Inverse problem with two-parametric families of planar orbits

As a possible extension of recent work we study the following version of the inverse problem in dynamics: Given a two-parametric familyf(x, y, b)=c of plane curves, find an autonomous dynamical system for which these curves are orbits.We derive a new linear partial differential equation of the first order for the force componentsX(x, y) andY(x, y) corresponding to the given family. With the aid of this equation we find that, depending on the given functionf, the problem may or may not have a solution. Based on given criteria, we present a full classification of the various cases which may arise.     

Tectonic and stratigraphic implications of the relative ages of venusian plains and wrinkle ridges

A major ongoing controversy concerns the style of crustal evolution on Venus. At one extreme is a directional model that proposes a sequence of depositional and deformational events that occur at specific times in the evolution of the crust and that are global in extent. At the other extreme is a model that argues for different ages of these events in different places on the planet. A test of the directional model is here focused on whether wrinkle ridges formed at a single time in the recorded crustal history of Venus. Where sets of wrinkle ridges intersect it commonly is possible to determine that one set is older than the other. Also, the deformation responsible for wrinkle ridges is, in places, clearly progressive with respect to stratigraphic material units. These observations are not consistent with a specific single time for the formation of wrinkle ridges within the stratigraphic sequence. Within an area including about 1/3 of the surface of Venus 15% of craters that are younger than regional plains are older than wrinkle ridges, 85% are younger than wrinkle ridges. Taking 750 myr as a reasonable mean age for the regional plains, this implies that the mean age of wrinkle ridges is ∼110 myr younger than the mean age of plains. Solomon et al. (1999, Science 286, 87) propose that the emplacement of a large volume of plains lava would lead to a major atmospheric temperature increase. Their model predicts thermal stresses in the lithosphere that, at shallow depth, would reach peak compressive stresses in about 100 myr, a number very similar to the time lag between plains emplacement and wrinkle ridge formation indicated by the crater data. The thermal compressive stresses responsible for wrinkle ridges would be maintained at a level sufficient to deform basalt for at least 100 myr and possibly for as long as 350 myr. These time intervals are not really short compared to the mean age of the plains. Finally, because wrinkle ridges are demonstrably younger than the plains they deform, they cannot be related to the processes that formed the plains and thus should not be used to define a “plains with wrinkle ridges” unit.     

Site evaluation and RFI spectrum measurements in Portugal at the frequency range 0.408–10 GHz for a GEM polarized galactic radio emission experiment

We probed for radio frequency interference (RFI) at three potential galactic emission mapping experiment (GEM) sites in Portugal using custom made omnidirectional disconic antennas and directional pyramidal horn antennas. For the installation of a 10-m dish dedicated to the mapping of polarized galactic emission foreground planned for 2005–2007 in the 5–10 GHz band, the three sites chosen as suitable to host the antenna were surveyed for local radio pollution in the frequency range 0.01–10 GHz. Tests were done to look for radio broadcasting and mobile phone emission lines in the radio spectrum. The results show one of the sites to be almost entirely RFI clean and showing good conditions to host the experiment.     

Quantized Ray Theory for Non-Zero Focal Depths

The relation between p-Δcurves for surface and deep focus sources is investigated in order to construct synthetic body wave seismograms for non-zero focal depths by the quantized ray theory algorithm. The transformation of a surface focus p-Δ curve into a deep focus p-Δ curve is denned in terms of that curve which corresponds to surface focus rays reflected from the depth at which the deep focus is located. By analogy with the geometry of the surface focus formulation, paths of integration to obtain absolute travel-time and velocity-depth curves can be denned in the p-Δ plane. Explicit inversion from deep focus data is possible only when the velocity-depth structure above the depth of focus is known. Through a comparison of short period quantized ray theory synthetic seismograms with similar Cagniard-de Hoop computations, it is shown that quantized ray theory can be used for accurate predictions of body wave amplitude behaviour corresponding to a wide range of focal depths.     

Correlations between seabirds and ocenic fronts around the Pribilof Islands,Alaska

Located on the extensive continental shelf of the Bering Sea, the Pribilof Islands, Alaska are the site of one of the largest breeding colonies of seabirds in the northern hemisphere. During summer these islands are surrounded by a front that separates vertically homogeneous waters from well stratified waters farther seaward. We studied the front with hydrographic data and the bird distributions with concurrent counts during summer 1977 and spring, summer and fall 1978. Murres (Uria lomvia and U. aalge) sitting on the water aggregated near the front during summer 1977 and probably during summer 1978. Other species, such as northern fulmars (Fulmarus glacialis) and auklets (Aethia pusilla and A. cristatella) were unaffected by the front. We hypothesize that the aggregation of the murres was related to an enhanced availability of their food near the front.     

Toxicological Study of Fluorescent Hydrologic Tracer Dye Effects on Cave Bacteria

Fluorescent dyes are commonly used as hydrologic tracers in a variety of surface and subsurface environments, including karst aquifers and caves, but the fragile nature of karstic groundwater ecosystems suggests a cautious approach to selecting dyes. This study tested the effects of four fluorescent dye tracers (uranine, eosin, pyranine, sulforhodamine B) on microorganisms from Fort Stanton Cave, New Mexico, United States. Toxicity of the dyes was tested on bacteria isolated from the cave and on a sediment sample collected adjacent to Snowy River in Fort Stanton Cave. The isolates showed minimal inhibition by the four dyes in an agar diffusions assay. Minimum inhibitory concentrations calculated from liquid culture assays of one isolate were 35 g/L for uranine, 3.5 g/L for eosin, 0.1 g/L for pyranine, and 10 mg/L for sulforhodamine B. A ¹⁴C-glucose radiotracer experiment showed zero inhibition of overall microbial activity in a sediment sample at all dye concentrations, except at 350 g/L eosin. Thus, there are no cave-specific findings to indicate that Fort Stanton's microbes are especially sensitive to these commonly used dyes. Moreover, a literature survey of mutagenicity tests on these dyes indicates they are safe for environmental use. These results corroborate previous dye toxicity tests and suggest that these four dyes are suitable for use at Fort Stanton Cave in the concentration ranges commonly used for groundwater tracing. While broader testing of dyes with microbes from other caves is advised, the results suggest the dyes may be safe for all karst aquifers.     

Bedding Angle Identification from BIF Marker Shales via Modified Dynamic Time Warping

Mathematical Geosciences - When modelling a stratified orebody, accurately representing the dip and dip direction is important for accurate resource estimation. In the banded iron formation-hosted...     

A two-level perturbation method for connecting unstable periodic orbits with low fuel cost and short time of flight: application to a lunar observation mission

The proposed method connects two unstable periodic orbits by employing trajectories of their associated invariant manifolds that are perturbed in two levels. A first level of velocity perturbations is applied on the trajectories of the discretized manifolds at the points where they approach the nominal unstable periodic orbit in order to accelerate them. A second level of structured velocity perturbations is applied to trajectories that have already been subjected to first level perturbations in order to approximately meet the necessary conditions for a low \(\varDelta \text {V}\) transfer. Due to this two-level perturbation approach, the number of the trajectories obtained is significantly larger compared with approaches that employ traditional invariant manifolds. For this reason, the problem of connecting two unstable periodic orbits through perturbed trajectories of their manifolds is transformed into an equivalent discrete optimization problem that is solved with a very low computational complexity algorithm that is proposed in this paper. Finally, the method is applied to a lunar observation mission of practical interest and is found to perform considerably better in terms of \(\varDelta \text {V}\) cost and time of flight when compared with previous techniques applied to the same project.