Non-scattering wavenumbers and far field invisibility for a finite set of incident/scattering directions

We investigate a time harmonic acoustic scattering problem by a penetrable inclusion with compact support embedded in the free space. We consider cases where an observer can produce incident plane waves and measure the far field pattern of the resulting scattered field only in a finite set of directions. In this context, we say that a wavenumber is a non-scattering wavenumber if the associated relative scattering matrix has a non trivial kernel. Under certain assumptions on the physical coefficients of the inclusion, we show that the non-scattering wavenumbers form a (possibly empty) discrete set. Then, in a second step, for a given real wavenumber and a given domain D, we present a constructive technique to prove that there exist inclusions supported in D for which the corresponding relative scattering matrix is null. These inclusions have the important property to be impossible to detect from far field measurements. The approach leads to a numerical algorithm which is described at the end of the paper and which allows to provide examples of (approximated) invisible inclusions.Comment: 20 pages, 7 figure

The Gender Gap in Pensions: Differences Between Generations

Over successive generations, womens participation in the labour market has risen and their career breaks have become less frequent. The gender wage gap has narrowed. The time spent in education has increased. These socio-economic factors largely explain the reduction for future generations of the current gender differentials in pension levels and retirement ages. Nonetheless, the gender pension gap should remain significant. Men of the 1965-1974 generations retiring from the private sector should receive a pension that is more than 50% higher than womens. Although women are expected to participate more in the labour market, they often work part time and the gender wage gap is expected to remain significant. Changes in retirement system rules will influence future trends in pension levels. The gap between womens and mens pensions would have narrowed much more in future if the 1993 and 2003 reforms had not been implemented.Pensions, Gender Pension Gap, Microsimulation, Pension Reforms

Intraspecific variation in environmental and geographic space use: insights from individual movement data

Species’ ranges arise from the interplay between environmental preferences, biotic and abiotic environmental conditions, and accessibility. Understanding of – and predictive models on – species distributions often build from the assumption that these factors apply homogenously within each species, but there is growing evidence for individual variation. Here, I use movement data to investigate individual-level decisions and compromises regarding the different costs and benefits influencing individuals’ geographic locations, and the species-level spatial patterns that emerge from these. I first developed a new method that uses tracking data to quantify individual specialisation in geographic space (site fidelity) or in environmental space (environmental specialisation). Applying it to two species of albatrosses, I found evidence of site fidelity but weak environmental specialisation. My results have implications for how limited research efforts are best-targeted: if animals are generalists, effort are best spent by understanding in depth individual patterns, i.e., better to track fewer individuals for long periods of time; whereas if animals tend to be specialists, efforts should be dedicated to tracking as many individuals as possible, even if for shorter periods. I then investigated individual migratory strategies and their drivers in nine North American bird species, using ringing/recovery data. I found latitudinal redistribution of individuals within the breeding and non-breeding ranges that generally did not follow textbook patterns (‘chain migration’ or ‘leapfrog migration’). Migratory individuals tend to trade off the benefits of migration (better tracking of climatic niche; better access to resources) and its costs (increasing with migratory distance). I found that birds are more likely to remain as residents in areas with warmer winter temperatures, higher summer resource surpluses and higher human population densities (presumably because of a buffering effect of urban areas). Overall, my results highlight the importance of considering individual variation to understanding the ecological processes underpinning species’ spatial patterns.St John's College Benefactors' Scholarship Cambridge Philosophical Societ

