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.     

Access to New Endoperoxide Derivatives by Electrochemical Oxidation of Substituted 3‐Azabicyclo[4.1.0]hept‐4‐enes

A series of substituted 3‐azabicyclo[4.1.0]hept‐4‐ene derivatives were prepared and analysed by cyclic voltammetry. Preparative aerobic electrochemical oxidation reactions were then carried out. Three original endoperoxides were isolated, characterised and subjected to antimalarial and cytotoxicity activity assays.     

Experimental and numerical study of shock wave propagation in water generated by pulsed arc electrohydraulic discharges

The objective of this study is to simulate the propagation of the shock wave in water due to an explosion. The study is part of a global research program on the development of an alternative stimulation technique to conventional hydraulic fracturing in tight gas reservoirs aimed at inducing a distributed state of microcracking of rocks instead of localized fracture. We consider the possibility of increasing the permeability of rocks with dynamic blasts. The blast is a shock wave generated in water by pulsed arc electrohydraulic discharges. The amplitude of these shock waves is prescribed by the electrohydraulic discharges which generate high pressures of several kilobars within microseconds. A simplified method has been used to simulate the injected electrical energy as augmentation of enthalpy in water locally. The finite element code EUROPLEXUS is used to perform fluid fast dynamic computation. The predicted pressure is consistent with the experimental results. In addition, shock wave propagation characteristics predicted with simulation can be valuable reference for design of underwater structural elements and engineering of underwater explosion.     

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.

     

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.     

CO Adsorption on N2‐Precovered NaY Faujasite: A FTIR Analysis of the Resulting Adsorbed Species

To productively complete the information regarding the reversible adsorption of a gas mixture on the micropores of cationic zeolites, the adsorption of the two gases N₂ and CO on NaY faujasite is taken as a model case study. We analyze herein CO adsorption (77 K) on two distinct N₂‐precovered NaY sets (low and medium). We outline the continuous desorption of N₂ adducts during CO admittance to full N₂ desorption for the highest CO loadings. These features contrast with preceding results obtained for N₂ loading on CO‐precovered NaY. By comparing these results with the sole CO admission and combining both studies regarding the co‐adsorption sets, we demonstrate the influence of the basic strength of the two gases regarding the nature of the surface‐adsorbed species formed. We also propose and discuss a hypothesis regarding the formation of adsorbed mixed species having both N₂ and CO as ligands. These new findings strengthen the statistical response of IR signatures as a helpful proposal for analyzing adsorbed species and their assignments. This survey completes the molecular understanding of gas‐mixture adsorption that lacks experimental data to date.     

The Synthesis of a γ-Keto-α-amino Acid,a Key Intermediate in the Synthesis of Monatin,a New Natural Sweetener

An efficient method was developed for the synthesis of the ketoamino acid 2, a key intermediate in the synthesis of the novel sweet compound, monatin 1. Preparation of 2 entails coupling of a suitably protected indole acetate anion to an aspartic acid derivative.