Robe’s restricted problem of 2+2 bodies when the bigger primary is a Roche ellipsoid and the smaller primary is an oblate body

In this problem, one of the primaries of mass m ₁ is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ ₁. The smaller primary of mass m ₂ is an oblate body outside the Ellipsoid. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m ₂ is describing a circle around m ₁. The masses m ₃ and m ₄ mutually attract each other, do not influence the motions of m ₁ and m ₂ but are influenced by them. We have extended the Robe’s restricted three-body problem to 2+2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar in Ellipsoidal figures of equilibrium, Chap. 8, Dover, New York, 1987). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m ₂ (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m ₃ and m ₄ and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. In a system where the primaries are considered as Earth-Moon and m ₃,m ₄ as submarines, the equilibrium solutions of m ₃ and m ₄ respectively when the displacement is given in the direction of x ₁-axis or x ₂-axis are unstable.     

NETPATH-WIN: An interactive user version of the mass-balance model, NETPATH

NETPATH‐WIN is an interactive user version of NETPATH, an inverse geochemical modeling code used to find mass‐balance reaction models that are consistent with the observed chemical and isotopic composition of waters from aquatic systems. NETPATH‐WIN was constructed to migrate NETPATH applications into the Microsoft WINDOWS® environment. The new version facilitates model utilization by eliminating difficulties in data preparation and results analysis of the DOS version of NETPATH, while preserving all of the capabilities of the original version. Through example applications, the note describes some of the features of NETPATH‐WIN as applied to adjustment of radiocarbon data for geochemical reactions in groundwater systems.     

Fe XXI emission line ratios as electron temperature diagnostics for the coronae of cool stars

A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, ) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the B _z component specified at the boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ² u + ² u. Specifying two scalar functions, B _x and B _y on the intersection of the lateral part of the boundary with one selected plane z = constant, and using B _z inside the , we have found B _x and B _y throughout .The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B does not exceed 1.0%. Boundary conditions for the B calculation were taken as given by the analytic LFFF solution B. Comparison of B with B, which was calculated by the potential non-photospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume.The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.     

Resonance in a geo-centric satellite due to earth’s equatorial ellipticity

The resonances in a geocentric satellite due to earth’s equatorial ellipticity have been investigated. The resonance at five points resulting from the commensurability between the mean motion of the satellite and the earth’s equatorial ellipticity is analyzed. The amplitude and the time period of the oscillation have been determined by using the procedure of Brown and Shook. A comparison of their effects on the orbital elements has also been studied. It is observed that the amplitude and the time period of the oscillation decrease as Γ (angle measured from the minor axis of the earth’s equatorial ellipse to the projection of the satellite on the plane of the equator) increases in the first quadrant for all the resonance cases.     

Photoionization Cross-Section of Chlorine-like Iron

Semi-relativistic calculations are performed for the photoionization of Fe X (an important coronal ion) from its ground state 3s²3p $^{5}(^{2}P^{0}_{3/2})$ and the first two excited states 3s²3p $^{5}(^{2}P^{0}_{1/2})$ and 3s3p $^{6}(^{2}S_{1/2})$ using the Breit?CPauli R-matrix method. A lowest 41 state eigenfunction expansion for Fe XI is employed to ensure an extensive treatment of auto ionizing resonances that affect the effective cross-sections. In the present calculations, we have considered all the important physical effects like channel coupling, exchange and short range correlation. The present calculations using the lowest 41 target levels of Fe XI in the LSJ coupling scheme are reported and we expect that the present results should enable more accurate modelling of the emission spectrum of highly excited plasma from the optical to the far UV region.     

Visibility Graph Analysis of the 2003–2012 Earthquake Sequence in the Kachchh Region of Western India

A visibility graph (VG) is a rather novel statistical method in earthquake sequence analysis; it maps a time series into networks or graphs, converting dynamical properties of the time series into topological properties of networks. By using the VG approach, we defined the parameter window mean interval connectivity time <T_c>, that informs about the mean linkage time between earthquakes. We analysed the time variation of <T_c> in the aftershock-depleted catalogue of Kachchh Gujarat (Western India) seismicity from 2003 to 2012, and we found that <T_c>: i) changes through time, indicating that the topological properties of the earthquake network are not stationary; and, ii) appeared to significantly decrease before the largest shock (M5.7) that occurred on March 7, 2006 near the Gedi fault, an active fault in the Kachchh region.     

X-ray emission characteristics of flares associated with CMEs

We present the study of 20 solar flares observed by “Solar X-ray Spectrometer (SOXS)” mission during November 2003 to December 2006 and found associated with coronal mass ejections (CMEs) seen by LASCO/SOHO mission. In this investigation, X-ray emission characteristics of solar flares and their relationship with the dynamics of CMEs have been presented. We found that the fast moving CMEs, i.e., positive acceleration are better associated with short rise time (< 150 s) flares. However, the velocity of CMEs increases as a function of duration of the flares in both 4.1–10 and 10–20 keV bands. This indicates that the possibility of association of CMEs with larger speeds exists with long duration flare events. We observed that CMEs decelerate with increasing rise time, decay time and duration of the associated X-ray flares. A total 10 out of 20 CMEs under current investigation showed positive acceleration, and 5 of them whose speed did not exceed 589 km/s were associated with short rise time (< 150 s) and short duration (< 1300 s) flares. The other 5 CMEs were associated with long duration or large rise time flare events. The unusual feature of all these positive accelerating CMEs was their low linear speed ranging between 176 and 775 km/s. We do not find any significant correlation between X-ray peak intensity of the flares with linear speed as well as acceleration of the associated CMEs. Based on the onset time of flares and associated CMEs within the observing cadence of CMEs by LASCO, we found that in 16 cases CME preceded the flare by 23 to 1786 s, while in 4 cases flare occurred before the CME by 47 to 685 s. We argue that both events are closely associated with each other and are integral parts of one energy release system.     

Lower Groundwater 14C Age by Atmospheric CO2 Uptake During Sampling and Analysis

Uptake of atmospheric CO₂ during sample collection and analysis, and consequent lowering of estimated ages, has rarely been considered in radiocarbon dating of groundwater. Using field and laboratory experiments, we show that atmospheric CO₂ can be easily and rapidly absorbed in hyperalkaline solutions used for the extraction of dissolved inorganic carbon, resulting in elevated ¹⁴C measurements. Kinetic isotope fractionation during atmospheric CO₂ uptake may also result in decrease of δ¹³C, leading to insufficient corrections for addition of dead carbon by geochemical processes. Consequently, measured ¹⁴C values of groundwater should not be used for age estimation without corresponding δ¹³C values, and historical ¹⁴C data in the range of 1 to 10% modern Carbon should be re‐evaluated to ensure that samples with atmospheric contamination are recognized appropriately. We recommend that samples for ¹⁴C analysis should be collected and processed in the field and the laboratory without exposure to the atmosphere. These precautions are considered necessary even if ¹⁴C measurements are made with an accelerator mass spectrometer.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

Studies of the atmospheric stability characteristics during the solar eclipse of February 16, 1980

Observations made with a monostatic sodar and from a 120 m instrumented tower have been used to study the variations in the atmospheric boundary layer at Tarapur (19° 50 N, 72° 41 E) during the solar eclipse of February 16, 1980. Atmospheric instability was reduced below normal values during the eclipse but the atmosphere at no time became stable.