Equilibrium points and zero velocity surfaces in the restricted four-body problem with solar wind drag

We have analyzed the motion of an infinitesimal mass in the restricted four-body problem with solar wind drag. It is assumed that the forces which govern the motion are mutual gravitational attractions of the primaries, radiation pressure force and solar wind drag. We have derived the equations of motion and found the Jacobi integral, zero velocity surfaces, and particular solutions of the system. It is found that three collinear points are real when the radiation factor 0<β<0.1 whereas only one real point is obtained when 0.125<β<0.2. The stability property of the system is examined with the help of Poincaré surface of section (PSS) and Lyapunov characteristic exponents (LCEs). It is found that in presence of drag forces LCE is negative for a specific initial condition, hence the corresponding trajectory is regular whereas regular islands in the PSS are expanded.     

An assessment of groundwater salinization in Haryana state in India using hydrochemical tools in association with GIS

Unplanned abstraction of groundwater due to various land use land cover activities and variations in monsoonal rainfall have greatly affected the availability and quality of groundwater resources in semi-arid regions of India. In the present study, a study of the hydrogeochemical characteristics of groundwater was undertaken in the Sonipat district of Haryana in India together with the use of stable isotope (δ¹⁸O and δD) measurements and GIS analysis. A total of 53 groundwater samples were collected from seven blocks of the district, and 14 water quality parameters and stable isotopes (δ¹⁸O and δD) were analysed to infer hydrogeochemical processes taking place in the area. The integration of hydrochemistry with GIS is very helpful to understand the factors governing in the area. The majority of the samples showed Na–Cl type of hydrochemical facies. The trilinear plot for major cations and anions in groundwater indicates dominance of sodium, calcium, chloride and bicarbonate ions. Nitrate plumes in the groundwater appear to be migrating in groundwater from the central and south-western parts of the area towards the urbanized areas. A total of 64% of the samples exceed the maximum permissible limit of 1.5 mg/L given by WHO for fluoride. Besides natural sources such as silicate and carbonate weathering, ion exchange, and reverse ion exchange, the leaching of surficial salts and untreated industrial wastes along with unregulated abstraction are contributing to poor groundwater quality in the study area. An assessment of saturation indices has shown that groundwater in the area is unsaturated with respect to anhydrite, halite and gypsum suggesting significant contribution of Ca²⁺, Mg²⁺ and other ions in the groundwater. A scatter plot of δ¹⁸O versus Cl also suggests mixing of saline water with fresh groundwater.     

Comparison of high performance liquid chromatography and fluorometric ocean colour pigments

The accuracy of satellite derived chlorophylla (chla) using empirical algorithms (OC2 and OC4) is about ± 30–35%, which is attributed mainly to the sensor and atmospheric constraints and also the bio-optical algorithms. However errors inin situ measurement of chla may also contribute to the retrieval accuracy. The fluorometric method of chla measurement can significantly under or overestimate chla concentrations. This is mainly because of the overlap of the absorption and fluorescence bands of co-occurring chlorophyllsb andc, chlorophyll degradation products, and accessory pigment. Accurate chla measurements are important for validating satellite derived chla accuracy and algorithm development. The focus of this study was to understand the discrepancy between fluorometric and HPLC (High Performance Liquid Chromatography) derived chla using unialgal cultures, natural field samples from Bedford Basin and samples from MinOx cruise to analyse divinyl chla. Approximately 50% underestimation of chla both in the natural samples as well as cultured samples has been observed by fiuorometer. The results of MinOx cruise data indicated shifting of the blue absorption maxima towards longer wavelengths (~450nm), which is consistent with high concentration of divinyl chla (chla ₂) associated with prochlorophytes.     

