thompson differences were not significant. However, in Lake Thompson the PCA clearly separated the pre-fire from the fire period but not the fire from the post-fire periods. In both lakes chironomid composition changed in relation to the period of higher prevalence of fires, which in turn implies catchment changes, pollution, and other anthropogenic impacts. Particularly a marked change in mesotrophic/eutrophic taxa was detected, reflecting an increase in nutrient input due to deforestation. Our findings point out that the lacustrine ecosystems are still affected by the impact of fires and the subsequent increase in nutrient supply that occurred almost 50 years ago. No sign of reverting to pre-disturbance conditions was observed, which makes these lakes highly sensitive to current human-induced impacts.     

Tracer hydrology of the data-scarce and heterogeneous Central American Isthmus

Numerous socio-economic activities depend on the seasonal rainfall and groundwater recharge cycle across the Central American Isthmus. Population growth and unregulated land use changes resulted in extensive surface water pollution and a large dependency on groundwater resources. This work combines stable isotope variations in rainfall, surface water, and groundwater of Costa Rica, Nicaragua, El Salvador, and Honduras to develop a regionalized rainfall isoscape, isotopic lapse rates, spatial–temporal isotopic variations, and air mass back trajectories determining potential mean recharge elevations, moisture circulation patterns, and surface water–groundwater interactions. Intra-seasonal rainfall modes resulted in two isotopically depleted incursions (W-shaped isotopic pattern) during the wet season and two enriched pulses during the mid-summer drought and the months of the strongest trade winds. Notable isotopic sub-cloud fractionation and near-surface secondary evaporation were identified as common denominators within the Central American Dry Corridor. Groundwater and surface water isotope ratios depicted the strong orographic separation into the Caribbean and Pacific domains, mainly induced by the governing moisture transport from the Caribbean Sea, complex rainfall producing systems across the N-S mountain range, and the subsequent mixing with local evapotranspiration, and, to a lesser degree, the eastern Pacific Ocean fluxes. Groundwater recharge was characterized by (a) depleted recharge in highland areas (72.3%), (b) rapid recharge via preferential flow paths (13.1%), and enriched recharge due to near-surface secondary fractionation (14.6%). Median recharge elevation ranged from 1,104 to 1,979 m a.s.l. These results are intended to enhance forest conservation practices, inform water protection regulations, and facilitate water security and sustainability planning in the Central American Isthmus.     

Comparative study of the kinetics of the thermal decomposition of synthetic and natural siderite samples

The mechanism of the thermal decomposition of two siderites (a pure synthetic and a natural Mg-containing sample) has been determined from comparison of the results obtained from linear heating rate (TG) and constant rate thermal analysis (CRTA) experiments in high vacuum. The thermal decomposition of the synthetic siderite takes place approximately 200 K below the decomposition temperature of the natural sample. The mechanism and the product of the thermal decomposition are different for the siderite samples. In fact, an A₂ kinetic model describes the thermal decomposition of the synthetic siderite, whereas the thermal decomposition of the natural sample obeys an F₁ kinetic law. Decomposition products of the synthetic siderite are iron and magnetite, those of the natural siderite are wüstite and minor magnetite. Received: 22 July 1999 / Accepted: 12 February 2000     

Gas composition of Popocatépetl Volcano between 2007 and 2008: FTIR spectroscopic measurements of an explosive event and during quiescent degassing

On December 1, 2007, the solar absorption infrared spectra of the Popocatépetl volcanic plume was recorded during an eruptive event and complementarily on November 17, 2008, the passive quiescent degassing was measured from the same site. A portable FTIR spectrometer with a scanning mirror for fast tracking of the sun provided the flexibility, quality, and simplicity needed for field deployment. Slant columns of the gases SO₂, HCl, HF, and SiF₄ were retrieved and strong differences could be observed when comparing gas ratios in both time periods. During the explosive eruption, the SO₂/HCl ratio was three times greater and the HF/HCl ratio was slightly smaller than during passive degassing.While the ratios among SO₂, HCl, HF, and SiF₄ describe the chemical composition of the volcanic gas mixture, the SiF₄/HF ratio provides information about the equilibrium temperatures of the stored gases which in this study were calculated at 150° and 185 °C for the explosive and quiescent degassing episodes, respectively. We conclude that cooling of lava domes in the crater precedes Vulcanian explosions as suggested by Schaaf et al (2005). Based on SO₂ flux (Grutter et al., 2008) and measurements and data from the November 2008 event, the average fluxes for HCl, HF, SiF₄, and F through quiescent degassing are estimated to be 204, 22.7, 9.8, and 31.7 tons/day, respectively. These values are similar to those reported by Love et al. (1998) more than 10 yrs ago.     

