Directions and possibilities of mathematical geology

This paper considers the present state of mathematical geology. Three directions are recognized: applied, theoretical, and mathematical. Applied mathematical geology includes formal use of mathematics to solve problems and computer processing of data. Success is achieved by a correspondence of mathematical methods used to the nature of geological data. This correspondence can be demonstrated by purely mathematical means. Theoretical mathematical geology uses mathematics as a language of geology; however, a number of methodological problems must be solved: formalization of initial geological concepts and creation of a strict conceptual basis, substantiation of initial principles of mathematical simulation, creation of theoretical geological models, problems of elementary and coincidence in geology, and methodological substantiations of possibilities of any mathematical model to approximate geological models. The essense and significance of these problems are considered. The main task of mathematical geology is to prove its correspondence to the nature of the geological objects studied, geological data obtained, and geological problems solvable. Finally, the main problems of mathematical geology are not so much mathematical as geological and methodological.     

Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time-varying suction

Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) (frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.     

Magnetic reconnection in high-temperature plasma of solar flares

Quasi-steady high-temperature current sheets are an energy source during the main or hot phase of solar flares. Such sheets are shown to be stabilized with respect to the tearing instability by a small transverse component of magnetic field existing in the sheets.     

Diurnal photometric conditions at Teide observatory and long-term solar irradiance variations

Monochromatic extinction coefficients at four wavelengths have been obtained over a period of more than two years at the Observatorio del Teide (Izaña Tenerife) using a full disc, direct sunlight, quadruple photometer devoted to the detection of integral luminosity oscillations of the Sun. The mean extinction coefficients (0.13 at 500 nm) show a seasonal variation of about 15%, the best atmospheric conditions being in winter and autumn. Moreover, in anyone day the extinction coefficient in the afternoon is always lower than the one in the morning by 7%. A one-year period fluctuation, with an amplitude of 0.035 mag, has been identified in the instrumental magnitudes outside the atmosphere, and is interpreted as the variation produced by the different Sun-Earth distance from winter to summer. Finally, the study made to detect periodic time fluctuations in both, Sun's magnitude and extinction coefficients, has given null results at levels of 0.04 and 1.8%, respectively.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

Observations of interstellar HOCO+: abundance enhancements toward the galactic center

A survey of the 4(04)-3(03) and 1(01)-0(00) transitions of HOCO+ has been made toward several molecular clouds. The HOCO+ molecule was not observed in any sources except Sgr B2 and Sgr A. The 5(05)-4(04) and 4(14)-3(13) transitions were also detected toward Sgr B2. The results indicate that gas phase CO2 is not a major carbon reservoir in typical molecular clouds. In Sgr B2, the HOCO+ antenna temperature exhibits a peak approximately 2' north of the Sgr B2 central position (Sgr B2[M]) and the 4(04)-3(03) line emission is extended over a approximately 10' x 10' region. The column density of HOCO+ at the northern peak in Sgr B2 is approximately 3 x 10(14) cm-2, and the fractional abundance relative to H2 > or = 3 x 10(-10), which is about 2 orders of magnitude greater than recent predictions of quiescent cloud ion-molecule chemistry.     

Identification of the interstellar cyanomethyl radical (CH2CN) in the molecular clouds TMC-1 and Sagittarius B2

We report the astronomical identification of the cyanomethyl radical, CH2CN, the heaviest nonlinear molecular radical to be identified in interstellar clouds. The complex fine and hyperfine structures of the lowest rotational transitions at about 20.12 and 40.24 GHz are resolved in TMC-1, where the abundance appears to be about 5 x 10(-9) relative to that of H2. This is significantly greater than the observed abundance of CH3CN (methyl cyanide) in TMC-1. In Sgr B2 the hyperfine structure is blended in the higher frequency transitions at 40, 80, and 100 GHz, although the spin-rotation doubling is clearly evident. Preliminary searches in other sources indicate that the distribution of CH2CN is similar to that for such carbon chain species as HC3N or C4H.     

Heterodyne spectroscopy of the 158 micron C II line in M42

We have obtained velocity-resolved spectra of the 12C II 157.8 microns 2P3/2-2P1/2 fine structure line in the M42 region of Orion. Observations at 0.8 km s-1 resolution with a laser heterodyne spectrometer show multiple velocity components in some locations, with typical linewidths of 3-5 km s-1. Spectra of theta 1C and BN-KL also show weak emission from the F = 2-1 hyperfine component of the equivalent 13C II line. From the observed 12C II/13C II line intensity ratios, we deduce that the 12C II emission is optically thick with tau approximately 5 at both positions. Excitation temperatures of 128 K and 90 K, together with column densities of approximately 1 x 10(19) cm-2 and approximately 4 x 10(18) cm-2, are derived for theta 1C and BN-KL, respectively.     

A new approach to the possibilities of Σ(D)-dependence and distances of the supernova remnants

A new way of choosing of the calibrators for constructing (D)-dependence of supernova remnants (SNR) is suggested. A knowledge of the distance of an SNR is not sufficient to consider it as a calibrator. It is shown that neither more accurate determination of distance to calibrators, nor an increase in their number, nor an increase in the precision of the remnant angular size and radio flux determination can lead to a considerable improvement of simple (D)-dependence which is suggested in the given work.For remnants with small surface brightnesses there is no (D)-dependence at all. The most accurate remnant distances currently known, are given: these are liable to change only after a large amount of additional observational data accurately compiled.