The disturbance due to a point source in a homogeneous liquid layer over a heterogeneous liquid half-space

Summary The problem of a periodic point source in a homogeneous liquid layer overlying a heterogeneous liquid half-space is discussed. After obtaining the formal solution, the path of integration for the displacement potential of the layer is transformed from the positive real axis to the positive imaginary axis and the Sommerfeld contour and the latter is further distorted to the modified Sommerfeld contour. The residues of the integrand at the poles contained within the Sommerfeld loop constitute the normal mode solution to the problem. The integrands in the expressions for the integrals along the imaginary axis are expanded in a series of negative powers of exponentials and then some of the terms in these expansions are evaluated approximately. This gives various waves reflected from the interface and the integral along the Sommerfeld loop vanishes. The frequency equation is obtained, also by the principle of constructive interference. An expression for the reflection coefficient at an interface of two liquid media, the upper medium being homogeneous and the lower one inhomogeneous, is obtained.     

Explosive felsic volcanism at Palaeo-Mesoproterozoic boundary from Vindhyan Supergroup,Son Valley,Central India—Evidences of crustal contamination

Vindhyan basin witnessed a widespread explosive type of felsic volcanism at Palaeo-Mesoproterozoic boundary which is manifested as Chopan porcellanite shale. This is exposed as a linear belt along the Son valley in Central India. Porcellanite shale is pyroclastics deposit comprising strongly welded to unwelded ignimbrites. CIA values coupled with A–CN–K systematics provide strong evidence regarding their igneous origin and proximity of the source. The pyroclastics are rhyodacitic to rhyolitic in nature. The enriched LREE, LILE, depleted HFSE and incompatible element ratios such as Nb/Th, La/Sm and Zr/Nb indicate contamination and mixing between mantle-derived rocks and the average continental crust. Five distinct phases of volcanic activity have been identified based on field observations and petrological evidences. Pyroclastics at various stratigraphic levels indicate repeated occurrences of intrabasinal felsic volcanism, pointing to episodic extension, rifting and eruption over a period of time. The present studies have suggested that volcanic activity in Son valley and pyroclastic detritus resulted from a common chamber due to the rejuvenation and activation of deep seated faults like Son-Narmada lineament.     

Biosorption studies on shelled Moringa oleifera Lamarck seed powder: Removal and recovery of arsenic from aqueous system

The present study explores the unexploited sorption property of the shelled Moringa oleifera seeds (SMOS) for decontamination of arsenic from water bodies. Sorption studies (batch experiments) result into the standardization of optimum conditions for removal of 60.21% As(III) and 85.60% As(V) as follows: biomass dosage (2.0 g), metal concentration (25 mg/L), contact time (60 min) and volume of the test solution (200 ml) at pH 7.5 and 2.5, respectively. The adsorption data are fitted with Langmuir isotherm. Surface area has been measured using BET surface area analyzer. Morphological changes observed in scanning electron micrograph of native and treated SMOS indicates the existence of biosorption process. Fourier transform infrared spectrometry of exhausted seed biomass highlights protein/amino acid–arsenic interactions responsible for sorption phenomenon. Regeneration has also been attempted for several cycles with a view to restore the sorbent to its original state. The sorption capacity of the regenerated biomass remained almost constant after three cycles of sorption process, suggesting that the lifetime cycle was sufficient for continuous application. The findings open up new avenues in the decontamination of arsenic using SMOS from arsenic contaminated water, as domestic and environment-friendly safe technology.     

Do increasing horizontal resolution and downscaling approaches produce a skillful thunderstorm forecast?

