IMPLICIT NONLINEAR NORMAL MODE INITIALIZATION:A MULTIGRID APPROACH

The implicit nonlinear normal mode initialization (INMI) is applied to a tropical limited area shallow water modelin spherical coordinates.The boundary condition for the INMI scheme is based on the boundary formulation of themodel.The INMI scheme is found to be very efficient in suppressing spurious gravity wave oscillation and providing awell balanced initial data set for the model.The INMI scheme involves solving a number of elliptic type equations withvarying complexity.and hence an efficient numerical technique is required for solving such equations.In order to makeINMI computationally more attractive,we are employing the multigrid method for solving all the elliptic type equationsin the INMI scheme.The numerical procedures for the development of such multigrid solvers are briefly described.     

Long-period oscillations of sunspots according to simultaneous ground-based and space observations

An analysis of oscillatory processes with periods not shorter than several tens of minutes in three isolated sunspots, which were observed during identical periods in the optical and radio bands, is illustrated. SDO/HMI magnetograms at an interval of 45 s and radio maps at a wavelength of 1.76 cm, obtained using a Nobeyama radioheliograph (NoRH), have been used. The time profiles, which were constructed based on the NoRH and SDO/HMI data, indicate that the oscillations of the radioemission correlate with those of the sunspot magnetic field. The wavelet spectra and cross-wavelet transform reveal common oscillation periods of 30–40, 70–100, and 150–200 min. The identical oscillation periods, found using fundamentally different methods from ground-based and space observations, confirm the solar nature of these oscillations, which can be interpreted as oscillations of a sunspot as a whole.     

Electromagnetic research in the ocean

The results of electromagnetic researches at sea and in the oceans are considered. Those in the U.S.S.R. are given particular attention.     

Photogrammetric survey of the structural geology of the Sudbury-McGregor Bay District,Ontario, Canada

New information is presented regarding the structural geology of the Huronian rocks (Middle Precambrian) of the Sudbury-McGregor Bay district of Ontario, Canada. Using standard photogrammetric techniques a base map of the area was prepared from photographs taken at a height of about 11,000 m. Extrapolation from the work ofYoung &Church (1966) together with the evidence deduced from the aerial photographs facilitated the construction of a lithological map at the scale of 1∶187,500 (Fig. 2). From this map large scale type 2 interference pattern is recognised (seeRamsay, 1967) and a tentative structural history is suggested for the area.     

Simulation of the molecular mass distributions of Si anions on the liquidus of the Na<Subscript>2</Subscript>O-SiO<Subscript>2</Subscript> system with regard for the disproportionation of <Emphasis Type="Italic">Q</Emphasis> structons

A new version of the STRUCTON (2009) computer model is proposed for the simulation of the molecular mass distributions (MMD) characterizing the diversity of anions in silicate melts depending on their polymerization and temperature. In contrast to earlier versions, the new version of the model accounts for disproportionation reactions of Q ⁿ species and makes use of their proportions in the statistical simulations of the origin of real Si-O complexes. The new potentialities of the STRUCTON program package are illustrated by its application to studying the structural-chemical characteristics of melts in the Na₂O-SiO₂ system along its liquidus line, including the points of eutectics and phase transitions at 0.333 ≤ $ N_{SiO_2 } $ N_{SiO_2 } < 0.500. This problem is solved with the use of a temperature-composition dependence of polymerization constants K _p ^Na in the Toop-Samis approximation. The variations in K _p ^Na were proved to be as large as three orders of magnitude due to both the temperature effect at a constant composition and the composition effect at a constant temperature. The results of the MMD simulations on the liquidus show that the concentration of the SiO₄⁴⁻ ion strongly decreases, and the proportion of chain species increases compared to those at a stochastic distribution. The concentration of the Si₂O₇⁶⁻ anion reaches its maximum (∼42%) at 40 mol % in the liquid, i.e., the composition of Na₆Si₂O₇. At $ N_{SiO_2 } $ N_{SiO_2 } > 0.40, this ion dominates over the SiO₄⁴⁻ monomer. More silicic melts with $ N_{SiO_2 } $ N_{SiO_2 } ≥ 0.45, are dominated by (Si _n O_3n )³ⁿ⁻ ring species, and the concentrations of these species are related as (Si₃O₉)⁶⁻ > (Si₄O₁₂)⁸⁻ > (Si₅O₁₅)¹⁰⁻. The maximum concentration of these flat rings also occurs near the composition of stoichiometric metasilicate with Si/O = 0.333. The comparison of the dependence of the average size of anions i _av and the average number of their species on depolymerization indicates that a change in the proportion of Q ⁿ species in melt at decreasing temperature results in structural restyling and an increase in the average size of Si-O complexes. The average number of anion species thereby decreases compared to that in a stochastic MMD. The results presented in this publication direct the progress in the thermodynamic theory of silicate melts to a new avenue that makes use of the capabilities and advantages of the ion-polymer model, the theory of associated solutions, spectroscopic data, and the experimental study of variations in oxide activities depending on composition and temperature.     

A new model of edge-to-edge contact for three dimensional discontinuous deformation analysis

A robust contact theory can be regarded as key to three dimensional discontinuous deformation analyses (3D-DDA). Not only must this theory provide an efficient algorithm to judge the type and location of contacts but also it must be able to present comprehensive formulations for every kind of contact (open, sliding and locked contact). There are six types of contact in three dimensional discontinuous deformation analyses (vertex-to-vertex, vertex-to-edge, vertex-to-face, edge-to-edge, edge-to-face and face-to-face) that can be converted to vertex-to-face and edge-to-edge contacts. This paper presents a new model of edge-to-edge contact to three dimensional discontinuous deformation analyses (3D-DDA). This new model considers both kinds of edge-to-edge contact (cross-over and parallel edge-to-edge contact) and presents a criterion for inter-penetration. Sub matrices of normal and shear spring and friction force are derived by geometrical analysis and penalty method. This new model is implemented in a 3D-DDA computer programme, and the example results demonstrate the validity of the model.