Behaviour of a new type of Runge–Kutta methods when integrating satellite orbits

Recently, González, Martín and Farto have developed new numerical methods (RKGM methods) of Runge–Kutta type and fixed step size for the numerical integration of perturbed oscillators. Moreover, it seems natural to study the behaviour of these new methods for the accurate integration of orbital problems after the application of linearizing transformation, such us KS or BF due to the fact that in these variables, the structure of the problem is of the form of perturbed oscillators, for which the methods constructed are indicated. In this paper, we check the efficiency of these new methods when integrating the satellite problem. The RKGM methods show a very good behaviour when they compete with other, classical and special, methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Late Mesozoic and Cenozoic palaeomagnetism of Australia–II. Implications for geomagnetism and true polar wander

Summary. New palaeomagnetic results from Australia indicate that throughout the Cenozoic era the continent lay further south than suggested by hot-spot data. Moreover, while hot spots give a uniform rate of drift during most of the Cenozoic, the drift rate obtained from apparent polar wander varies considerably.
The discrepancies between the palaeomagnetic and hot-spot results are analysed by comparing the Australian data with those of Europe and the central Pacific. The analysis suggests that the discrepancies are due to: (1) departures of the Earth's magnetic field from the geocentric axial dipole model, and (2), either true polar wander or a non-axial inclined dipole component. It is found that since the mid-Tertiary the dominant non-dipole component has been a quadrupole, and that during this period both the quadrupolar field and the true polar displacement/non-axial dipole component decreased progressively. During the Quaternary, and also at the earliest Tertiary, the non-dipole components appear to have been moderate or small.
The comparison of data sets demonstrates that considerable errors may be incurred when Cenozoic, and presumably earlier, poles from one geographic region are used to derive those of another, widely separated, region. The results also imply that absolute plate velocities estimated from palaeomagnetic data can contain substantial errors, and that hot-spot data may need significant adjustments for true polar wander to yield correct palaeolatitudes.
Finally, the new early Tertiary pole for Australia is used in conjunction with updated early Tertiary poles from other lithospheric plates to reapply the McKenzie test for true polar wander. The results indicate a small true polar displacement since the beginning of the Tertiary. The amount and direction of the displacement, however, differ from those generally obtained from hot-spot data.     

A quantitative comparison of vector magnetic field measurement and analysis techniques

We make a quantitative comparison between spectral vs filter measurement and analysis techniques for extraction of solar vector magnetic fields from polarimetric data using as a basis the accurately calibrated, high angular resolution Stokes profile data from the Advanced Stokes Polarimeter. It is shown that filter-based measurements deliver qualitative images of the field alignment for sunspots that are visually similar to images derived from the more detailed analysis of the Stokes profiles. However, quantitative comparison with least-squares fits to the full Stokes profiles show that both the strength of the field predicted by the filter-based analysis and its orientation contain substantial errors. These errors are largest for plage regions outside of sunspots, where the field strengths are inferred to be only a fraction of their true values, and errors in the orientation of 40–50° are common. Within sunspots, errors of 20° are commonplace. The greatest source of these errors is the inability of the filter-based measurements to account for the small fill fraction of magnetic fields or, equivalently, scattered light in the instrument, which reduce the degree of polarization. The uncertainties of the full profile fitting methods are also discussed, along with the errors introduced by coarser wavelength sampling of the observed Stokes profiles. The least-squares fitting procedure operates best when the profiles are sampled at least as frequently as one Doppler width of the line.On leave from the Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The instrumental polarization of a Gregory-Coudé telescope

We calculate a theoretical model of the polarization properties of a Gregory-Coudé telescope to predict the behaviour of the German Gregory-Coudé Telescope installed at the Observatorio del Teide (Spain). Measurements of the real effects produced by this telescope acting upon light of known polarization are compared with the model. We estimate an uncertainty in its predictions of about 10%, which is produced by the uncertainties of the (complex) refractive index of the metallic layers covering the mirrors. The paper concludes by briefly considering the way in which the plain telescope changes the Stokes' profiles.     

Earthquake distribution and volcanism in Kamchatka,Kurile Islands,and Hokkaido Part 1: Kamchatka and northern Kuriles

Summary The morphology of the Wadati-Benioff zone in the region of Kamchatka and Northern Kuriles, based on the distribution of 1102 earthquake foci, verified the existence of an intermediate depth aseismic gap and its relation to active andesitic volcanism. A system of deep seismically active fracture zones, genetically connected with the process of subduction, was delineated in the continental plate and confirmed by the results of deep seismic sounding. Two of these fractures, dipping toward the subduction zone, may be considered as the principal feeding channels for active and Holocene volcanoes of the continental volcanic belts of Kamchatka.     

Remarks on the statistical stability of the geophysical triplet

Summary Theorem of the stability of the geophysical triplet and baroclinic fluid are presented, based on the equivalence of dynamic systems of the hydrodynamic type, founded on a certain class of regular non-linear systems.

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On the algebraic structure of particle motion in a field of turbulence

Summary The motion of particles in a turbulent flow is described by means of algebraic physics. The initial concepts are structurally ordered groupoids, algebras of observables, logically dependent on them, with couplings and the non-canonic transition between two Hamiltonians. The non-canonic transition leads to the substitution of time t by a new parameter. Its real counterpart gives the lower limit of the size of the time step in the differential equation of transfer, based on the semi-empirical image of turbulent diffusion.

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