A Karst Feature Predictability Model within Barber County, Kansas

This research consisted of two topics: 1) geographic predictive models of karst features and 2), a petrographic study examining the lithology of the study area. The study area is a privately owned ranch in the Gypsum Hills of Barber County, Kansas and is known to have karst features. Two predictive models for karst features were utilized. Previously identified features, Light Detection and Ranging (LiDAR), and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) imagery aided in the creation of these predictive models. These predictability models also used the ESRI ArcMap software platform. The data for these models consists of slope, aspect, nearest neighbor elevation, Normalized Difference Vegetation Index (NDVI), land cover/land use, distance to geomorphic features, surface geology, and other attributes calculated in ArcMap. Other software platforms were also used in the creation of these models (Microcomputer Digital Elevation Models (MicroDEM), System for Automated Geoscientific Analyses (SAGA) GIS and Environment for Visualizing Images (ENVI) for imagery analysis). To test these models, features were identified using the sink-fill function in ArcMap on hillshade layers generated from LiDAR data. Field validation of these models successfully identified 52% of the validation points as having karst features, as well as 12 additional points in high probability areas that were visited. A total of 38 additional points (a 51% increase in the karst database) were added to the karst inventory for the property. Understanding the distribution and occurrence of karst features will help landowners mitigate risk such as collapse leading to structural damage and aquifer contamination. Although this model focused on Barber County, Kansas, the techniques and approaches used by these two models may be useful in creating future predictive models in other karst areas. The petrographic portion of this research identified two geologic sedimentary facies using petrographic thin sections from various karst features. The two facies were: 1) Algal Mat and 2) Peloidal. These facies are very close to one another spatially when plotted by sample location within the property. The relative elevation of these facies places the Algal Mat facies below the Peloidal facies. This suggests that there are multiple facies that control karst feature formation as opposed to only the basal carbonates suggested by previous studies

Point Charge Self-Energy in the General Relativity

Singularities in the metric of the classical solutions to the Einstein equations (Schwarzschild, Kerr, Reissner -- Nordstr\"om and Kerr -- Newman solutions) lead to appearance of generalized functions in the Einstein tensor that are not usually taken into consideration. The generalized functions can be of a more complex nature than the Dirac \d-function. To study them, a technique has been used based on a limiting solution sequence. The solutions are shown to satisfy the Einstein equations everywhere, if the energy-momentum tensor has a relevant singular addition of non-electromagnetic origin. When the addition is included, the total energy proves finite and equal to $mc^2$, while for the Kerr and Kerr--Newman solutions the angular momentum is $mc {\bf a}$. As the Reissner--Nordstr\"om and Kerr--Newman solutions correspond to the point charge in the classical electrodynamics, the result obtained allows us to view the point charge self-energy divergence problem in a new fashion.Comment: VI Fridmann Seminar, France, Corsica, Corgeze, 2004, LaTeX, 6 pages, 2 fige