The timely prediction of thunderstorms (TS) is always a challenging task for operational and research community. The present study is aimed to address the credibility of the high grid-spacing and downscaling approach for improved simulation of TS. Fourteen TS are simulated with different domain configurations using weather research and forecasting (WRF) model. Two nested domains with 9–3 km (known as DD3), and 6–2 km (DD2), and 3 km single domain (SD3) are considered for simulations. Results indicate that the high-resolution DD2 has improved 2-m temperature (T2), 2-m relative humidity (RH2), and 10-m wind speed (WS10) at different stages of TS. The average mean error of T2 and RH2 in the DD2 experiment is 0.7 °C, ??6% during the mature stage, and 0.2 °C, ??4% at dissipating stage. The error in SD3 and DD3 is relatively higher (9–17% for T2 and 20–60% for RH2). Better horizontal and vertical representation of thermodynamic variables in DD2 run reinforces the atmosphere to initiate and intensify the convection in the right place. The DD2 could show slightly higher instability (convective available potential energy, CAPE, 3188 J kg^?1) as compared with DD3 (3164 J kg^?1) and SD3 (3020 J kg^?1). The model is biased to simulate early TS activity. DD2 run could simulate the formation, mature and dissipation stages with fewer timing errors (??1.35 h, ??1.5 h, and ??2.6 h, respectively) than other experiments. The critical success index of the DD2 run is higher for all the rainfall thresholds; however, it is more than 0.2 up to 2.5 mm h^?1. The results highlight that high resolution nested configuration yields better simulation skills than the single domain configuration.

     

Stability regions of equilibrium points in restricted four-body problem with oblateness effects

In this paper, we extend the basic model of the restricted four-body problem introducing two bigger dominant primaries m ₁ and m ₂ as oblate spheroids when masses of the two primary bodies (m ₂ and m ₃) are equal. The aim of this study is to investigate the use of zero velocity surfaces and the Poincaré surfaces of section to determine the possible allowed boundary regions and the stability orbit of the equilibrium points. According to different values of Jacobi constant C, we can determine boundary region where the particle can move in possible permitted zones. The stability regions of the equilibrium points expanded due to presence of oblateness coefficient and various values of C, whereas for certain range of t (100≤t≤200), orbits form a shape of cote’s spiral. For different values of oblateness parameters A ₁ (0<A ₁<1) and A ₂ (0<A ₂<1), we obtain two collinear and six non-collinear equilibrium points. The non-collinear equilibrium points are stable when the mass parameter μ lies in the interval (0.0190637,0.647603). However, basins of attraction are constructed with the help of Newton Raphson method to demonstrate the convergence as well as divergence region of the equilibrium points. The nature of basins of attraction of the equilibrium points are less effected in presence and absence of oblateness coefficients A ₁ and A ₂ respectively in the proposed model.     

Estimation of model parameter of Sumatra earthquake using empirical Green’s function technique and generation of hypothetical earthquake scenario for Andaman Island, India

Empirical Green??s function (EGF) technique is considered to be most effective technique for simulation of ground motions due to a finite earthquake source. In the present paper, this technique has been used to simulate ground motion due to a great earthquake. The coastal region of Sumatra Island has been visited by a great earthquake on December 26, 2004. This earthquake has been recorded at several broadband stations including a nearest broadband station PSI in Indonesia. The shear wave contributions in both horizontal components have been simulated at PSI station using EGF technique. The comparison of simulated and observed waveform has been made for various possibilities of rupture parameters in terms of root mean square error. The final rupture model supports rupture velocity of 3.0?km/s with nucleation point supporting northward propagating rupture that coincide with high-slip asperity defined by Sorensen et al. (Bull Seism Soc Am 97:S139?CS151, 2007). The final modeling parameters have been used to simulate record at MDRS station in coastal state of Tamilnadu, India. In an attempt to model a scenario of great earthquake in the Andaman Island, a hypothetical rupture plane is modeled in this region. The event occurred on August 10, 2008 of magnitude 6.2 (M _w ) recorded on strong motion array at Port Blair has been used as EGF to simulate records due to the hypothetical great earthquake. Possibilities of earthquake due to the oblique strike-slip and thrust mechanism have been modeled in the present paper. Several possibilities of nucleation point for both cases has been considered, and it is seen that variation of peak ground acceleration at Port Blair station for strike-slip and thrust mechanism is 126?C738 gals and 647?C2,571 gals, respectively, which indicate high seismic hazard potential of Andaman Island.