Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

Detection of a new interstellar molecular ion, H2COH+ (protonated formaldehyde)

A new interstellar molecular ion, H2COH+ (protonated formaldehyde), has been detected toward Sgr B2, Orion KL, W51, and possibly in NGC 7538 and DR21(OH). Six transitions were detected in Sgr B2(M). The 1(1,0)-1(0,1) transition was detected in all sources listed above. Searches were also made toward the cold, dark clouds TMC-1 and L134N, Orion (3N, 1E), and a red giant, IRC + 10216, without success. The excitation temperatures of H2COH+ are calculated to be 60-110 K, and the column densities are on the order of 10(12)-10(14) cm-2 in Sgr B2, Orion KL, and W51. The fractional abundance of H2COH+ is on the order of 10(-11) to 10-(9), and the ratio of H2COH+ to H2CO is in the range 0.001-0.5 in these objects. The values in Orion KL seem to be consistent with the "early time" values of recent model calculations by Lee, Bettens, & Herbst, but they appear to be higher than the model values in Sgr B2 and W51 even if we take the large uncertainties of column densities of H2CO into account. We suggest production routes starting from CH3OH may play an important role in the formation of H2COH+.     

Octahedral-site Fe2+ quadrupole splitting distributions from Mössbauer spectroscopy along the (OH, F)-annite join

We have performed a detailed Mössbauer study of synthetic annites on the (OH, F)-join. Recently developed data treatment and spectral analysis methods were used to extract true intrinsic Fe²⁺ quadrupole splitting distributions (QSDs) that represent the most information that can be resolved from the spectra. The overall room temperature (RT) QSDs can be consistently interpreted in terms of four QSD contributions (or populations) centered at: QS_HH2.55 mm/s for Fe²⁺O₄(OH)₂ octahedra (cis and trans not resolved), QS_HF 2.35 mm/s for Fe²⁺O₄(OH)F octahedra (cis and trans not resolved), QS_cFF2.15 mm/s for cis-Fe²⁺O₄F₂ octahedra, and QS_tFF 1.5 mm/s for trans-Fe²⁺O₄F₂ octahedra. Each such contribution has a width ( 0.2 mm/s) caused by distortions of the octahedra. Minor contributions due to Fe²⁺O₅(OH) and Fe²⁺O₅F octahedra probably also contribute to the overall Fe²⁺ QSDs. The ferric iron spectral components were also characterized. Here, two distinct types of octahedral Fe³⁺ contributions are seen and interpreted as being due mainly to Fe³⁺O₅OH and Fe³⁺O₅F octahedra, respectively. Tetrahedral Fe³⁺ is seen only in the OH-annite end-member and the total Fe³⁺ content drops significantly on addition of F. On leave from: Department of Materials Physics, University of Science and Technology Beijing, 100083 Beijing, China     

Extreme value analysis of diamond-size distributions

Extreme value analysis provides a semiparametric method for analyzing the extreme long tails of skew distributions which may be observed when handling mining data. The estimation of important tail characteristics, such as the extreme value index, allows for a discrimination between competing distribution models. It measures the thickness of such long tailed distributions, if only a limited sample is available. This paper stresses the practical implementation of extreme value theory, which is used to discriminate a lognormal from a mixed lognormal distribution in a case study of size distributions for alluvial diamonds.     

Hydromagnetic Rayleigh problem for a porous wall in slip flow regime

An analysis of the Rayleigh problem in MHD for a porous wall in a slip flow regime is considered. The normal velocity of suction/injection at the wall is assumed to be time dependent. The solution of the problem is obtained in the form of a power series, in terms of known functions. The variations of the velocity field and the skin friction are shown graphically and are followed by a quantitative discussion.Science Update, The Pioneer, India, 21 July 1995 edition     

On estimates of lower and upper limits for the masses of compact components in close binaries

A method of determination of limits for a compact component mass on the base of disk emission lines parameters is described. Lower limit of the mass depends upon the distance between maxima in double peaked lines, the upper the full width of the line. The method is tested for some cataclysmic variables with well known masses of compact components. We obtain a lower limit for the mass of the compact object in the close binary SS433 is 4.9M . This component is apparently a black hole.     

Differences in the emission line spectrum at maximum and minimum of the nuclear brightness of the Seyfert galaxy NGC 7469

We have compiled data on relative intensties, fluxes and profiles of emission lines of the NGC 7469 nuclear spectrum observed in the optical region by many authors during 1966–1986. The aim of our investigation is to reveal differences in the characteristics of the emission lines in maxima and minima of the nuclear brightness. The distinction was revealed for relative intensities, fluxes and profiles. During the extreme maxima profiles ofH ,H andH lines, colour indices of the nucleus and its high level of accretion rate resemble those of QSOs. On the other hand, during the deep minimum 1989 the nucleus had the properties of a Sy2 type. There is a relation between variable fluxes ofH and [OIII] 5007 Å lines which is different for the minima and maxima of the nuclear brightness. The fluxes of the [OIII] 5007 Å line during the minima of the nuclear brightness are systematically higher than those in maxima. The above mentioned peculiarities of the emission lines in the NGC 7469 nucleus can be understood in terms of the increase of electron temperature, electron density and velocities of the nuclear gas from minimum to maximum.     

Propagation of solar cosmic rays: Diffusion versus focused diffusion

This paper is designed to bring to the attention the fact that the effect of focusing of solar energetic particles is always essential as compared with scattering, no matter how small the value of the mean free path may be. That is why, an ordinary (focusing-free) diffusion approach can not be applied to the solar cosmic ray transport. In the case of high-energy solar particles, the focused diffusion is demonstrated to lead to a power law decay of energetic particle intensity much like an ordinary diffusion. However, the power law index of the decay is renormalized by the focusing.