Mathematical Analysis of a Model of River Channel Formation

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin.     

Precursory seismicity of the 1994 eruption of Popocatépetl Volcano,Central Mexico

Popocatépetl Volcano is located in the central Mexican Volcanic Belt, within a densely populated region inhabited by over 20 million people. The eruptive history of this volcano indicates that it is capable of producing a wide range of eruptions, including Plinian events. After nearly 70 years of quiescence, Popocatépetl reawakened in December 21, 1994. The eruptive activity has continued up until the date of this submission and has been characterized by a succession of lava dome growth-and-destruction episodes, similar to events that have apparently been typical for Popocatépetl since the fourteenth century. In this regime, the episodes of effusive and moderately explosive activity alternate with long periods of almost total quiescence. In this paper we analyze five years of volcano-tectonic seismicity preceding the initial eruption of the current episode. The evolution of the V-T seismicity shows four distinct stages, which we interpret in terms of the internal processes which precede an eruption after a long period of quiescence. The thermal effects of a magma intrusion at depth, the fracturing related to the slow development of magma-related fluid pathways, the concentration of stress causing a protracted acceleration of this process, and a final relaxation or redistribution of the stress shortly before the initial eruption are reflected in the rates of V-T seismic energy release. A hindsight analysis of this activity shows that the acceleration of the seismicity in the third stage asymptotically forecast the time of the eruption. The total seismic energy release needed to produce an eruption after a long period of quiescence is related to the volume of rock that must be fractured so imposing a characteristic threshold limit for polygenetic volcanoes, limit that was reached by Popocatépetl before the eruption.     

Seed germination of wild,in situ-managed,and cultivated populations of columnar cacti in the Tehuacán-Cuicatlán Valley,Mexico

Seed germination was compared among wild, in situ-managed (wild plants let standing in areas cleared for agriculture), and cultivated populations of the columnar cacti Stenocereus pruinosus, Polaskia chichipe, Myrtillocactus schenckii, and Polaskia chende, species representing a gradient from higher to lower management intensity, respectively. We hypothesized that seeds from cultivated populations have higher water requirements to germinate than seeds of other populations, and that such difference is stronger in species more intensely managed. Germination was evaluated under water potential treatments at 0.0, ?0.2, and ?0.4 MPa. Interspecific differences were identified; germination rates markedly decreased in S. pruinosus and P. chichipe as water potential reduced. M. schenckii seeds germinated better at ?0.2 MPa, and seeds of P. chende in all treatments. Seed germination of wild and cultivated populations was similar in all cases and, therefore, at the population level domestication does not appear to have influenced variations in germination of the studied cacti species. However, experiments to test whether germination of seeds from plants with clear signs of domestication differs with seeds from other plants and their differential germination and seedling survival in wild, in situ-managed and cultivated environments could help to precise the influence of domestication on these plants.     

Removal of Pilosocereus leucocephalus (Cactaceae,tribe Cereeae) seeds by ants and their potential role as primary seed dispersers

Myrmecochory sensu stricto is uncommon in Neotropical forests. In these ecosystems the role of ants as secondary dispersers of non-myrmecochorous seeds is well known, however, the primary dispersal of this type of seed by ants has been poorly documented. Only a few anecdotal observations scattered throughout the literature report the removal of these seeds from fruit on the plant by ants. We show experimentally that ants are able to remove more pulp and seeds from fruit on the branches than do flying vertebrates in Pilosocereus leucocephalus, a columnar cactus bearing typically ornithochorous fruit. In addition, experiments emulating seed cleaning revealed that cleaned seeds germinate earlier. These results suggest a possible role of ants as primary cactus dispersers; one that requires more extensive research on seed fate and seedling establishment success.     

The role of iron and sulfur in the visual appearance of lake sediment varves

Easily discernible sediment varves (annual laminations) may be formed in temperate zone lakes, and reflect seasonal changes in the composition of the accumulating material derived from the lake and its catchment (minerogenic and organic material). The appearance of varves may also be influenced by chemical processes. We assessed the role of iron (Fe) and sulfur (S) in the appearance of varves in sediments from Lake Nylandssjön in northern Sweden. We surveyed Fe in the lake water and established whether there is internal transport of Fe within the sediment. We used a unique collection of seven stored freeze cores of varved sediment from the lake, collected from 1979 to 2004. This suite of cores made it possible to follow long-term changes in Fe and S in the sediment caused by processes that occur in the lake bottom when the sediment is ageing. We compared Fe and S concentrations using X-ray fluorescence spectroscopy (XRF) in specific years in the different cores. No diagenetic front was found in the sediment and the data do not suggest that there is substantial vertical transport of Fe and S in the sediment. We also modeled Fe and S based on thermodynamic, limnological, and sediment data from the lake. The model was limited to the five components H⁺, e^?, Fe³⁺, SO₄ ^2?, H₂CO₃ and included the formation of solid phases such as Fe(OH)₃ (amorphous), FeOOH (aged, microcrystalline), FeS and FeCO₃. Modeling showed that there are pe (redox) ranges within which either FeS or Fe(OH)₃/FeOOH is the only solid phase present and there are pe ranges within which the two solid phases co-exist, which supports the hypothesis that blackish and grey-brownish layers that occur in the varves were formed at the time of deposition. This creates new possibilities for deciphering high-temporal-resolution environmental information from varves.     

Ionospheric electromagnetic perturbations observed on DEMETER satellite before Chile M7.9 earthquake

Based on the ionospheric electromagnetic data observed on DEMETER satellite of France, the ionospheric electromagnetic signals were analyzed within 10 days before Chile M7.9 earthquake on November 14, 2007. It is found that, low frequency electromagnetic disturbances began to increase in a large scale of latitude, and reached to a maximum one week prior to the earthquake, and at about three days before the quake, the peak values shifted to lower latitude. Taking three days as a group, spatial images of a fe...