Inverse boundary value problem for the Helmholtz equation: quantitative conditional Lipschitz stability estimates

We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional Lipschitz stability estimate for the inverse problem holds in the case of wavespeeds that are a linear combination of piecewise constant functions (following a domain partition) and gives a framework in which the scheme converges. The stability constant grows exponentially as the number of subdomains in the domain partition increases. We establish an order optimal upper bound for the stability constant. We eventually realize computational experiments to demonstrate the stability constant evolution for three dimensional wavespeed reconstruction.Comment: 21 pages, 7 figures. arXiv admin note: text overlap with arXiv:1406.239

Fluid-structure interaction and homogenization: from spatial averaging to continuous wavelet transform

Fluid-structure interaction (FSI) is classicaly modeled according a separated and local approach. It enables to take full advantage of the numerical methods specifically designed for each medium. However, it requires to take great care of the interface, and to exchange, between the algorithms, the information related to boundary conditions [1]. This treatment of the interface can quickly become too cumbersome in complex flow geometries, as in the industrial case study driving this work: an inviscid compressible flow interacting with French PWR fuel assemblies (Fig. 1a). In such specific applications, where the solid medium exhibits a discontinuous but periodic design, an homogenized and global approach is preferred [2]. Inspired by porous media [3, 4], multiphase flows, or Large Eddy Simulation (LES), it relies on a spatial averaging of the balance equations, thus allowing to remove all interfaces. However, such filtering techniques exhibit two major limitations: first, they do not deal properly with boundary conditions, due to the non-commutativity between the filtering operator and spatial derivatives, as detailed in [5, 6, 7] for LES; second, filtering implies loss of microscopic information, and thus requires a closure model to describe interactions between resolved and unresolved scales

Higher-order Kerr terms allow ionization-free filamentation in gases

We show that higher-order nonlinear indices ($n_4$, $n_6$, $n_8$, $n_{10}$) provide the main defocusing contribution to self-channeling of ultrashort laser pulses in air and Argon at 800 nm, in contrast with the previously accepted mechanism of filamentation where plasma was considered as the dominant defocusing process. Their consideration allows to reproduce experimentally observed intensities and plasma densities in self-guided filaments.Comment: 11 pages, 6 figures (11 panels

4f-5d transitions of Pr3+ in elpasolite lattices

The 4f5d→4f2 emission spectra of Cs2MPrCl6 (M = Na,Li) and CS2NaYCl6:Pr3+ have been recorded at temperatures down to 10 K. The spectra of Pr3+ in the cubic host Cs2NaYCl6 are the most clearly resolved, and 15 transitions to terminal crystal field levels of symmetry representations Γ5g and Γ4g have been observed and assigned, thereby inferring that the symmetry representation of the lowest 4f5d crystal field level is Γ3u. Each transition is characterized by strong progressions in two totally symmetric vibrational modes. The relative displacement of the potential energy curves for the 4f2 and 4f5d crystal field levels, along the α1g internal mode coordinate, is small, being only about 5 pm. The 10-K ultraviolet absorption spectra of CS2NaYCl6:Pr3+ are assigned to transitions from the [3H4] Γ1g electronic ground state to terminal Γ4u crystal field levels of 4f5d. Nontotally symmetric gerade vibrational modes only provide minor intensity contributions. The large energy gap between the d-f emission and f-d absorption spectra of Pr3+ in the cubic elpasolite host is rationalized. The 8-K excitation spectra of Cs2NaPrCl6 and Cs2NaYCl6:Pr3+, excited by synchrotron radiation, show that the transitions to 4f5d fall into two groups. The energy levels and wave vectors of the (independent) 4f2 and 4f5d configurations of Pr3+ have been calculated using a model which includes spin-orbit coupling and crystal field and Coulomb interactions, as well as the configuration interaction of 4f2 with 4f6p. Using the eigenvector of the predominantly high-spin, lowest excited crystal field level of 4f5d, the emission intensities are reasonably well simulated. However, the refinement of the 4f2→4f5d absorption intensities requires a more detailed knowledge of the crystal field energy level scheme of 4f5d. The configuration interaction of 4f5d with 4f6s and 4f5g is discussed.published_or_final_versio

Spectral dependence of purely-Kerr driven filamentation in air and argon

Based on numerical simulations, we show that higher-order nonlinear indices (up to $n_8$ and $n_{10}$, respectively) of air and argon have a dominant contribution to both focusing and defocusing in the self-guiding of ultrashort laser pulses over most of the spectrum. Plasma generation and filamentation are therefore decoupled. As a consequence, ultraviolet wavelength may not be the optimal wavelengths for applications requiring to maximize ionization.Comment: 14 pages, 4 figures (14 panels

Josephson junctions and superconducting quantum interference devices made by local oxidation of niobium ultrathin films

We present a method for fabricating Josephson junctions and superconducting quantum interference devices (SQUIDs) which is based on the local anodization of niobium strip lines 3 to 6.5 nm-thick under the voltage-biased tip of an Atomic Force Microscope. Microbridge junctions and SQUID loops are obtained either by partial or total oxidation of the niobium layer. Two types of weak link geometries are fabricated : lateral constriction (Dayem bridges) and variable thickness bridges. SQUIDs based on both geometries show a modulation of the maximum Josephson current with a magnetic flux periodic with respect to the superconducting flux quantum h/2e. They persist up to 4K. The modulation shape and depth for SQUIDs based on variable thickness bridges indicate that the weak link size becomes comparable to the superconducting film coherence length which is of the order of 10nm.Comment: 12 page

Validating two-dimensional leadership models on three-dimensionally structured fish schools

Identifying leader–follower interactions is crucial for understanding how a group decides where or when to move, and how this information is transferred between members. Although many animal groups have a three-dimensional structure, previous studies investigating leader–follower interactions have often ignored vertical information. This raises the question of whether commonly used two-dimensional leader–follower analyses can be used justifiably on groups that interact in three dimensions. To address this, we quantified the individual movements of banded tetra fish (Astyanax mexicanus) within shoals by computing the three-dimensional trajectories of all individuals using a stereo-camera technique. We used these data firstly to identify and compare leader–follower interactions in two and three dimensions, and secondly to analyse leadership with respect to an individual's spatial position in three dimensions. We show that for 95% of all pairwise interactions leadership identified through two-dimensional analysis matches that identified through three-dimensional analysis, and we reveal that fish attend to the same shoalmates for vertical information as they do for horizontal information. Our results therefore highlight that three-dimensional analyses are not always required to identify leader–follower relationships in species that move freely in three dimensions. We discuss our results in terms of the importance of taking species' sensory capacities into account when studying interaction networks within groups

People making deontological judgments in the Trapdoor dilemma are perceived to be more prosocial in economic games than they actually are

Why do people make deontological decisions, although they often lead to overall unfavorable outcomes? One account is receiving considerable attention: deontological judgments may signal commitment to prosociality and thus may increase people’s chances of being selected as social partners–which carries obvious long-term benefits. Here we test this framework by experimentally exploring whether people making deontological judgments are expected to be more prosocial than those making consequentialist judgments and whether they are actually so. In line with previous studies, we identified deontological choices using the Trapdoor dilemma. Using economic games, we take two measures of general prosociality towards strangers: trustworthiness and altruism. Our results procure converging evidence for a perception gap according to which Trapdoor-deontologists are believed to be more trustworthy and more altruistic towards strangers than Trapdoor-consequentialists, but actually they are not so. These results show that deontological judgments are not universal, reliable signals of prosociality