A postulate leading to the Titius-Bode law

The revised Titius-Bode law (Balsano and Hughes, 1979) giving distances of planets from the Sun shows integers that recall the Bohr law in the early quantum theory of hydrogen atom. The author searchs for a formalism, similar to the Sommerfeld's one accounting for the planetary distribution of the solar system. It is shown that such a formalism might be started with the assumed relation $$\int_{r_0 }^{r_n } {U(r)dr = nk,} $$ whereU(r) stands for the gravitation potential created by the Sun at distancer,k=cte,r _o=cte,r _n=distance of then ^th planet andn=1, 2, 3... Although the inspiration of the present note came from the early quantum theory, it is emphasized that there is no connection between the above assumed equation and the Sommerfeld quantum rule, but a pure formal similarity. the true significance of that equation is still unknown. It is either a fortuitous coincidence leading to the T-B law or any possible unsuspected property of gravitation.     

Sur un modele explicitant les differents types morphologiques des galaxies

In the now classical Lindblad-Lin density-wave theory, the linearization of the collisionless Boltzmann equation is made by assuming the potential functionU expressed in the formU=U ₀ + \(\tilde U\) +... WhereU ₀ is the background axisymmetric potential and \(\tilde U<< U_0 \) . Then the corresponding density distribution is \(\rho = \rho _0 + \tilde \rho (\tilde \rho<< \rho _0 )\) and the linearized equation connecting \(\tilde U\) and the component \(\tilde f\) of the distribution function is given by $$\frac{{\partial \tilde f}}{{\partial t}} + \upsilon \frac{{\partial \tilde f}}{{\partial x}} - \frac{{\partial U_0 }}{{\partial x}} \cdot \frac{{\partial \tilde f}}{{\partial \upsilon }} = \frac{{\partial \tilde U}}{{\partial x}}\frac{{\partial f_0 }}{{\partial \upsilon }}.$$ One looks for spiral self-consistent solutions which also satisfy Poisson's equation $$\nabla ^2 \tilde U = 4\pi G\tilde \rho = 4\pi G\int {\tilde f d\upsilon .} $$ Lin and Shu (1964) have shown that such solutions exist in special cases. In the present work, we adopt anopposite proceeding. Poisson's equation contains two unknown quantities \(\tilde U\) and \(\tilde \rho \) . It could be completelysolved if a second independent equation connecting \(\tilde U\) and \(\tilde \rho \) was known. Such an equation is hopelesslyobtained by direct observational means; the only way is to postulate it in a mathematical form. In a previouswork, Louise (1981) has shown that Poisson's equation accounted for distances of planets in the solar system(following to the Titius-Bode's law revised by Balsano and Hughes (1979)) if the following relation wasassumed $$\rho ^2 = k\frac{{\tilde U}}{{r^2 }} (k = cte).$$ We now postulate again this relation in order to solve Poisson's equation. Then, $$\nabla ^2 \tilde U - \frac{{\alpha ^2 }}{{r^2 }}\tilde U = 0, (\alpha ^2 = 4\pi Gk).$$ The solution is found in a classical way to be of the form $$\tilde U = cte J_v (pr)e^{ - pz} e^{jn\theta } $$ wheren = integer,p =cte andJ _v (pr) = Bessel function with indexv (v ² =n ² + α²). By use of the Hankel function instead ofJ _v (pr) for large values ofr, the spiral structure is found to be given by $$\tilde U = cte e^{ - pz} e^{j[\Phi _v (r) + n\theta ]} , \Phi _v (r) = pr - \pi /2(v + \tfrac{1}{2}).$$ For small values ofr, \(\tilde U\) = 0: the center of a galaxy is not affected by the density wave which is onlyresponsible of the spiral structure. For various values ofp,n andv, other forms of galaxies can be taken into account: Ring, barred and spiral-barred shapes etc. In order to generalize previous calculations, we further postulateρ ₀ =kU ₀/r ², leading to Poisson'sequation which accounts for the disc population $$\nabla ^2 U_0 - \frac{{\alpha ^2 }}{{r^2 }}U_0 = 0.$$ AsU ₀ is assumed axisymmetrical, the obvious solution is of the form $$U_0 = \frac{{cte}}{{r^v }}e^{ - pz} , \rho _0 = \frac{{cte}}{{r^{2 + v} }}e^{ - pz} .$$ Finally, Poisson's equation is completely solvable under the assumptionρ =k(U/r ². The general solution,valid for both disc and spiral arm populations, becomes $$U = cte e^{ - pz} \left\{ {r^{ - v} + } \right.\left. {cte e^{j[\Phi _v (r) + n\theta ]} } \right\},$$ The density distribution along the O _z axis is supported by Burstein's (1979) observations.     

