A SOLAR α - ω DYNAMO STUDY AND ITS TRANSITION TO CHAOS

In this contribution we present a nonlinear dynamo model, described by an infinite dimensional system of differential equations, whose solutions depend on the essential parameter D, the dynamo number. The solutions and the bifurcation points of the system are determined with the help of a new developed computer code. We show that, depending on D, stationary, oscillatory and chaotic solutions, which are characterized by Lyapunov exponents, result. We find that the solar dynamo may operate either in the chaotic or in the stable limit cycle domain, depending on the characteristic value of the dynamo number or the motion of the convection zone.     

Mechanized Algebraic Operations (MAO)

A software package for Mechanized Algebraic Operations (MAO) is described. With MAO one is able to manipulate on the computer Poisson series in literal form. The system is operational; it has application in the fields of celestial mechanics, astrodynamics, and nonlinear mechanics. Besides describing the system, the present paper suggests various techniques to prepare problems such that they lend themselves for an automated treatment with MAO. Optimized implementation of the general subroutines is discussed.     

General time elements for the two body problem

When integrating a perturbed two-body problem, very often the propagation of the numerical error is reduced by using a new time variables defined by dt/ds=|q| ⁿ , (|q| is the radial distance,t the time). This paper introduces a time element for such transformations, i.e., a new variablet _n is defined so that dt _n/ds=1+ (perturbing terms) andt=F _n(t_n), whereF _n is a known function. The time element equation should be useful in reducing the error in the determination of the timet.F _n is given explicitly forn=1, 3/2, 2, 5/2 and 3, and a general expression is given for other values.The work was performed while the author was an NRC Senior Research Associate, Goddard Space Flight Center, Greenbelt, Md., U.S.A.     

Chlorite dissolution in the acid ph-range: a combined microscopic and macroscopic approach

The dissolution of chlorite with intermediate Fe-content was studied macroscopically via mixed flow experiments as well as microscopically via atomic force microscopy (AFM). BET surface area normalized steady state dissolution rates at 25 °C for pH 2 to 5 vary between 10⁻¹² and 10⁻¹³ mol/m^2.s. The order of the dissolution reaction with respect to protons was calculated to be about 0.29. For pH 2 to 4, chlorite was found to dissolve non-stoichiometrically, with a preferred release of the octahedrally coordinated cations. The additional release of octahedrally coordinated cations may be due to the transformation of chlorite to interstratified chlorite/vermiculite from the grain edges inward.In-situ atomic force microscopy performed on the basal surfaces of a chlorite sample, which has been preconditioned at pH 2 for several months, indicated a defect controlled dissolution mechanism. Molecular steps with height differences which correspond to the different subunits of chlorite, e.g. TOT sheet and brucite like layer, originated at surface defects such or compositional inhomogenities or cracks, which may be due to the deformation history of the chlorite sample. In contrast to other sheet silicates, at pH 2 nanoscale etch pits occur on the chlorite basal surfaces within flat terraces terminated by a TOT-sheet as well as within the brucite like layer. The chlorite basal surface dissolves layer by layer, because most of the surface defects are only expressed through single TOT or brucite-like layers. The defect controlled dissolution mechanism favours dissolution of molecular steps on the basal surfaces compared to dissolution of the grain edges. At pH 2 the dissolution of the chlorite basal surface is dominated by the retreat of 14 Å steps, representing one chlorite unit cell.The macroscopic and microscopic chlorite dissolution rates can be linked via the reactive surface area as identified by AFM. The reactive surface area with respect to dissolution consists of only 0.2% of the BET-surface area. A dissolution rate of 2.5 × 10⁻⁹ mol/m²s was calculated from macroscopic and microscopic dissolution experiments at pH 2, when normalized to the reactive surface area.     

The extent of lunar regolith mixing

The activity of solar cosmic-ray-produced⁵³Mn has been measured as a function of depth in the upper 100 g/cm² (～55 cm) of lunar cores 60009–60010 and 12025–12028. Additional samples which supplement our earlier work were analyzed from the Apollo 15 and 16 drill stems. These data, taken in conjunction with our previously published results and the²²Na and²⁶Al data of the Battelle Northwest group, indicate that in at least three of the four cases studied the regolith has been measureably disturbed within the last 10 m.y. In one case gardening to 19 g/cm² is required. Activities measured in the uppermost 2 g/cm² indicate frequent mixing within this depth range. No undisturbed profiles were observed nor were any major discontinuities observed in the profiles. The Monte Carlo gardening model of Arnold has been used to derive profiles for the gardened moon-wide average of⁵³Mn and²⁶Al as a function of depth. The⁵³Mn and²⁶Al experimental results are compared with these theoretical predictions. Agreement is good in several respects, but the calculated depths of disturbance appear to be too low.