Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Agpaitic magmatism at Norra Kärr? RbSr isotopic evidence

RbSr isotopic analyses of 10'whole-rock samples from the controversial peralkaline Norra Kärr complex of southern Sweden suggest an age (1580±62 m.y.) considerably older than had previously been anticipated, and indicate an initial ⁸⁷Sr/⁸⁶Sr ratio of 0.7072±0.0035 (errors at 2σ). The isotopic data are consistent with a primary magmatic origin for the Norra Kärr agpaites, but data from 8 mineral separates show that they have experienced at least one period of metamorphic disturbance since the original intrusion; the last episode of isotopic readjustment must have occurred after 1250 m.y. before present, and is attributed to the Sveconorwegian (Grenville) metamorphism.     

A comparison of the photospheric and interplanetary magnetic fields during the flight of Mariner IV

The polarity of the interplanetary magnetic field observed by the Mariner IV spacecraft is compared to the polarity of the photospheric magnetic field observed with the solar magnetograph at Mt. Wilson Observatory. Unlike the results obtained from observations during the flight of IMP-I, these polarities are not well correlated when the photospheric polarity is determined from data along a narrow latitudinal strip. It is suggested that the structure of the interplanetary field is often related to major features in the photospheric field that are observed over a broad range of solar latitudes.     

Inverse Analysis of Deep Excavation Using Differential Evolution Algorithm

This paper presents the applications of the differential evolution (DE) algorithm in back analysis of soil parameters for deep excavation problems. A computer code, named Python‐based DE, is developed and incorporated into the commercial finite element software ABAQUS, with a parallel computing technique to run an FE analysis for all trail vectors of one generation in DE in multiple cores of a cluster, which dramatically reduces the computational time. A synthetic case and a well‐instrumented real case, that is, the Taipei National Enterprise Center (TNEC) project, are used to demonstrate the capability of the proposed back‐analysis procedure. Results show that multiple soil parameters are well identified by back analysis using a DE optimization algorithm for highly nonlinear problems. For the synthetic excavation case, the back‐analyzed parameters are basically identical to the input parameters that are used to generate synthetic response of wall deflection. For the TNEC case with a total of nine parameters to be back analyzed, the relative errors of wall deflection for the last three stages are 2.2, 1.1, and 1.0%, respectively. Robustness of the back‐estimated parameters is further illustrated by a forward prediction. The wall deflection in the subsequent stages can be satisfactorily predicted using the back‐analyzed soil parameters at early stages. Copyright © 2014 John Wiley & Sons, Ltd.     

Neutron Stars with a Quark Core. II. Basic Integral and Structural Parameters

A broad sample of computed realistic equations of state of superdense matter with a quark phase transition is used to construct a series of models of neutron stars with a strange quark core. The integral characteristics of the stellar configurations are obtained: gravitational mass, rest mass, radius, relativistic moment of inertia, and red shift from the star's surface, as well as the mass and radius of the quark core within the allowable range of values for the central pressure. The parameters of some of the characteristic configurations of the calculated series are also given and these are studied in detail. It is found that a new additional region of stability for neutron stars with strange quark cores may exist for some models of the equation of state.     

Cloud effects on air-sea interactions during the 1979 Indian summer monsoon as studied from satellite observations

Summary The Indian summer monsoon, one of the earth's most vigorous and energetic seasonally occurring weather events, influences the global atmospheric circulation. Its onset, duration, and intensity are governed by large- and meso-scale geophysical processes, such as surface solar heating and air-sea interactions. In this paper, using innovative combinations of satellite sensor data, we investigate some of these fundamental processes which are closely tied to clouds and control the monsoon system's evolution. The study, which focuses on the monsoon period of June, 1979, examines the low-frequency variability of clouds and their effects on air-sea processes through an analysis of the complex influence clouds play on the surface heat and water budgets. First, the effects of clouds on both the solar and longwave components of the surface radiation budget are assessed using a cloud radiative forcing parameter. While the effects of clouds on the long-wave irradiance act in a manner opposite to their effects on the shortwave irradiance, only a partial compensation is found to take place and the net effect results in a maximum cloud forcing of 60 Wm^–2 in the southwestern Arabian Sea. Second, employing satellite-derived precipitation and evaporation estimates, the paper analyzes the net surface fresh water budget variability around the monsoon onset. This budget is important in that fresh water affects the upper ocean density distribution and, consequently, the thermohaline circulation. Two regions are found to dominate the analysis: the western Arabian Sea, where evaporation is dominant by more than 10 mm day^–1, and the eastern Arabian Sea, where precipitation is dominant by more than 10 mm day^–1. Thus, a strong zonal gradient of fresh water at the surface is established during the monsoon. The last topic investigated is the intraseasonal variability of convection as analyzed using a cloud parameter indicative of deep convection. Cloud oscillations of 30–50 days, associated with the different phases of the monsoon, are found to propagate northward in the eastern Indian Ocean and eastward in the Bay of Bengal. Our analysis not only supports the hypothesis that the 30–50-day oscillation is driven by deep convection but also, and more importantly, suggests that the ocean thermal forcing is modulated by 30–50-day oscillations through cloud-induced surface radiative forcing. Although the results presented are limited in scope and preliminary because of the diffculty in quantifying the accuracy of the parameters examined, they do demonstrate: 1) the role of clouds in modulating the surface heat and water budgets, 2) the advantage of using combinations of multi-sensor and multi-platform satellite observations to quantify interrelated surface heat/water budget processes, and 3) the potential to examine the intraseasonal variability of air-sea interaction processes associated with the monsoon, even though these processes are not directly measurable from space.With 6 FiguresB. DiJulio passed away in September 1990.     

A NEW APPROACH TO THE INVERSION OF SEISMIC DATA*

A new inversion method for seismic reflection data is based on impedance concepts and uses transformations to reduce the essentially non-linear problem to a linear eigenvalue formulation without approximation. A set of reflection data has been inverted using this method. The characteristic impedances of the layers so determined are compared with log data from a reference borehole.