A conceptual framework and its application for addressing leakage: the case of avoided deforestation

One of the most challenging technical issues associated with project-based mechanisms is that of leakage. A conceptual framework is proposed for the identification and analysis of leakage potentially generated by a project. The categorization of leakage based on the actors responsible for their manifestation is proposed, which divides sources of leakage into primary and secondary types. It is the actors or agents responsible for the baseline activities that cause primary leakage. Secondary leakage occurs when the project’s outputs create incentives for third parties to increase emissions elsewhere. This distinction, based on the source of leakage, provides a basis for the analysis outlined in the paper. The extent and type of leakage will vary depending on the project typology and design. Using a decision tree approach, the process of identifying potential sources of leakage is demonstrated for the case study of avoided deforestation projects. If the main elements determining a baseline are properly identified and understood, in particular the ‘baseline agents’, a combination of the decision tree approach and apportioning responsibility, can assist in the quantification and monitoring of primary leakage. An analysis at the project design stage can also assist in minimizing the risk of future leakage. Econometric methods may prove more useful in analyzing secondary leakage.     

Imagining difference: the experiences of 'transnational' Indian IT professionals in Germany

In this paper we explore the motivations to migrate and the migration experiences of 22 Indian IT professionals in Germany. When studying skilled migration, Germany is an interesting case as it struggled with waves of extreme right activities whilst trying to attract IT professionals from outside the European Union at the same time. In this context, we are interested in the conflicts that the migrants may experience as a result of their desire or obligation to move, their specific cultural baggage and the way in which they encounter the different sides of German society.     

Magnitude and variation in the contribution of bank erosion to the suspended sediment load of the River Severn,UK

The wide range of studies describing the role of bank erosion in fluvial sediment supply have mostly lumped amounts of bank erosion into coarse temporal units, such as years. This paper investigates sediment yields from individual bank erosion events within the upper River Severn, UK (basin area 380 km²). Manual erosion pins and photo-electronic erosion pins were used to estimate bank erosion, and turbidity meters were used to determine suspended sediment transport. At the annual time-scale, the silt-clay fraction of bank-derived sediment accounted for an equivalent of 17 per cent of the suspended load, increasing to an average of 38 per cent at the monthly timescale, and then to an average of 64 per cent at the event timescale. This research highlighted that for an upland catchment, bank erosion was an important supply of suspended sediment, and that for some flood events bank erosion can supply more sediment than is transported. © 1997 John Wiley & Sons, Ltd.     

The daily‐scale entrance dynamics of intermittently open/closed estuaries

Intermittently open/closed estuaries (IOCE) are a dynamic form of estuary characterised by periodic entrance closure to the ocean. Entrance closure is a function of the relative balance between on and offshore sediment transport with closures occurring during periods of low fluvial discharge whereby the estuary ebb‐tidal prism is reduced. Although the broad scale processes of entrance closure are becoming better understood, there remains limited knowledge on channel morphodynamics during an individual closure event. In this study, the entrance dynamics of three IOCE on the coast of Victoria, Australia, were monitored over a daily timescale following both artificial and natural openings. The influence of changing marine and fluvial conditions on the relative sedimentation rate within the entrance channel was examined. IOCE in Victoria showed two distinct modes of entrance closure: (a) lateral accretion, whereby the estuary gradually closes by longshore drift‐driven spit growth during low river flows; and (b) vertical accretion, where the channel rapidly aggrades under high (> 2 m), near‐normal waves. During storms, when fluvial discharge and wave heights simultaneously increase, large swells will not always close the mouth due to an increase in the ebb‐tidal prism. The estuary water depth and the maximum channel dimensions following opening were not proportional to the opening duration, with this being a function of the wave and fluvial conditions occurring following lagoon drainage. Based on the findings of this work, implementing a successful artificial entrance opening is dependent on reduced onshore sedimentation rates which occur when wave energy is low (< 2 m Hs) relative to river flow. Copyright © 2017 John Wiley & Sons, Ltd.     

