Non-linear normal modes,invariance, and modal dynamics approximations of non-linear systems

Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation.     

CoI-Catalyzed Barbier Reactions of Aromatic Halides with Aromatic Aldehydes and Imines

The reductive Barbier coupling of aromatic halides and electrophiles has been achieved using a CoBr₂/1,10-phenanthroline catalytic system and over stoichiometric amounts of zinc. The reaction displayed a broad scope of substrates, including (hetero)aryl chlorides as pro-nucleophiles and aldehydes or imines as electrophiles, leading to diarylmethanols and diarylmethylamines in moderate to excellent yields, respectively.     

Adaptive estimation of the stationary density of a stochastic differential equation driven by a fractional Brownian motion

Statistical Inference for Stochastic Processes - We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove...     

Operando Isotopic Exchange in Solid Oxide Fuel Cells: Oxygen-Transport Dependency on Applied Potential

The oxygen isotopic exchange technique is a powerful tool to investigate the oxygen transport kinetics in an oxide solid. In a solid oxide fuel cell, isotopic surface exchange and diffusion coefficients are classically determined by using the Isotopic Exchange Depth Profiling method followed by ex situ SIMS characterizations. Despite its relevance, the utilization of in situ or operando techniques to measure the isotopic exchange under an electrical bias remains marginal. We developed here a set-up which enables operando monitoring of oxygen exchange in SOFC type cells under polarization. The system has been used for studying the oxygen mobility dependency upon polarization on a symmetrical Pt/YSZ/Pt cell (YSZ: yttria-stabilized zirconia). Homomolecular and heterolytic exchange reactions were undertaken to investigate the oxygen activation step and discriminate the limiting step among the sequence of elementary steps which constitute the oxygen transport process in the SOFC system. Oxygen ions incorporation into the dense ionic conductor was identified to be the rate determining step, and its first order rate constant dependency on applied potential was established.     

基于耦合道Gamow壳模型计算17O和17F的能谱以及16O(p,p)反应的微分散射截面

利用耦合道Gamow壳模型计算了17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射截面。结果表明，17O和17F中非束缚共振态能级的核子发射宽度的计算需要合理地考虑连续态耦合效应。计算得到的17O和17F的低激发能谱以及16O(p,p)反应的低能弹性散射激发函数都与实验数据吻合较好。这说明基于现实核力的计算可更好地描述16O(p,p)反应的低能弹性散射截面。     

Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.