Convergence order of implicit Euler numerical scheme for maximal monotone differential inclusions

In the present work, we deal with the convergence of a class of numerical schemes for maximal monotone evolution systems in the particular case where the maximal monotone term is a subdifferential of a convex proper and lower semi-continuous function and the right-hand side depends on time and on solution. More precisely, we focus on an implicit Euler scheme and we show that the order of this scheme is one. Finally, some applications are given for a large class of rheological models.     

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.     

Sensitivity of a Lamb wave sensor with 2 microm AlN membrane

Anti-symmetrical Lamb wave mode A0 presents a large sensitivity to mass loading and can be used in contact with liquids with a small attenuation. The advantages of this system are the possibility to get a large mass sensitivity. The sensitivity increases when the thickness of membrane decreases. Therefore the problem is to obtain thin piezoelectric membranes. A membrane of AlN with a thickness of 2 microm has been made. The measured mass sensitivity with a fluid is 200 cm(2) g(-1). In a practical use point of view, the problem in this kind of sensor is its temperature sensitivity. In order to reduce effective temperature sensitivity, a device with thin metallic strips is presented. On the same membrane two different waves with perpendicular propagating directions are produced. Experimentally, temperature sensitivity is rather different depending on the propagation direction but mass sensitivity is almost the same, this allows distinguishing temperature effects from those due to mass loading on the frequency shift measurements.     

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.     

Order-based error for managing ensembles of surrogates in mesh adaptive direct search

We investigate surrogate-assisted strategies for global derivative-free optimization using the mesh adaptive direct search (MADS) blackbox optimization algorithm. In particular, we build an ensemble of surrogate models to be used within the search step of MADS to perform global exploration, and examine different methods for selecting the best model for a given problem at hand. To do so, we introduce an order-based error tailored to surrogate-based search. We report computational experiments for ten analytical benchmark problems and three engineering design applications. Results demonstrate that different metrics may result in different model choices and that the use of order-based metrics improves performance.     

Branching random walk with trapping zones

We consider a branching random walk with values in a certain set $\mathbb{S}$, where the branching mechanism is different according to whether particles (individuals) are in a certain so called trapping set $A?\mathbb{S}$ or not. We are then interested, under different scenarios, in properties of either the transient random measure describing distribution of individuals on $\mathbb{S}$ over time or its asymptotic behaviour.     

Probing supported model and native membranes using AFM

Atomic Force Microscopy (AFM) has gained lots of interest since its ability to get high resolution imaging in liquid environment. In the last years, this technique was particularly successful in probing the surface of membrane model systems of biological interest and spectacular results have been obtained with native specialized membranes. In this review, we aim at highlighting the recent developments that illustrate the unique powerfulness of AFM in determining the nanoscale organization of membranes and their local physical properties. An important part will focus on AFM high resolution imaging of transmembrane proteins in model and native membranes and on the study of few applications such as biosensors. An overview of main recent developments of AFM as well as new possibilities gained by combination with other techniques will also be addressed.     

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.