The quasi integrals

The usual Von Zeipel transformations of the Hamiltonian Mechanics are presented, they lead to state functions with extremely slow variations: the quasi-integrals.The Von Zeipel transformations are implicit: an explicit and direct construction of the quasi-integrals is also presented and the quasi-invariance property of these functions is demonstrated.These results are applied to the problem of the motion of artificial satellites perturbed by the zonal harmonics of the Earth potential, the quasi-integral is given, it is then so constant that the problem can be considered as integrable.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Heat flow near obstacles in the solar convection zone

Disturbances in the heat flow in the solar convection zone are calculated with a turbulent thermal diffusion coefficient based on a mixing length approximation. As a consequence of the radiative boundary condition at the surface and the strong increase of the diffusion coefficient with depth, the convection zone resembles a thermally superconducting shell enclosed between a thin surface layer and an interior core of low thermal conductivity. Thermal disturbances originating in the convection zone do not penetrate into the interior, and penetrate only weakly through the solar surface. A thermally isolating obstacle buried entirely in the convection zone casts a shadow of reduced temperature at the solar surface; the brightening surrounding this shadow is undetectable. The shadow is weak unless the object is located close to the surface (less than 2000 km). Assuming a sunspot to be an area of reduced thermal conductivity which extends a finite depth into the convection zone, the heat flow around this obstacle is calculated. The heat flux blocked below the spot (missing flux) spreads over a very extended area surrounding the spot. The brightening corresponding to this missing flux is undetectable if the reduction of the thermal conductivity extends to a depth greater than 1000 km. It is concluded that no effect other than a decrease of the convective efficiency is needed to explain the temperature change observed at the solar surface in and around a sunspot. The energy balance is calculated between magnetic flux tubes, oriented vertically in the solar surface, (magnetic elements in active regions and the quiet network) and their surroundings. Near the visible surface radiation enters the tube laterally from the surrounding convection zone. The heating effect of this influx is important for small tubes (less than a few arcseconds). Due to this influx tubes less than about 1 in diameter can appear as bright structures irrespective of the amount of heat conveyed along the tube itself. Through the lateral influx, small tubes such as are found in the quiet network act as little leaks in the solar surface through which an excess heat flux escapes from the convection zone.     

Deep drilling at the Siljan Ring impact structure: oxygen-isotope geochemistry of granite

The Siljan Ring is a 362-Ma-old impact structure formed in 1700-Ma-old I-type granites. A 6.8-km-deep borehole provides a vertical profile through granites and isolated horizontal diabase sills. Fluid-inclusion thermometry, and oxygen-isotope compositions of vein quartz, granite, diabase, impact melt, and pseudotachylite, reveal a complex history of fluid activity in the Siljan Ring, much of which can be related to the meteorite impact. In granites from the deep borehole, ¹⁸O values of matrix quartz increase with depth from near 8.0 at the surface to 9.5 at 5760 m depth. In contrast, feldspar ¹⁸O values decrease with depth from near 10 at the surface to 7.1 at 5760 m, forming a pattern opposite to the one defined by quartz isotopic compositions. Values of ¹⁸O for surface granites outside the impact structure are distinct from those in near-surface samples from the deep borehole. In the deep borehole, feldspar coloration varies from brick-red at the surface to white at 5760 m, and the abundances of crack-healing calcite and other secondary minerals decrease over the same interval. Superimposed on the overall decrease in alteration intensity with depth are localized fracture zones at 4662, 5415, and 6044 m depth that contain altered granites, and which provided pathways for deep penetration of surface water. The antithetic variation of quartz and feldspar ¹⁸O values, which can be correlated with mineralogical evidence of alteration, provides evidence for interaction between rocks and impact-heated fluids (100–300° C) in the upper 2 km of the pluton. Penetration of water to depths below 2 km was restricted by a general decrease in impact-fracturing with depth, and by a 60-m-thick diabase sill at 1500 m depth that may have been an aquitard. At depths below 4 km in the pluton, where water/rock ratios were low, oxygen isotopic compositions preserve evidence for limited high-temperature (>500° C) exchange between alkali feldspar and fluids. The high-temperature exchange may have been a post-impact event involving impact-heated fluids, or a post-magmatic event.     

Karst database development in Minnesota: design and data assembly

The Karst Feature Database (KFD) of Minnesota is a relational GIS-based Database Management System (DBMS). Previous karst feature datasets used inconsistent attributes to describe karst features in different areas of Minnesota. Existing metadata were modified and standardized to represent a comprehensive metadata for all the karst features in Minnesota. Microsoft Access 2000 and ArcView 3.2 were used to develop this working database. Existing county and sub-county karst feature datasets have been assembled into the KFD, which is capable of visualizing and analyzing the entire data set. By November 17 2002, 11,682 karst features were stored in the KFD of Minnesota. Data tables are stored in a Microsoft Access 2000 DBMS and linked to corresponding ArcView applications. The current KFD of Minnesota has been moved from a Windows NT server to a Windows 2000 Citrix server accessible to researchers and planners through networked interfaces.     

Changes in American urban floodplain occupancy since 1958: the experiences of nine cities

In 1958, researchers from the University of Chicago documented increases in the number of structures in the floodplains of 17 American cities, a phenomenon attributed to the prevalence of flood control structures. Because federal policies have shifted to managing floodplains, this paper updates the 1958 study for nine of the cities. Several trends are apparent. Development pressures determine flood-plain encroachment; floodplain management regulations have been implemented where it was easiest to do so. Further, structural measures continue to dominate. Thus, while many local officials are becoming more aware of advantages of flood-plain regulation, implementation and enforcement are inconsistent and uneven.     

Improved Petrological Modal Analyses from X-ray Powder Diffraction Data by use of the Rietveld Method I. Selected Igneous, Volcanic, and Metamorphic Rocks

Mineral modes have been determined for specimens of eight rocktypes from CuK X-ray powder diffraction data using the Rietveldmethod. The samples include two granites, a granodiorite, adamellite,gabbro, basalt, trachyte, and two granulite-facies metamorphicrocks. Up to eight individual mineral components have been measuredin each sample (no glassy phases were observed), with a detectionlimit of {small tilde}1 wt.%, depending on the mineral assemblage.Marked variations in grain size (i.e., granite vs. trachyte)provide no difficulties for the X-ray method. The X-ray resultscompare very favourably with (1) optical modes determined forthe medium–coarse-grained samples by point counting, (2)normative calculations obtained using locally enhanced catanormand mesonorm software, and (3) corresponding Rietveld modesdetermined, for two samples, from neutron powder data. Wheredifferences occur, these are discussed in relation to the limitationsof each of the methods. The improved accuracy of the X-ray method is due primarily tothe incorporation of the full diffraction profile in the Rietveldanalysis calculations, and the elimination of preferred orientationby collecting the data from samples packed in glass capillaries(i.e., Debye–Scherrer mode). The good agreement of theX-ray and neutron modes shows that the usual problems encounteredwith microabsorption, extinction, and sampling are of littleconcern in these rocks. The results highlight one of the majoradvantages provided by Rietveld modal analysis over the moretraditional ‘reference intensity’ X-ray methods,namely, that the crystal chemistry (and thus the calibrationconstants) of the individual phases can be adjusted dynamicallyduring each individual analysis. This not only provides moreaccurate phase abundances, but also gives important supplementaryinformation about the mineralogy of the major components.