The deglaciation of the western sector of the Irish Ice Sheet from the inner continental shelf to its terrestrial margin

This paper provides a new deglacial chronology for retreat of the Irish Ice Sheet from the continental shelf of western Ireland to the adjoining coastline, a region where the timing and drivers of ice recession have never been fully constrained. Previous work suggests maximum ice-sheet extent on the outer western continental shelf occurred at ~26–24 cal. ka BP with the initial retreat of the ice marked by the production of grounding-zone wedges between 23–21.1 cal. ka BP. However, the timing and rate of ice-sheet retreat from the inner continental shelf to the present coast are largely unknown. This paper reports 31 new terrestrial cosmogenic nuclide (TCN) ages from erratics and ice-moulded bedrock and three new optically stimulated luminescence (OSL) ages on deglacial outwash. The TCN data constrain deglaciation of the near coast (Aran Islands) to ~19.5–18.5 ka. This infers ice retreated rapidly from the mid-shelf after 21 ka, but the combined effects of bathymetric shallowing and pinning acted to stabilize the ice at the Aran Islands. However, marginal stability was short-lived, with multiple coastal sites along the Connemara/Galway coasts demonstrating ice recession under terrestrial conditions by 18.2–17. ka. This pattern of retreat continued as ice retreated eastward through inner Galway Bay by 16.5 ka. South of Galway, the Kilkee–Kilrush Moraine Complex and Scattery Island moraines point to late stage re-advances of the ice sheet into southern County Clare ~14.1–13.3 ka, but the large errors associated with the OSL ages make correlation with other regional re-advances difficult. It seems more likely that these moraines are the product of regional ice lobes adjusting to internal ice-sheet dynamics during deglaciation in the time window 17–16 ka.     

Soil water movement and nutrient cycling in semi-arid rangeland: vegetation change and system resilience

Recent decades have seen rapid intensification of cattle production in semi-arid savannah ecosystems, increasingly on formalized ranch blocks. As a result, vegetation community changes have occurred, notably bush encroachment (increased bush dominance) in intensively grazed areas. The exact causes of this vegetation change remain widely debated. Previous studies have suggested: (i) increased leaching of water and nutrients into the subsoil in intensively grazed areas provides deeper rooting bush species with a competitive advantage for soil water and nutrients, and (ii) nutrient leaching may be exacerbated by nutrient inputs from cattle dung and urine. Our research in the Eastern Kalahari showed that in infertile sandy soils both the magnitude of soil water and concentration of soil nutrients leached into the subsoil is largely unaffected by the ecological and biochemical effects of increased cattle use. We found that despite the high soil hydraulic conductivity ( &greaterno;12 cm h⁻¹), relatively high subsoil moisture contents and the restriction of water movement to matrix flow pathways prevent leaching losses beyond the rooting zone of savannah grass species. No significant differences in patterns of soil water redistribution were noted between bush dominant and grass dominant sites. We also found that the low nutrient status of Kalahari soils and leachate movement as matrix flow combine to allow nutrient adsorption on to soil particles. Nutrient adsorption ensures that nitrogen and phosphorus cycling remains topsoil dominated even following the removal of vegetation and direct nutrient inputs in cattle dung and urine. This conclusion refutes environmental change models that portray increases in the leaching of soil water and available nitrogen as a major factor causing bush encroachment. This provides a possible explanation for the now widely cited, but hitherto unexplained, resilience of dryland soils. We suggest that infertile sandy soils appear resilient to changes in soil water distribution and nutrient availability caused by increased cattle use. Hence, soil characteristics contribute to the resilience to permanent ecological change that is increasingly recognized as an attribute of semi-arid rangelands. © 1998 John Wiley & Sons, Ltd.     

Simulation of the 2004 tsunami of Les Saintes in Guadeloupe (Lesser Antilles) using new source constraints

Natural Hazards - The arc of the Lesser Antilles is associated with a significant tectonic activity due to the subduction of the Atlantic oceanic plate under the Caribbean plate. Earthquakes in...     

Borehole temperatures, climate change and the pre-observational surface air temperature mean: allowance for hydraulic conditions

Joint analysis of surface air temperature series recorded at weather stations together with the inversion of the temperature-depth profiles logged in the near-by boreholes enables an estimate of the conditions existing prior to the beginning of the meteorological observation, the so-called pre-observational mean (POM) temperature.Such analysis is based on the presumption of pure diffusive conditions in the underground. However, in real cases a certain subsurface fluid movement cannot be excluded and the measured temperature logs may contain an advective component. The paper addresses the correction for the hydraulic conditions, which may have perturbed the climate signal penetrating from the surface into the underground. The method accounts for vertical conductive and vertical advective heat transport in a 1-D horizontally layered stratum and provides a simultaneous evaluation of the POM-temperature together with the estimate of the Darcy fluid velocity. The correction strategy is illustrated on a synthetic example and its use is demonstrated on temperature logs measured in four closely spaced boreholes drilled near Tachlovice (located about 15 km SW of Prague, Czech Republic). The results revealed that in a case of moderately advectively affected subsurface conditions (fluid velocities about 10⁻⁹ m/s), the difference between POM-values assessed for a pure conductive approach and for combined vertical conductive/advective approach may amount up to 0.3–0.5 K, the value comparable with the amount usually ascribed to the 20th century climate warming.