446 research outputs found
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
Development and mechanical characterization of porous titanium bone substitutes
The authors wish to thank Dr J.-M. Hiver from Institut Jean Lamour, Ecole des Mines de Nancy for his participation in the computed tomography analysis of the porous samplesCommercially Pure Porous Titanium (CPPTi) can be used for surgical implants to avoid the stress shielding effect due to the mismatch between the mechanical properties of titanium and bone. Most researchers in this area deal with randomly distributed pores or simple architectures in titanium alloys. The control of porosity, pore size and distribution is necessary to obtain implants with mechanical properties close to those of bone and to ensure their osseointegration. The aim of the present work was therefore to develop and characterize such a specific porous structure. First of all, the properties of titanium made by Selective Laser Melting (SLM) were characterized through experimental testing on bulk specimens. An elementary pattern of the porous structure was then designed to mimic the orthotropic properties of the human bone following several mechanical and geometrical criteria. Finite Element Analysis (FEA) was used to optimize the pattern. A porosity of 53% and pore sizes in the range of 860 to 1500 μm were finally adopted. Tensile tests on porous samples were then carried out to validate the properties obtained numerically and identif the failure modes of the samples. Finally, FE elastoplastic analyses were performed on the porous samples in order to propose a failure criterion for the design of porous substitutes
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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
Diffraction par un obstacle situé dans un réseau de plaques semi-infinies
International audience ; L'objet de cette Note est de proposer une méthode pour l'étude de la diffraction par un réseau de plaques horizontales semi-infinies localement perturbé par un obstacle. La méthode proposée couple une équation variationnelle posée dans un domaine borné entourant l'obstacle et une équation pseudo-différentielle écrite sur la droite verticale située à l'extrémité des plaques. Après avoir donné une formulation variationnelle du problème, on montre que celui-ci relève de l'alternative de Fredholm, en dehors des fréquences de résonance du réseau
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 -coercivity approach, we first prove that the problem is well-posed in the classical framework 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 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
Development and mechanical characterization of porous titanium bone substitutes
The authors wish to thank Dr J.-M. Hiver from Institut Jean Lamour, Ecole des Mines de Nancy for his participation in the computed tomography analysis of the porous samplesCommercially Pure Porous Titanium (CPPTi) can be used for surgical implants to avoid the stress shielding effect due to the mismatch between the mechanical properties of titanium and bone. Most researchers in this area deal with randomly distributed pores or simple architectures in titanium alloys. The control of porosity, pore size and distribution is necessary to obtain implants with mechanical properties close to those of bone and to ensure their osseointegration. The aim of the present work was therefore to develop and characterize such a specific porous structure. First of all, the properties of titanium made by Selective Laser Melting (SLM) were characterized through experimental testing on bulk specimens. An elementary pattern of the porous structure was then designed to mimic the orthotropic properties of the human bone following several mechanical and geometrical criteria. Finite Element Analysis (FEA) was used to optimize the pattern. A porosity of 53% and pore sizes in the range of 860 to 1500 μm were finally adopted. Tensile tests on porous samples were then carried out to validate the properties obtained numerically and identif the failure modes of the samples. Finally, FE elastoplastic analyses were performed on the porous samples in order to propose a failure criterion for the design of porous substitutes
Rayonnement sonore dans un écoulement subsonique complexe en régime harmonique (analyse et simulation numérique du couplage entre les phénomènes acoustiques et hydrodynamiques)
La thèse porte sur la simulation, en régime fréquentiel, du rayonnement acoustique en écoulement subsonique quelconque et dans un domaine infini. L'approche choisie s'appuie sur la résolution d'un système équivalent aux équations d'Euler linéarisées : le modèle de Galbrun. Ce modèle repose sur une représentation mixte Lagrange-Euler et aboutit à une équation dont l'unique inconnue est la perturbation du déplacement Lagrangien. Une des difficultés de l'approche de Galbrun est qu'une discrétisation directe de cette équation par une méthode d'éléments finis standard n'est pas stable. Un moyen de contourner cet obstacle est d'écrire une équation augmentée en ajoutant une nouvelle inconnue, le rotationnel du déplacement, appelée par abus vorticité. Cette approche conduit à un système qui couple une équation de type équation des ondes avec une équation de transport en régime fréquentiel. Et elle permet l'utilisation de couches parfaitement adaptées (PML) pour borner le domaine de calcul. La première partie du manuscrit est dédiée à l étude de l équation de transport harmonique et de sa résolution numérique, en particulier par un schéma de type Galerkin discontinu. Un des points délicats est lié au caractère oscillant des solutions de l'équation. Une fois cette étape franchie, la résolution du problème de propagation acoustique a été abordée. Une approximation basée sur l'utilisation d'éléments finis mixtes continus-discontinus avec couches parfaitement adaptées (PML) a été étudiée. En particulier, les caractères bien posés des problèmes continu et discret ainsi que la convergence du schéma numérique ont été démontrés sous certaines conditions sur l'écoulement porteur. Enfin, une mise en œuvre a été effectuée. Les résultats montrent la validité de cette approche mais aussi sa pertinence dans le cas d'écoulements complexes, voire d'écoulements dits instablesThis thesis deals with the numerical simulation of time harmonic acoustic propagation in an arbitrary mean flow in an unbounded domain. Our approach is based on an equation equivalent to the linearized Euler equations called the Galbrun equation. It is derived from a mixed Eulerian-Lagrangian formulation and results in a single equation whose only unknown is the perturbation of the Lagrangian displacement. A direct solution using finite elements is unstable but this difficulty can be overcome by using an augmented equation which is constructed by adding a new unknown, the vorticity, defined as the curl of the displacement. This leads to a set of equations coupling a wave like equation with a time harmonic transport equation which allows the use of perfectly matched layers (PML) at artificial boundaries to bound the computational domain. The first part of the thesis is a study of the time harmonic transport equation and its approximation by means of a discontinuous Galerkin scheme, the difficulties coming from the oscillating behaviour of its solutions. Once these difficulties have been overcome, it is possible to deal with the resolution of the acoustic propagation problem. The approximation method is based on a mixed continuous-Galerkin and discontinuous-Galerkin finite element scheme. The well-posedness of both the continuous and discrete problems is established and the convergence of the approximation under some mean flow conditions is proved. Finally a numerical implementation is achieved and numerical results are given which confirm the validity of the method and also show that it is relevant in complex cases, even for unstable flowsTOULOUSE-INSA-Bib. electronique (315559905) / SudocSudocFranceF
An alternative to Dirichlet-to-Neumann maps for waveguides
International audienceWe are interested by the treatment of the radiation condition at infinity for the numerical solution of a problem set in an unbounded waveguide. We propose an alternative to the classical approach involving a modal expression of Dirichlet-to-Neumann (DtN) operators. This method is particularly simple to implement since it only requires the solution of boundary value problems with local boundary conditions. The corresponding approximate solution is comparable in accuracy to the one obtained by truncating the infinite series in the DtN maps
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