On the photo-gravitational restricted four-body problem with variable mass

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393–394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86–97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses \(m_{1}\), \(m_{2}\) and \(m_{3}\) in an equilateral triangle with \(m_{2}=m_{3}\) will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters \(\gamma (\frac{m \ \text{at time} \ t}{m \ \text{at initial time}}, 0<\gamma\leq1 )\), \(\alpha\) (the proportionality constant in Jeans’ law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), \(0\leq\alpha\leq2.2\)), the mass parameter \(\mu=0.005\) and radiation parameters \(q_{i}, (0< q_{i}\leq1, i=1, 2, 3)\). All the libration points are non-collinear if \(q_{2}\neq q_{3}\). It has been observed that the collinear and out-of-plane libration points also exist for \(q_{2}=q_{3}\). In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton–Raphson basins of attraction are also discussed.     

Analysis of mobility data – A focus on Mobile Mapping Systems

ABSTRACT

The increasing availability of devices to capture the position of moving objects (and other environmental information) leads to a very large amount and variety of mobility data. In order to obtain important information about the objects, their behavior or the environment of the objects, an automatic analysis is required. This article highlights current research questions in the context of the analysis of mobility data and presents them on the basis of work carried out at the Institute of Cartography and Geoinformatics (ikg) at Leibniz University of Hannover, Germany. A focus is put on the analysis and exploitation of information from Mobile Mapping vehicles.     

“Terrae motus factus est”: earthquakes in Switzerland before A.D. 1000. A critical approach

We focus on Swiss earthquakes in antiquity and the early medieval period before A.D. 1000. We have information on less than half a dozen earthquakes within this era, since written records for the first half of the first millennium A.D. are minimal, and there is little hope of finding more written evidence for earthquakes. Furthermore, interpreting the documents at hand is somewhat complex. For the 6th century Gregory of Tours in Historia Francorum gives hints of a rockslide near the castle Tauredunum (Le Grammont) in the Swiss canton Valais, an event that has been considered in the literature as caused by an earthquake. The Carolingian period (ca. 750–950) included the rise of some very important cultural centers in various parts of today’s Switzerland. For instance, the ecclesiastical culture in St. Gallen generated a remarkable number of written records, which survived for our use in a unique manner. From the 9th and 10th centuries, we have evidence for earthquakes in the years 849, 867, 902, and 944. However, information on them remains so scarce that their location and intensity are generally difficult to assess. Nevertheless, the finding of a new document - a memoir written by the abbot of Reichenau - offers some insight into the A.D. 849 event and its reportedly aftershocks.

Feasibility of utilizing wavelet phase to map the CO2 plume at the Ketzin pilot site,Germany

Spectral decomposition is a powerful tool that can provide geological details dependent upon discrete frequencies. Complex spectral decomposition using inversion strategies differs from conventional spectral decomposition methods in that it produces not only frequency information but also wavelet phase information. This method was applied to a time‐lapse three‐dimensional seismic dataset in order to test the feasibility of using wavelet phase changes to detect and map injected carbon dioxide within the reservoir at the Ketzin carbon dioxide storage site, Germany. Simplified zero‐offset forward modelling was used to help verify the effectiveness of this technique and to better understand the wavelet phase response from the highly heterogeneous storage reservoir and carbon dioxide plume. Ambient noise and signal‐to‐noise ratios were calculated from the raw data to determine the extracted wavelet phase. Strong noise caused by rainfall and the assumed spatial distribution of sandstone channels in the reservoir could be correlated with phase anomalies. Qualitative and quantitative results indicate that the wavelet phase extracted by the complex spectral decomposition technique has great potential as a practical and feasible tool for carbon dioxide detection at the Ketzin pilot site.     

Chemical characteristics of PM<Subscript>10</Subscript> aerosols and airmass trajectories over Bay of Bengal and Arabian Sea during ICARB

