Asymptotic preserving HLL schemes

This work concerns the derivation of HLL schemes to approximate the solutions of systems of conservation laws supplemented by source terms. Such a system contains many models such as the Euler equations with high friction or the M1 model for radiative transfer. The main difficulty arising from these models comes from a particular asymptotic behavior. Indeed, in the limit of some suitable parameter, the system tends to a diffusion equation. This article is devoted to derive HLL methods able to approximate the associated transport regime but also to restore the suitable asymptotic diffusive regime. To access such an issue, a free parameter is introduced into the source term. This free parameter will be a useful correction to satisfy the expected diffusion equation at the discrete level. The derivation of the HLL scheme for hyperbolic systems with source terms comes from a modification of the HLL scheme for the associated homogeneous hyperbolic system. The resulting numerical procedure is robust as the source term discretization preserves the physical admissible states. The scheme is applied to several models of physical interest. The numerical asymptotic behavior is analyzed and an asymptotic preserving property is systematically exhibited. The scheme is illustrated with numerical experiments. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1396–1422, 2011     

Biotic and abiotic experimental identification of bacterial influence on calcium isotopic signatures

In this study, we tested experimentally the influence of plant and bacterial activities on the calcium (Ca) isotope distribution between soil solutions and plant organs. Abiotic apatite weathering experiments were performed under two different pH conditions using mineral and organic acids. Biotic experiments were performed using either apatite or Ca-enriched biotite substrates in the presence of Scots pines, inoculated or not with the rhizosphere bacterial strain Bulkholderia glathei PML1(12), or the B. glathei PML1(12) alone. For each experiment, the percolate was collected every week and analyzed for Ca concentrations and Ca isotopic ratios. No Ca isotopic fractionation was observed for the different abiotic experimental settings. This indicates that no Ca isotopic fractionation occurs during apatite dissolution, whatever the nature of the acid (mineral or organic). The main result of the biotic experiments is the 0.22 ‰ (44)Ca enrichment recorded for a solution in contact with Scots pines grown on the bacteria-free apatite substrate. In contrast, the presence of bacteria did not cause Ca isotopic fractionation of the solution collected after 14 weeks of the experiments. These preliminary results suggest that bacteria influence the Ca isotopic signatures by dissolving Ca from apatite more efficiently. Therefore, Ca isotopes might be suitable for detecting bacteria-mediated processes in soils.     

Nanoelectromechanical systems

Nanoelectromechanical systems (NEMS) are nano-to-micrometer scale mechanical resonators coupled to electronic devices of similar dimensions. NEMS show promise for fast, ultrasensitive force microscopy and for deepening our understanding of how classical dynamics arises by approximation to quantum dynamics. This article begins with a survey of NEMS and then describes certain aspects of their classical dynamics. In particular, we show that for weak coupling the action of the electronic device on the mechanical resonator can be effectively that of a thermal bath, this despite the device being a driven, far-from-equilibrium system.     

Asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation terms

We devise a new class of asymptotic‐preserving Godunov‐type numerical schemes for hyperbolic systems with stiff and nonstiff relaxation source terms governed by a relaxation time ε. As an alternative to classical operator‐splitting techniques, the objectives of these schemes are twofold: first, to give accurate numerical solutions for large, small, and in‐between values of ε and second, to make optional the choice of the numerical scheme in the asymptotic regime ε tends to zero. The latter property may be of particular interest to make easier and more efficient the coupling at a fixed spatial interface of two models involving very different values of ε. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Anatomy of a polarization switch of a vertical-cavity semiconductor laser

Using a streak camera we have measured the three Stokes polarization parameters during a polarization switch of a vertical-cavity semiconductor laser. The switch occurs along a corkscrew path on the Poincare sphere and takes on average a few nanoseconds; this value agrees with a theoretical treatment based upon the Fokker-Planck equation.     

Shock Profiles for the Shallow-Water Exner Models

This article is devoted to analyzing some ambiguities coming from a class of sediment transport models. The models under consideration are governed by the coupling between the shallow-water and the Exner equations. Since the PDE system turns out to be an hyperbolic system in non conservative form, ambiguities may occur as soon as the solution contains shock waves. To enforce a unique definition of the discontinuous solutions, we adopt the path-theory introduced by Dal Maso, LeFLoch and Murat [18]. According to the path choices, we exhibit several shock definitions and we prove that a shock with a constant propagation speed and a given left state may connect an arbitrary right state. As a consequence, additional assumptions (coming from physical considerations or other arguments) must be chosen to enforce a unique definition. Moreover, we show that numerical ambiguities may still exist even when a path is chosen to select the system's solution.