Deep into oceanic N₂ fixation

International audienc

Dissolved organic matter uptake by <i>Trichodesmium </i>in the Southwest Pacific

International audienceThe globally distributed diazotroph Trichodesmium contributes importantly to nitrogen inputs in the oligotrophic oceans. Sites of dissolved organic matter (DOM) accumulation could promote the mixotrophic nutrition of Trichodesmium when inorganic nutrients are scarce. Nano-scale secondary ion mass spectrometry (nanoSIMS) analyses of individual trichomes sampled in the South Pacific Ocean, showed significant 13 C-enrichments after incubation with either 13 C-labeled carbohydrates or amino acids. These results suggest that DOM could be directly taken up by Trichodesmium or primarily consumed by heterotrophic epibiont bacteria that ultimately transfer reduced DOM compounds to their host trichomes. Although the addition of carbohydrates or amino acids did not significantly affect bulk N 2 fixation rates, N 2 fixation was enhanced by amino acids in individual colonies of Trichodesmium. We discuss the ecological advantages of DOM use by Trichodesmium as an alternative to autotrophic nutrition in oligotrophic open ocean waters. Nitrogen is recognized as the proximate limiting nutrient for primary production in the oceans 1. The oceanic nitrogen reservoir is controlled by a balance between fixed nitrogen gains (via dinitrogen-N 2-fixation) and losses (denitrification) 2. While global nitrogen budget estimations determine that denitrification exceeds N 2 fixation considerably 3 , recent improvements in the 15 N 2 isotope tracer method used to measure biological N 2 fixation have evidenced that formerly published rates could be underestimated by a factor of ~2 to 6 4–8 , and thus could be high enough to balance denitrification on a global basis. However, the variability among N 2 fixation rates obtained when using the two different methods (adding 15 N 2 as a bubble or pre-dissolved in seawater) 4,9 can be high 7 and at times not significant 10–12. A mechanistic understanding of which factors determine the degree of discrepancy between the two 15 N 2 methods is currently lacking. Moreover, marine pelagic N 2 fixation had been long attributed to the tropical and subtropical latitudinal bands of the ocean, e.g. 13 , while other ecological niches such as high latitude waters, oxygen minimum zones and the vast dark realm of the ocean (below the euphotic zone) are now recognized as active N 2 fixation sites 14–16. It is likely that the inclusion of these previously unaccounted for active N 2 fixation sites will be more important in equilibrating denitrification and N 2 fixation rates than the underestimation of rates due to discrepancies between isotopic tracer methods. In chronically stratified open ocean regions such as the vast subtropical gyres, primary production depends largely on external fixed nitrogen inputs provided by N 2 fixation performed by prokaryotes termed 'diazotrophs'. Diazotrophic cyanobacteria are photosynthetic prokaryotes (with the exception of the photoheterotrophic Candidatus Atelocyanobacterium thalassa which cannot photosynthesize) 17 that thrive in oligotrophic tropical and subtropical waters of the oceans where they provide an important source of fixed nitrogen for other phyto-plankton 13. Despite being classically regarded as photoautotrophs, some unicellular diazotrophic cyanobacteria like Cyanothece are able to take up dissolved organic matter (DOM) molecules photoheterotrophically 18. As well, various filamentous diazotrophic cyanobacteria such as Anabaena bear genes for amino acids transport, which may be used to incorporate amino acids from the in situ DOM pool, or to assimilate amino acids self-produced during diazotrophic growth 19

On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients

International audienceWe investigate in a 2D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with a negative permittivity. Using the $\texttt{T}$-coercivity approach, we first prove that the problem is well-posed in the classical framework $H^1_{loc}$ if the negative permittivity does not lie in some critical interval whose definition depends on the shape of the device. When the latter has corners, for values inside the critical interval, unusual strong singularities for the electromagnetic field can appear. In that case, well-posedness is obtained by imposing a radiation condition at the corners to select the outgoing black-hole plasmonic wave, that is the one which carries energy towards the corners. A simple and systematic criterion is given to define what is the outgoing solution. Finally, we propose an original numerical method based on the use of Perfectly Matched Layers at the corners. We emphasize that it is necessary to design an $\textit{ad hoc}$ technique because the field is too singular to be captured with standard finite element methods

Iterative methods for scattering problems in isotropic or anisotropic elastic waveguides

International audienceWe consider the time-harmonic problem of the diffraction of an incident propagative mode by a localized defect, in an infinite straight isotropic elastic waveguide. We propose several iterative algorithms to compute an approximate solution of the problem, using a classical finite element discretization in a small area around the perturbation, and a modal expansion in unbounded straight parts of the guide. Each algorithm can be related to a so-called domain decomposition method, with or without an overlap between the domains. Specific transmission conditions are used, so that only the sparse finite element matrix has to be inverted, the modal expansion being obtained by a simple projection, using the Fraser bi-orthogonality relation. The benefit of using an overlap between the finite element domain and the modal domain is emphasized, in particular for the extension to the anisotropic case. The transparency of these new boundary conditions is checked for two- and three-dimensional anisotropic waveguides. Finally, in the isotropic case, numerical validation for two- and three-dimensional waveguides illustrates the efficiency of the new approach, compared to other existing methods, in terms of number of iterations and CPU time

A complex-scaled boundary integral equation for time-harmonic water waves

This paper presents a novel boundary integral equation (BIE) formulation for the two-dimensional time-harmonic water-waves problem. It utilizes a complex-scaled Laplace's free-space Green's function, resulting in a BIE posed on the infinite boundaries of the domain. The perfectly matched layer (PML) coordinate stretching that is used to render propagating waves exponentially decaying, allows for the effective truncation and discretization of the BIE unbounded domain. We show through a variety of numerical examples that, despite the logarithmic growth of the complex-scaled Laplace's free-space Green's function, the truncation errors are exponentially small with respect to the truncation length. Our formulation uses only simple function evaluations (e.g. complex logarithms and square roots), hence avoiding the need to compute the involved water-wave Green's function. Finally, we show that the proposed approach can also be used to find complex resonances through a \emph{linear} eigenvalue problem since the Green's function is frequency-independent