For the first time, chemical characterization of PM₁₀ aerosols was attempted over the Bay of Bengal (BoB) and Arabian Sea (AS) during the ICARB campaign. Dominance of SO ₄ ^2? , NH ₄ ⁺ and NO ₃ ^? was noticed over both the regions which indicated the presence of ammonium sulphate and ammonium nitrate as major water soluble particles playing a very important role in the radiation budget. It was observed that all the chemical constituents had higher concentrations over Bay of Bengal as compared to Arabian Sea. Higher concentrations were observed near the Indian coast showing influence of landmass indicating that gaseous pollutants like SO₂, NH₃ and NO _x are transported over to the sea regions which consequently contribute to higher SO ₄ ^2? , NH ₄ ⁺ and NO ₃ ^? aerosols respectively. The most polluted region over BoB was 13°?19°N and 70°?90°E while it was near 11°N and 75°E over AS. Although the concentrations were higher over Bay of Bengal for all the chemical constituents of PM₁₀ aerosols, per cent non-sea salt (nss) fraction (with respect to Na) was higher over Arabian Sea. Very low Ca2+ concentration was observed at Arabian Sea which led to higher atmospheric acidity as compared to BoB. Nss SO ₄ ^2? alone contributed 48% of total water soluble fraction over BoB as well as AS. Ratios SO ₄ ^2? /NO _? ³ over both the regions (7.8 and 9 over BoB and AS respectively) were very high as compared to reported values at land sites like Allahabad (0.63) and Kanpur (0.66) which may be due to very low NO.3 over sea regions as compared to land sites. Air trajectory analysis showed four classes: (i) airmass passing through Indian land, (ii) from oceanic region, (iii) northern Arabian Sea and Middle East and (iv) African continent. The highest nss SO ₄ ^2? was observed during airmasses coming from the Indian land side while lowest concentrations were observed when the air was coming from oceanic regions. Moderate concentrations of nss SO2. 4 were observed when air was seen moving from the Middle East and African continent. The pH of rainwater was observed to be in the range of 5.9–6.5 which is lower than the values reported over land sites. Similar feature was reported over the Indian Ocean during INDOEX indicating that marine atmosphere had more free acidity than land atmosphere.     

Analysis of Y-component of Geomagnetic Field and SYM-H Index Using Wavelet Multiresolution Analysis

Geomagnetism and Aeronomy - Electrodynamical coupling between the solar wind’s plasma and the Earth’s magnetosphere creates geomagnetic disturbances recorded on the ground. This work...     

Festkontaktierte potentiometrische Elektroden für Sulfatbestimmungen in wässrigen Lösungen

Solid‐contacted Potentiometric Electrodes for Measurements of Sulfate Ions in Aqueous Solutions A solid‐contact electrode for potentiometric measurement of sulfate ions in aqueous solutions was developed and examined. The electrode is based on a PVC membrane which contains the ionophore 3‐decyl‐1,5,8‐triazacyclodecan‐2,4‐dione (DTADD). Instead of the usual inner fluid junction, a polypyrrole layer applied on the inner side of the PVC membrane was employed as inner solid contact. The performance of this electrode was compared to solid‐state sulfate‐selective electrodes with the ionophore α,α′‐bis(N′‐phenylthioureylene)‐m‐xylene (BTH) and to electrodes in the coated‐wire configuration. For the parameters sensitivity, selectivity, and long‐term stability, electrodes with the DTADD ionophore show improved properties. In the sulfate concentration range of 5·10^–5...10^–2 mol L^–1 the slope of the response is –(26.8 ± 0.5) mV/decade. The new solid contact sulfate electrodes showed a very low drift of the electrode potential within a period of 150 days when the electrode was stored in 10^–2 M Na₂SO₄. In Na2SO4 solutions of the pH range of 4...9 the electrode potentials were constant. The 95% response time was about 10 s when the sulfate concentration was changed from 10^–4 mol L^–1 to 10^–3 mol L^–1. The selectivity with DTADD ionophore relating to the nitrate ions is higher than the selectivity with BTH. Improvements are also made in comparison with sulfate‐selective electrodes described in the literature which contain other ionophores with fluid inner reference electrolytes.     

Permafrost occurrence during the Last Permafrost Maximum in the Western Carpathian Mountains of Slovakia as inferred from cryogenic cave carbonate

Coarse crystalline cryogenic cave carbonate (CCC) forms during the slow freezing of standing water pools and represents indirect proof of freezing temperature in the past. The dating by U‐series of CCC deposits from nine caves in the Western Carpathians Mountains of Slovakia suggests that freezing conditions, and possible permafrost conditions, occurred during the Last Permafrost Maximum (LPM, c. 20–18 ka BP). The CCC deposits occur in caves at elevations of between 800 and 1800 m a.s.l. They point to widespread alpine permafrost, the lower limit of discontinuous/sporadic permafrost being approximately 800 m a.s.l. The thickness of permafrost probably varied between 30 and 180 m. In the Vysoké Tatry Mountains at altitudes of ～1800 m a.s.l., one occurrence of CCC suggests that subzero temperatures may have penetrated to a depth of over 285 m.