Maximal displacement of a supercritical branching random walk in a time-inhomogeneous random environment

The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this paper is to analyze a time-inhomogeneous model with two levels of randomness. In the first step a sequence of branching laws is sampled independently according to a distribution on the set of point measures’ laws. Conditionally on the realization of this sequence (called environment) we define a branching random walk and find the asymptotic behavior of its maximal particle. It is of the form $V_n?\phi logn+o_{\mathbf{P}}(logn)$, where $V_n$ is a function of the environment that behaves as a random walk and $\phi >0$ is a deterministic constant, which turns out to be bigger than the usual logarithmic correction of the homogeneous branching random walk.     

Harnessing the Lewis Acidity of HFIP through its Cooperation with a Calcium(II) Salt: Application to the Aza‐Piancatelli Reaction

A method to extend the scope of the aza‐Piancatelli reaction between 2‐furylcarbinols and anilines is depicted. We found that 1,1,1,3,3,3‐hexafluoro‐2‐propanol (HFIP) is the solvent of choice for this transformation, as it outcompetes the usual solvents in terms of rate and yield. Side reactions and other issues raised by the title reaction are prevented, thereby providing an avenue to complex molecules that were previously inaccessible. Lewis acidity studies and computations were carried out to unveil the role of HFIP. Based on these results, we propose that HFIP is, in fact, acting as a Lewis acid and that its acidity can be enhanced when combined with a calcium(II) salt.     

Rapid analysis of organic acids in plant extracts by capillary electrophoresis with indirect UV detection: directed metabolic analyses during metal stress

A fast, reliable capillary zone electrophoresis (CZE) method with indirect UV detection was optimized and validated to determine the main organic acids contained in plants. Citric, malic, succinic, oxalic, formic, fumaric, acetic acids, and phosphate were quantified. A rapid separation while keeping a good resolution was obtained by optimizing capillary length, separation voltage, electrolyte composition, and pH. Analyses were performed in a 30 cm uncoated fused-silica capillary (length to the detector window) in the co-electroosmotic mode with reversed electroosmotic flow and anodic detection using a -30 kV separation voltage. The pH 9.0 electrolyte contained 3 x 10(-4)mol/L tetradecyltrimethylammonium and 10(-2)mol/L trimellitate. Separation with baseline return was achieved in 100 s. Linearity, detection limits, repeatability, reproducibility, and recoveries were evaluated. Mean precision values of 0.2 and 3.4% for migration times and time-corrected peak areas, respectively, enabled accurate identification and quantification whether in standard solutions or in samples. Such performances were perfectly adapted to high-throughput routine determinations of organic acids in research or industry. Organic acids were assayed in different plant tissues and cells, including sycamore, arabidopsis, buttercup, and pea. Citrate and malate were the most abundant in all plants tested with concentrations reaching 18.9 and 22.3 micromol/g fresh matter, respectively. Cadmium effect on pea leaves metabolism was also assessed.     

Two grid refinement methods in the lattice Boltzmann framework for reaction-diffusion processes in complex systems

This paper studies the optimisation of a numerical model and a computer code to solve numerically reaction-diffusion processes in environmental or biological systems with complicated geometries and mixtures of reactions including time and spatial scales extending over several order of magnitude. In particular, we consider different grid refinement techniques in the framework of a lattice Boltzmann solver for reaction-diffusion systems. Two new grid refinement methods are proposed, which are both quantitatively good. The first method is based on the matching of the concentration profiles and fluxes across two adjacent sub-domains, while the second method is based on nested subgrids. The focus of our study is the trade off between accuracy and CPU time. We show how the different parameters of the method, such as the refinement factors, the location of the boundary between different grids or coupling methods at the interface affect the quality of the numerical solution and the efficiency of the method.     

Numerical Study of a Forced Pendulum with Friction

We first describe the model of a forced pendulum with viscousdamping and Coulomb friction. Then we show that a unique local solutionof the mathematically well-posed problem exists. An adapted numericalscheme is built. Attention is devoted to the study of the nonlinearbehaviour of a pendulum via a numerical scheme with small constant timesteps. We describe the global behaviour of the free and forcedoscillations of the pendulum due to friction. We show that chaoticbehaviour occurs when friction is not too large. Lyapunov exponents arecomputed and a Melnikov relation is obtained as a limit of regularisedCoulomb friction. For larger friction, asymptotic behaviour correspondsto equilibrium.     

Fronts Between Periodic Patterns for Bistable Recursions on Lattices

Bistable space–time discrete systems commonly possess a large variety of stable stationary solutions with periodic profile. In this context, it is natural to ask about the fate of trajectories composed of interfaces between steady configurations with periodic pattern and in particular, to study their propagation as traveling fronts. Here, we investigate such fronts in piecewise affine bistable recursions on the one-dimensional lattice. By introducing a definition inspired by symbolic dynamics, we prove the existence of front solutions and uniqueness of their velocity, upon the existence of their ground patterns. Moreover, the velocity dependence on parameters and the co-existence of several fronts with distinct ground patterns are also described. Finally, robustness of the results to small $C^1$ -perturbations of the piecewise affine map is argued by mean continuation arguments.     

Shorter and modular synthesis of hemicryptophane-tren derivatives

Hemicryptophanes are host molecules with many applications as supramolecular catalysts or in ion selective recognition. A very convenient and efficient modular approach for the synthesis of hemicryptophane-tren (tren, tris(2-aminoethyl)-amine) derivatives has been developed. For instance, hemicryptophane 1 was synthesized at the gram scale in four steps from vanillyl alcohol compared to the previous seven-step procedure. The size, shape, and functionalities of the molecular cavity were also easily modified.