Linear stability of WENO schemes coupled with explicit Runge–Kutta schemes

This paper focuses on the results of the linear stability analysis of the finite‐difference weighted essentially non‐oscillatory (WENO) schemes with optimal weights. The standard WENO schemes between the third and 11th order, the order‐optimised WENO schemes of the sixth and eighth order and the bandwidth‐optimised WENO schemes of the third and fourth order are considered. Several explicit Runge–Kutta schemes including the recently published strong stability‐preserving explicit Runge–Kutta schemes are considered for time discretisation. The stability limits as well as dissipation and dispersion properties dependent on the Courant–Friedrichs–Lewy number are presented for a hyperbolic model equation. The different combinations of space and time discretisation schemes are compared in terms of their accuracy and efficiency. For a parabolic model equation, the viscous term is discretised with high‐order central differences. The stability limits for the parabolic problem are presented as well. Numerical results of linear test cases are shown. Copyright © 2011 John Wiley & Sons, Ltd.     

Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data and applications to nonlinear elasticity

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$. More precisely, for any $1<q<(p+1)/2$ we construct $W^{1,q}$-bi-Sobolev maps with identity boundary conditions; for $f\in L^{\infty }$, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.     

Back to the future: A retrospective assessment of model‐based scenarios for the management of the shrimp fishery in French Guiana facing global change

While the number of models dedicated to predicting the consequences of alternative resource management strategies has increased, instances in which authors look back at past predictions to learn from discrepancies between these and observed developments are scarce. In the past decades, the French Guiana shrimp fishery has experienced shrimp market globalization and decreasing levels of shrimp recruitment due to environmental changes. In 2006, a bio‐economic model of this fishery was developed to simulate its possible responses to economic and environmental scenarios up to 2016. Here, we compare here these predictions to the observed trajectories. While the number of active vessels corresponds to that which was predicted, the estimated shrimp stock does not. Important driving factors had not been anticipated, including a general strike, natural disasters, and the end of the global financial crisis. These results show the importance of participative approaches involving stakeholders in the co‐construction and shared representation of scenarios. Recommendations for resource managers

• Effective fisheries resources management and a fortiori, the capacity of the fisheries to adapt to global change, requires understanding of both ecological and economics dynamics.
• The temporal trajectory of the trawling shrimp fisheries has been well monitored, and the decline of both stock and fleet is understood regarding ecological and economic changes: Changes in the environmental conditions of shrimp recruitment, and oil price increase and selling price decrease.
• However, our bio‐economic modeling work showed that, even with a good understanding of the dynamics explaining past trajectories, unpredictable events (strike, natural disasters…) have acted as other key driving factors altering the capacity of the model to represent possible futures.
• These results led us to recommend a better integration of the expertise of social and political scientists in developing models of bio‐economic systems to increase the quality of scenario predictions, and to argue for more participative approaches involving the stakeholders.

     

Naphthalene Exchange in [Re(η6-napht)2]+ with Pharmaceuticals Leads to Highly Functionalized Sandwich Complexes [M(η6-pharm)2]+ (M=Re/99mTc)

Bis-arene sandwich complexes are generally prepared by the Fischer-Hafner reaction, which conditions are incompatible with most O- and N- functional groups. We report a new way for the synthesis of sandwich type complexes [Re(η⁶-arene)₂]⁺ and [Re(η⁶-arene)(η⁶-benzene)]⁺ from [Re(η⁶-napht)₂]⁺ and [Re(η⁶-napht)(η⁶-benzene)]⁺, with functionalized arenes and pharmaceuticals. N-methylpyrrolidine (NMP) facilitates the substitution of naphthalene with the incoming arene. A series of fully characterized rhenium sandwich complexes with simple arenes, such as aniline, as well as with active compounds like lidocaine and melatonin are presented. With these rhenium compounds in hand, the radioactive sandwich complexes [^99mTc(η⁶-pharm)₂]⁺ (pharm=pharmaceutical) can be unambiguously confirmed. The direct labelling of pharmaceuticals with ^99mTc through η⁶-coordination to phenyl rings and the confirmation of the structures with the rhenium homologues opens a path into molecular theranostics.     

In Vitro Antiplasmodial and Cytotoxic Activities of Compounds from the Roots of Eriosema montanum Baker f. (Fabaceae)

Malaria remains one of the leading causes of death in sub-Saharan Africa, ranked in the top three infectious diseases in the world. Plants of the Eriosema genus have been reported to be used for the treatment of this disease, but scientific evidence is still missing for some of them. In the present study, the in vitro antiplasmodial activity of the crude extract and compounds from Eriosema montanum Baker f. roots were tested against the 3D7 strain of Plasmodium falciparum and revealed using the SYBR Green, a DNA intercalating compound. The cytotoxicity effect of the compounds on a human cancer cell line (THP-1) was assessed to determine their selectivity index. It was found that the crude extract of the plant displayed a significant antiplasmodial activity with an IC₅₀ (µg/mL) = 17.68 ± 4.030 and a cytotoxic activity with a CC₅₀ (µg/mL) = 101.5 ± 12.6, corresponding to a selective antiplasmodial activity of 5.7. Bioactivity-guided isolation of the major compounds of the roots’ crude extract afforded seven compounds, including genistein, genistin and eucomic acid. Under our experimental conditions, using Artemisinin as a positive control, eucomic acid showed the best inhibitory activity against the P. falciparum 3D7, a well-known chloroquine-sensitive strain. The present results provide a referential basis to support the traditional use of Eriosema species in the treatment of malaria.     

Q-switched Yb-doped nonlinear microstructured fiber laser for the emission of broadband spectrum

We report on an innovative configuration of a supercontinuum laser based on an Yb-doped nonlinear microstructured fiber. Due to this particular fiber design combining amplification and nonlinear properties, a wideband output spectrum is generated in the fiber under the Q-switched regime. By exploiting stimulated Brillouin scattering, high peak power pulses are achieved and contribute to a spectral broadening due to a nonlinear wavelength conversion process. Both infrared (1000-1200 nm) and visible (650-750 nm) spectra are generated with an average power of 200 mW.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

Numerical study of two-airfoil arrangements by a discrete vortex method

Theoretical and Computational Fluid Dynamics - The aerodynamic characteristics of two neighboring airfoils are greatly different from those of a single airfoil, for both attached and detached flow...