Matrix formulation of the Picard method for parallel computation

Celestial Mechanics and Dynamical Astronomy - The increasing availability of computing machines capable of parallel computation has accelerated interest in numerical methods that exhibit natural...     

On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus

The Principle of Least Interaction Action, which explains the observed preference in the Solar System for two-satellite resonant configurations, is shown to apply also to the Laplacean satellites of Jupiter and Uranus, in the sense that these triplet resonant structures lie close to configurations for which the time-mean of the action associated with the mutual interaction of the satellites is an overall minimum. Far from the minimum configuration, significant changes take place in the major semi-axes on time-scales ～10⁶-10⁷y. Both systems require times ～10⁸ y to come close to the minimum configuration; to approach resonance to the observed precision of the Laplace relationship (3×10^?4 for the Uranian case, 2×10^?7 for the Jovian case) requires, for both systems, a time closely comparable with the age of the solar system.     

Climate change projections for the Texas High Plains and Rolling Plains

Potential changes in future climate in the Texas Plains region were investigated in the context of agriculture by analyzing three climate model projections under the A2 climate scenario (medium–high emission scenario). Spatially downscaled historic (1971–2000) and future (2041–2070) climate datasets (rainfall and temperature) were downloaded from the North American Regional Climate Change Assessment Program (NARCCAP). Climate variables predicted by three regional climate models (RCMs) namely the Regional Climate Model Version3–Geophysical Fluid Dynamics Laboratory (RCM3-GFDL), Regional Climate Model Version3–Third Generation Coupled Global Climate Model (RCM3-CGCM3), and Canadian Regional Climate Model–Community Climate System Model (CRCM-CCSM) were evaluated in this study. Gaussian and Gamma distribution mapping techniques were employed to remove the bias in temperature and rainfall data, respectively. Both the minimum and maximum temperatures across the study region in the future showed an upward trend, with the temperatures increasing in the range of 1.9 to 2.9 °C and 2.0 to 3.2 °C, respectively. All three climate models predicted a decline in rainfall within a range of 30 to 127 mm in majority of counties across the study region. In addition, they predicted an increase in the intensity of extreme rainfall events in the future. The frost-free season as predicted by the three models showed an increase by 2.6–3.4 weeks across the region, and the number of frost days declined by 17.9 to 30 %. Overall, these projections indicate considerable changes to the climate in the Texas Plains region in the future, and these changes could potentially impact agriculture in this region.

     

Generalization of Lagrange's implicit function theorem to N-dimensions

A theorem for the inversion of a class of implicit functions, more general than the one considered by Lagrange, is proved. The inversion is developed as a power series in a small parameter. Recursive relations for the coefficients of the series are given.     

Short communication: Engineering properties of wetland plants with application to wave attenuation

This technical note presents empirically-derived values for biophysical attributes of several commonly occurring wetland plant species, including plant stem diameter and tapering, plant clump and stem spacing statistics, biomass, Young's modulus of elasticity, and bending strength. These parameters can be used to more realistically configure plant canopies in numerical and laboratory studies to further our understanding of wave attenuation by wetlands.     

Multistep methods of numerical integration using back-corrections

A new class of linear multistep methods is proposed for the solution of the equations of motion of certain dynamical systems encountered in celestial mechanics and astrodynamics. These methods are distinguished from the classical predictor-corrector methods in that they permit back-corrections of the solution to be made. As the integration advances in time, the numerical solution is corrected or improved at certain points in the past. The enhanced numerical stability of these methods allows the meaningful application of high-order algorithms. Consequently, stepsizes larger than those attainable with the classical methods may be adopted and thus greater over-all efficiency may be realized. The application of these methods to the problem of determining the orbit of an artificial satellite is accomplished and the results are compared with those obtained using classical methods.     

Will autogenic succession be sufficient to recover from vegetation cover loss or will soil condition need to be addressed in the arid lands of Kuwait?

Intervention is often required for the restoration of damaged arid ecosystems, particularly when the base environmental conditions are no longer suitable for autogenic recovery. Umm Nigga, in Kuwait, was damaged by overgrazing and destructive camping. It is unclear whether its restoration will require remediation of the soil conditions, or whether autogenic succession can occur once the area is fenced and released from this pressure. Thus, in this project, we assessed the current condition of the site by collecting soil samples and vegetation assessment within each ecosystem and determined suitable locations for the re-vegetation of native seeds and seedlings using geographical information system. Our results showed that the vegetation in the coastal portions of the ecosystem was not damaged. However, in the desert ecosystem locations, vegetation cover was very low and composed of very few species in the damaged areas but still, most soil nutrients were in supply similar to that in the control areas. We conclude that soil remediation and re-vegetation are, likely, not necessary to restore the damaged sites in any of these ecosystems. Rather, fencing alone will probably release the ecosystem. With these sites as a model, a conceptual framework is presented for arid ecosystem assessment and restoration planning.     

Evolution of a ‘Class Two’ family of periodic orbits in the general planar problem of three bodies

The elliptic restricted problem of three bodies with unit eccentricity of the primaries is used to generate a family of periodic orbits in the general problem of three bodies. The parameter of the family is the mass of one of the participating bodies. This varies from zero to a termination value. The mass ratio of the primaries of the unperturbed problem (three to five) is maintained throughout the generation of the family. In this way an asymmetry is introduced generalizing the Copenhagen elliptic problem as the generating model. All members of the family experience a close approach and a collision between the primaries during half of the period of the orbit, therefore, the family is classified as Class Two.