Full Moment Tensor Variations and Isotropic Characteristics of Earthquakes in the Gulf of California Transform Fault System

The full moment tensor is a mathematical expression of six independent variables; however, on a routine basis, it is a common practice to reduce them to five assuming that the isotropic component is zero. This constraint is valid in most tectonic regimes where slip occurs entirely at the fault surface (e.g. subduction zones); however, we found that full moment tensors are best represented in transform fault systems. Here we present a method to analyze source complexity of earthquakes of different sizes using a simple formulation that relates the elastic constants obtained from independent studies with the angle between the slip and the fault normal vector, referred to as angle \( \theta \) ; this angle is obtained from the full moment tensors. The angle \( \theta \) , the proportion of volume change \( \left( k \right) \) and the constant volume (shear) component \( \left( T \right) \) are numerical indicators of complexity of the source; earthquakes are more complex as \( \theta \) deviates from \( \pi /2 \) or as T and k deviate from zero as well. These parameters are obtained from the eigensolution of the full moment tensor. We analyzed earthquakes in the Gulf of California that exhibit a clear isotropic component and we observed that the constant volume parameter T is independent of scalar moments, suggesting that big and small earthquakes are equally complex. In addition, simple models of one single fault are not sufficient to describe physically all the combinations of \( \theta \) in a source type plot. We also found that the principal direction of the strike of the Transform Fault System in the Gulf of California is following the first order approximation of the normal surface of the full moment tensor solution, whereas for deviatoric moment tensors the principal direction does not coincide with the strike of the Transform Fault System. Our observations that small and large earthquakes are equally complex are in agreement with recent studies of strike-slip earthquakes.     

Yielding of rockfill in relative humidity-controlled triaxial experiments

The paper reports the results of suction-controlled triaxial tests performed on compacted samples of two well-graded granular materials in the range of coarse sand–medium gravel particle sizes: a quartzitic slate and a hard limestone. The evolution of grain size distributions is discussed. Dilatancy rules were investigated. Dilatancy could be described in terms of stress ratio, plastic work input and average confining stress. The shape of the yield locus in a triaxial plane was established by different experimental techniques. Yielding loci in both types of lithology is well represented by approximate elliptic shapes whose major axis follows approximately the K₀ line. Relative humidity was found to affect in a significant way the evolution of grain size distribution, the deviatoric stress–strain response and the dilatancy rules.     

The effect of the nanogranular nature of shale on their poroelastic behavior

Natural composite materials are highly heterogeneous porous materials, with porosities that manifest themselves at scales much below the macroscale of engineering applications. A typical example is shale, the transverse isotropic sealing formation of most hydrocarbon bearing reservoirs. By means of a closed loop approach of microporomechanics modeling, calibration and validation of elastic properties at multiple length scales of shale, we show that the nanogranular nature of this highly heterogeneous material translates into a unique poroelastic signature. The self-consistent scaling of the porous clay stiffness with the clay packing density minimizes the anisotropy of the Biot pore pressure coefficients; whereas the intrinsic anisotropy of the elementary particle translates into a pronounced anisotropy of the Skempton coefficients. This new microporoelasticity model depends only on two shale-specific material parameters which neatly summarize clay mineralogy and bulk density, and which makes the model most appealing for quantitative geomechanics, geophysics and exploitation engineering applications.     

Magnetic properties of lake sediments from Lake Chalco,central Mexico,and their palaeoenvironmental implications

Lake Chalco (99.0°W, 19.5°N) in the Basin of Mexico, was formed during the Pleistocene after the emplacement of the Chichinautzin volcanic field that closed the former drainage system. The lake sediment record has been influenced by a number of factors, including glacial–interglacial cycles, local volcanism, erosion of soils and anthropogenic disturbances. The magnetic properties of the lake sediments and the associated tephra layers of the last 16500 yr have been studied. It is found that the magnetic properties of the Lake Chalco sediments are very distinctive. Magnetic concentration varies by a factor of 1000 and magnetic stability also varies over an extremely wide range. The predominant magnetic mineral is titanomagnetite in addition to an imperfect antiferromagnetic phase, possibly goethite. An unusually large range of coercivities is found in certain of the tephras. Down‐core variations in magnetic properties closely follow climatic/environmental changes previously established by other proxy methods. The late Pleistocene and late Holocene lake sediments display a higher concentration of magnetic minerals than the early–middle Holocene sediments. In the non‐volcanic sediments, fluctuations in the magnetic concentration reflect changes in both the intensity of erosion, as represented by ferrimagnetic and paramagnetic minerals, and by the maturing of soils, as represented by geothite. Copyright © 2000 John Wiley & Sons, Ltd.     

Some analytical results about periodic orbits in the restricted three body problem with dissipation

We present some analytical results about the existence of periodic orbits for the planar restricted three body problem with dissipation considered recently by Celletti et?al. (CMDA 109, 265, 2011) We show that, under fairly general conditions on the dissipation term, the circular orbits cannot be continued to the dissipative framework. Moreover, we give general conditions for the occurrence or not of a Hopf bifurcation around the libration points L ₄ and L ₅. Our results are consistent with the numerical findings of Celletti et?al.