Dilational rheology of an air–water interface functionalized by biomolecules: the role of surface diffusion

As an attempt to develop a sensitive device for biomolecule detection, a micromechanical methodology based on the rheological change of an air–water interface is put forward (Berthier and Davoust, CEA/CNRS patent, PCT International Application WO 2003/080209 A3, 2003). Capillary waves induced from the vertical electrodynamic vibration of a brimful cylindrical tank filled with water stand as a good way to identify dilational elasticity and viscosity of an aging interface. Before, we were interested of the fact that complex wave number and the frequency of waves are obtained through an optical technique, which allows us to accurately recognize the whole interface geometry. These two parameters, a modeling based on a dispersion relation (Lucassen-Reynders and Lucassen, Adv Colloid Interface Sci, 2:347, 1969) and the surface mass transport equation, are jointly used to identify the surface diffusivity and the dilational rheology of the interface for a nonsoluble biochemical surfactant. Preliminary results obtained from a water surface functionalized by DNA, thanks to a lipidic monolayer, demonstrate the capabilities of the proposed methodology. The sensitivity of dilational rheology and the surface diffusivity on DNA adsorption on lipids is made evident.This paper was presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005.     

Kinematostatic modeling of compliant parallel mechanisms

The benefits of compliant mechanisms in terms of precision are not easy to exploit because of the limitations of the existing kinematic models used to analyze them. In practice, compliant mechanisms are more sensitive to external wrenches than conventional mechanisms. In this paper, based on the kinematic constraints and the static equilibrium between the joint coordinates and the external wrenches, a general kinematostatic model of compliant parallel mechanisms is presented. Then, this model is differentiated to provide a quasi-static model that makes it possible to calculate the variation of the pose as a linear function of the motion of the actuators and the variation of the external loads through two new matrices: the quasi-static Jacobian matrix and the Cartesian compliance matrix that give a simple and meaningful formulation of the model of the mechanism.     

New 3π‐2Spiro Ladder‐Type Phenylene Materials: Synthesis,Physicochemical Properties and Applications in OLEDs

New routes to ladder‐type phenylene materials 1 and 2 are described. The oligomers 1 and 2 , which possess a “3π‐2spiro” architecture, have been synthesized by using extended diketone derivatives 3 and 10 as key intermediates. The physicochemical properties of the new blue‐light emitter 2 were studied in detail and compared with those of the less‐extended 1 . Owing to the recent development of fluorenone derivatives and their corresponding more conjugated analogues as potential electron‐transport materials in organic light‐emitting diodes (OLEDs) and as n‐type materials for photovoltaic applications, we also report herein the thermal, optical and electrochemical behavior of the key intermediates, diketones 3 and 10 . Finally, the application of dispiro 2 as a new light‐emitting material in OLEDs is reported.     

Displacement convexity of entropy and related inequalities on graphs

We introduce the notion of an interpolating path on the set of probability measures on finite graphs. Using this notion, we first prove a displacement convexity property of entropy along such a path and derive Prékopa-Leindler type inequalities, a Talagrand transport-entropy inequality, certain HWI type as well as log-Sobolev type inequalities in discrete settings. To illustrate through examples, we apply our results to the complete graph and to the hypercube for which our results are optimal—by passing to the limit, we recover the classical log-Sobolev inequality for the standard Gaussian measure with the optimal constant.     

Conics in finite projective planes

There does not exist a general theory of conics in finite projective planes, because the many definitions of conics which are equivalent in desarguesian projective planes yield different types of conics in more general situations. Thus even the use of the word conic can lead to confusion, particularly in the finite case. This note is an attempt to clarify these various definitions and give as an example in a finite projective plane a von Staudt conic which is not an Ostrom conic. We conjecture that any finite projective plane admitting an Ostrom conic must be desarguesian.     

Homogenization of First Order Equations with (u/ε)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics

This paper is concerned with a result of homogenization of a non-local first order Hamilton–Jacobi equation describing the dislocations dynamics. Our model for the interaction between dislocations involves both an integro-differential operator and a (local) Hamiltonian depending periodicly on u/ε. The first two authors studied in a previous work homogenization problems involving such local Hamiltonians. Two main ideas of this previous work are used: on the one hand, we prove an ergodicity property of this equation by constructing approximate correctors which are necessarily non periodic in space in general; on the other hand, the proof of the convergence of the solution uses here a twisted perturbed test function for a higher dimensional problem. The limit equation is a nonlinear diffusion equation involving a first order Lévy operator; the nonlinearity keeps memory of the short range interaction, while the Lévy operator keeps memory of long ones. The homogenized equation is a kind of effective plastic law for densities of dislocations moving in a single slip plane.     

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so‐called word‐based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k ‐tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so‐called graph‐based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the graph‐based distribution, while they are exponentially generic in the word‐based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Ergodicity for a weakly damped stochastic non-linear Schrödinger equation

We study a damped stochastic non-linear Schr?dinger (NLS) equation driven by an additive noise. It is white in time and smooth in space. Using a coupling method, we establish convergence of the Markov transition semi-group toward a unique invariant probability measure. This kind of method was originally developed to prove exponential mixing for strongly dissipative equations such as the Navier-Stokes equations. We consider here a weakly dissipative equation, the damped nonlinear Schr?dinger equation in the one-dimensional cubic case. We prove that the mixing property holds and that the rate of convergence to equilibrium is at least polynomial of any power.     

A method for 13C‐labeling of metabolic carbohydrates within French bean leaves (Phaseolus vulgaris L.) for decomposition studies in soils

The molecular composition of plant residues is suspected to largely govern the fate of their constitutive carbon (C) in soils. Labile compounds, such as metabolic carbohydrates, are affected differently from recalcitrant and structural compounds by soil‐C stabilisation mechanisms. Producing ¹³C‐enriched plant residues with specifically labeled fractions would help us to investigate the fate in soils of the constitutive C of these compounds. The objective of the present research was to test ¹³C pulse chase labeling as a method for specifically enriching the metabolic carbohydrate components of plant residues, i.e. soluble sugars and starch. Bean plants were exposed to a ¹³CO₂‐enriched atmosphere for 0.5, 1, 2, 3 and 21 h. The major soluble sugars were then determined on water‐soluble extracts, and starch on HCl‐hydrolysable extracts. The results show a quick differential labeling between water‐soluble and water‐insoluble compounds. For both groups, ¹³C‐labeling increased linearly with time. The difference in δ¹³C signature between water‐soluble and insoluble fractions was 7‰ after 0.5 h and 70‰ after 21 h. However, this clear isotopic contrast masked a substantial labeling variability within each fraction. By contrast, metabolic carbohydrates on the one hand (i.e. soluble sugars + starch) and other fractions (essentially cell wall components) on the other hand displayed quite homogeneous signatures within fractions, and a significant difference in labeling between fractions: δ¹³C = 414 ± 3.7‰ and 56 ± 5.5‰, respectively. Thus, the technique generates labeled plant residues displaying contrasting ¹³C‐isotopic signatures between metabolic carbohydrates and other compounds, with homogenous signatures within each group. Metabolic carbohydrates being labile compounds, our findings suggest that the technique is particularly appropriate for investigating the effect of compound lability on the long‐term storage of their constitutive C in soils. Copyright © 2009 John Wiley & Sons, Ltd.     

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