The dynamo dilemma

The recent determination that the angular velocity of the Sun declines downward through the convective zone raises serious questions about the nature of the solar dynamo. The principal qualitative features of the Sun are the azimuthal fields that migrate toward the equator in association with an oscillating poloidal field which reverses at about the time of maximum appearance of bipolar magnetic regions. If decreases downward, or is negligible, the horizontal gradient in produces a dynamo with some of these essential characteristics. There is reason to think that the dynamo is confined to the lower half of the convective zone where has the opposite sign from the usual ( > 0 in the northern hemisphere) producing equatorward migration but reversing the sign of the associated poloidal field. Meridional circulation may play an essential role in shaping the dynamo. At the present time it is essential to measure accurately and determine the nature of the meridional circulation.Solar Cycle Workshop Paper.     

Annual variation of atmospheric carbonyl sulfide in the marine atmosphere in the Southern Indian Ocean

Measurements of the concentrations of carbonyl sulfide (COS) in the marine atmosphere were made over a period of two years in the southern Indian Ocean (Amsterdam Island, 37°50 S–77°31 E; March 1987–February 1988 and April 1989–February 1990). The mean atmospheric COS concentration for the whole period was 475±48 pptv (n=544). Atmospheric COS concentrations show no significant seasonal variation with a summer to winter ratio of 1.05. Taking into account the observed variability of the atmospheric COS concentration (10%), a value of 1.4 yr is estimated as a lower limit for the atmospheric COS lifetime. A comparison of the COS data at Amsterdam Island with those obtained in the Southern Hemisphere in the past 12 yr does not reveal any significant trend in the tropospheric background COS mixing ratio.     

Na-rich carbonate inclusions in perovskite and calzirtite from the Guli intrusive Ca-carbonatite,polar Siberia

Carbonate phases, some rich in Na₂O and comparatively rich in SrO and BaO, occur as inclusions in perovskite and calzirtite (Ca₂Zr₅Ti₂O₁₆) in the carbonatite of the Guli complex, Siberia. This is the first record of alkali carbonates, akin to nyerereite [Na₂Ca(CO₃)₂], in plutonic igneous rocks. The inclusion populations suggest that the parental magma of the complex was Ca-rich but developed Na-rich differentiates during the latest stages. This points to the dominant calcic carbonatites of the complex not being derivatives of alkali-rich parental carbonatites. These alkali-rich carbonate inclusions (and rare inclusions of djerfisherite) have been preserved due to the resistance of perovskite and calzirtite to processes of leaching, hydrothermal alteration and weathering.     

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.     

Can Brans-Dicke universes in five dimensions be interpreted as 4-dimensional general relativity cosmologies?

The 5-dimensional Jordan-Brans-Dicke cosmologies in vacuum are found for the Bianchi type I metric, their relation with general relativity cosmologies is studied. Two solutions are possible, both produce effective pressure and energy density in the 4-dimensional G.R.-universes. One is a power-law relation, with two cases, the first one is forp _eff=_eff and the other forp _eff=_eff(– 1 < < 1) has a behaviour as the open flat universe. The second solution is an exponential only valid forp _eff=–_eff. In all cases the three-space expansion reaches infinity ast and the fifth dimension can be made to decrease approaching zero. The scalar field can increase or decrease with time.     

The extinction of starlight revisited

The rigorous Kerker-Matijevi formulae for light scattering by co-axial double cylinders are used to calculate the extinction properties of hollow organic grains. A size distribution of such particles together with iron whiskers of radii 0.01 m, silica spheres of radius 0.03 m and free aromatic molecular clusters comprised of 50–100 atoms yield excellent agreement with data on the extinction of starlight. The mass ratios of silica to organics and of iron to organics are in good accord with cosmic abundance constraints.