‘Similar’ coordinate systems and the Roche geometry: application

A new equivalence relation, named relation of ‘similarity’ is defined and applied in the restricted three-body problem. Using this relation, a new class of trajectories (named ‘similar’ trajectories) are obtained; they have the theoretical role to give us new details in the restricted three-body problem. The ‘similar’ coordinate systems allow us in addition to obtain a unitary and an elegant demonstration of some analytical relations in the Roche geometry. As an example, some analytical relations published by Seidov (in Astrophys. J. 603:283, 2004) are demonstrated.     

Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

The restricted three-body problem in Schwarzschild's gravitational field is analyzed. The existen- ce of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.     

Zero is the only acceptable leakage rate for geologically stored CO 2 : an editorial comment

Leakage is one of the main concerns of all parties involved with the development of Carbon Capture and Storage. From an economic point of view, van der Zwaan and Gerlagh (2009) suggest that CCS remains a valuable option even with CO₂ leakage rate as high as of a few % per year. But what is valuable is, ultimately, determined by social preferences and parameters that are beyond economic modeling. Examining the point of view of four stakeholder groups: industry, policy-makers, environmental NGOs and the general public, we conclude that there is a social agreement today: zero is the only acceptable carbon leakage rate.     

The Restricted Three-Body Problem: Comments on the Rotational Effect

The synchronization between the orbital motion and axial rotation of the two component stars of a binary system is reviewed. Some previous published papers are mentioned and the general conclusion is outlined: If we shall use a rotating coordinate system synchronous with one of the two stellar axial rotations, it is not possible to obtain a Jacobi integral and the Roche geometry cannot be further analyzed. In addition, a theoretical approach is summarized in order to use the axial rotations of the two component stars, even if the constants of the stellar structure (k₂)₁, (k₂)₂must be taken into consideration. So it is found that if the stellar angular velocities are higher than the corresponding Keplerian angular velocity (ω_i≫ ω_k, i= ), the problem of the rotational effect could be of practical consideration. Finally, a theoretical relationship between the two constants (k₂)₁and (k₂)₂of the stellar structure is established.     

A Complex Filament Evolution

A complex filament composed by a main body a polar filament and a tail—a small filament situated between active regions, was observed between 6 and 14 January 2001. A decaying active region plays the role of attractor for this filament. We have studied the dynamics of the filament which disappeared in a spectacular CME, produced after a helical up-awarded movement of plasma in the filaments loops.     

Modern Sphagnumδ13C signatures follow a surface moisture gradient in two boreal peat bogs,James Bay lowlands,Québec

Carbon isotopic composition of Sphagnum macrofossils can potentially be used as a palaeohydrological tool for peat‐based climatic studies since a relationship between Sphagnum δ¹³C values and peatland surface moisture has been presented in previous studies. In order to verify this hypothesis, modern Sphagnum δ¹³C values were measured along a moisture (microtopographic) gradient in two boreal peat bogs. Isotopic measurements were performed on bulk material of S. fuscum, S. magellanicum, S. capillifolium and S. pulchrum. Isotopic variations found within and between Sphagnum species along the microtopographic gradient were compared using analysis of variance. A significant positive correlation (P < 0.0001) was found between Sphagnum δ¹³C values and their position along the surface moisture gradient. Results show that ¹³C‐depleted values are related to low water table depths (WTD), while ¹³C‐enriched values correspond to a water table that is close to the peat surface. Although the mechanisms underlying carbon fractionation processes in mosses are not well understood, we demonstrate that water resistance to CO₂ diffusion is an important fractionation process that is observed in bulk Sphagnum δ¹³C measurements, since drier and wetter samples exhibit consistent and very different isotopic signatures. Copyright © 2008 John Wiley & Sons, Ltd.     

Wind storm risk management: sensitivity of return period calculations and spread on the territory

Modeling and forecasting damage from wind storms is a major issue for insurance companies. In this article, we focus on the sensitivity of estimations of return periods for extreme events with respect to modeling assumptions and the type of input data. Numerous variables play a role: the quality of data concerning the location of insured buildings and weather report homogeneity, missing updates for correcting non-stationarities concerning the insurance portfolio history, ground roughness or climate change, the evolution of the model after an unprecedented event such as the Lothar storm observed in 1999 in Europe, temporal aggregation of daily events over several days, where events could span over several days up to one week, and storm trajectories, which could change due to global warming or sweep larger areas. Our work explores three important aspects. First, we highlight the geographic heterogeneity of the spatial distribution of wind speeds and the resulting damages. Therefore, we propose to partition the French territory into 6 relatively homogeneous storm zones, based on the dependence among observed wind speeds and geographic distance. Second, we extend a storm index—defined in Mornet et al. (Risk Anal 35:2029–2056, 2015)—to take into account geographic heterogeneity, and we analyze its tail behavior to show the difficulties met to obtain reliable results on extreme events. Third, we explore the calculation of Solvency Capital Requirements based on a model that we propose for the annual claim amount distribution. The purpose of our analysis is to quantify and to point out the high level of uncertainty in the computation of return periods and of other quantities strongly influenced by extreme events.     

Periodic motions in a gravitational central field with a rotating external force

We consider a Kepler problem, with an additional rotating external force, and study the existence of periodic solutions when a small perturbative term is introduced. Surprisingly enough, we always get at least one of such solutions. Moreover, if a nonresonance assumption is added, then the existence of a second solution is also proved.