Physical properties of LiMn2O4 spinel prepared at moderate temperature

A moderate-temperature method of preparation of the spinel LiMn₂O₄ was developed around 500 °C. Physical features of the products were identified by X-ray photoelectron spectroscopy, X-ray diffractometry, Raman scattering and FTIR spectroscopy. The electronic conductivity of LiMn₂O₄ has been studied as a function of annealing temperature. The product LiMn₂O₄ is identified as a micron-sized powder and analysis of the local environment is in good accordance with the classical structural model of Fd3m space group. LiMn₂O₄ exhibits an electrical conductivity of 1.9×10⁻⁵ S/cm at room temperature with an activation energy of 0.16 eV which corresponds to an electron hopping mechanism between the two charge states of Mn³⁺ and Mn⁴⁺ ions. A first-order phase transition is observed at 292 K.     

Studies of the local structure in LixNi0.7Co0.3O2 (0.5≤x≤1.0) cathode materials

Among the Li_xNi_1−yCo_yO₂ system, LiNi_0.7Co_0.3O₂ is being considered one of the best cathode materials due to its small volume cell expansion upon charge-discharge cycling. In order to study the modifications of structural and physical properties occurring in the cathode materials during charge, different Li_xNi_0.7Co_0.3O₂ samples (0.5 ≥ x ≥ 1.0) were prepared by electrochemical lithium deintercalation in non-aqueous cells. During the first charge of the Li//Li_xNi_0.7Co_0.3O₂ cell, the structural change in the cathode lattice was followed by both x-ray powder diffraction and FTIR spectroscopy at room temperature. A good correlation is found between XRD data and the local environment of the host lattice. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998     

From Multifractal Measures to Multifractal Wavelet Series

Given a positive locally finite Borel measure μ on R, a natural way to construct multifractal wavelet series is to set , where . Indeed, under suitable conditions, it is shown that the function F_μ inherits the multifractal properties of μ. The transposition of multifractal properties works with many classes of statistically selfsimilar multifractal measures, enlarging the class of processes which have self-similarity properties and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal nature of F_μ are studied. As an application, multifractal Gaussian processes associated with F_μ are created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced by Arnéodo et al.     

Observation of a motional Stark effect to determine the second-order Doppler effect

The high resolution two-photon spectroscopy of hydrogen is often limited by the second-order Doppler effect. To determine this effect, we apply a magnetic field perpendicular to the atomic beam. This field induces a quadratic motional Stark shift proportional, as the second-order Doppler effect, to v(2) (v atomic velocity). For some magnetic field, these two effects are opposite and the total shift due to the atomic velocity is reduced. We present the first observation of this effect for the 1S-3S transition in hydrogen.     

Continuous Limits of Classical Repeated Interaction Systems

We consider the physical model of a classical mechanical system (called “small system”) undergoing repeated interactions with a chain of identical small pieces (called “environment”). This physical setup constitutes an advantageous way of implementing dissipation for classical systems; it is at the same time Hamiltonian and Markovian. This kind of model has already been studied in the context of quantum mechanical systems, where it was shown to give rise to quantum Langevin equations in the limit of continuous time interactions (Attal and Pautrat in Ann Henri Poincaré 7:59–104, 2006), but it has never been considered for classical mechanical systems yet. The aim of this article is to compute the continuous limit of repeated interactions for classical systems and to prove that they give rise to particular stochastic differential equations (SDEs) in the limit. In particular, we recover the usual Langevin equations associated with the action of heat baths. In order to obtain these results, we consider the discrete-time dynamical system induced by Hamilton’s equations and the repeated interactions. We embed it into a continuous-time dynamical system and compute the limit when the time step goes to 0. This way, we obtain a discrete-time approximation of SDE, considered as a deterministic dynamical system on the Wiener space, which is not exactly of the usual Euler scheme type. We prove the L ^p and almost sure convergence of this scheme. We end up with applications to concrete physical examples such as a charged particle in a uniform electric field or a harmonic interaction. We obtain the usual Langevin equation for the action of a heat bath when considering a damped harmonic oscillator as the small system.     

Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space

Many materials contain inhomogeneities or inclusions that may greatly affect their mechanical properties. Such inhomogeneities are for example encountered in the case of composite materials or materials containing precipitates. This paper presents an analysis of contact pressure and subsurface stress field for contact problems in the presence of anisotropic elastic inhomogeneities of ellipsoidal shape. Accounting for any orientation and material properties of the inhomogeneities are the major novelties of this work. The semi-analytical method proposed to solve the contact problem is based on Eshelby’s formalism and uses 2D and 3D Fast Fourier Transforms to speed up the computation. The time and memory necessary are greatly reduced in comparison with the classical finite element method. The model can be seen as an enrichment technique where the enrichment fields from the heterogeneous solution are superimposed to the homogeneous problem. The definition of complex geometries made by combination of inclusions can easily be achieved. A parametric analysis on the effect of elastic properties and geometrical features of the inhomogeneity (size, depth and orientation) is proposed. The model allows to obtain the contact pressure distribution – disturbed by the presence of inhomogeneities – as well as subsurface and matrix/inhomogeneity interface stresses. It is shown that the presence of an inclusion below the contact surface affects significantly the contact pressure and subsurfaces stress distributions when located at a depth lower than 0.7 times the contact radius. The anisotropy directions and material data are also key elements that strongly affect the elastic contact solution. In the case of normal contact between a spherical indenter and an elastic half space containing a single inhomogeneity whose center is located straight below the contact center, the normal stress at the inhomogeneity/matrix interface is mostly compressive. Finally when the axes of the ellipsoidal inclusion do not coincide with the contact problem axes, the pressure distribution is not symmetrical.     

Wall modeling for implicit large-eddy simulation and immersed-interface methods

We propose and analyze a wall model based on the turbulent boundary layer equations (TBLE) for implicit large-eddy simulation (LES) of high Reynolds number wall-bounded flows in conjunction with a conservative immersed-interface method for mapping complex boundaries onto Cartesian meshes. Both implicit subgrid-scale model and immersed-interface treatment of boundaries offer high computational efficiency for complex flow configurations. The wall model operates directly on the Cartesian computational mesh without the need for a dual boundary-conforming mesh. The combination of wall model and implicit LES is investigated in detail for turbulent channel flow at friction Reynolds numbers from Re _τ  = 395 up to Re _τ =100,000 on very coarse meshes. The TBLE wall model with implicit LES gives results of better quality than current explicit LES based on eddy viscosity subgrid-scale models with similar wall models. A straightforward formulation of the wall model performs well at moderately large Reynolds numbers. A logarithmic-layer mismatch, observed only at very large Reynolds numbers, is removed by introducing a new structure-based damping function. The performance of the overall approach is assessed for two generic configurations with flow separation: the backward-facing step at Re _h = 5,000 and the periodic hill at Re _H = 10,595 and Re _H = 37,000 on very coarse meshes. The results confirm the observations made for the channel flow with respect to the good prediction quality and indicate that the combination of implicit LES, immersed-interface method, and TBLE-based wall modeling is a viable approach for simulating complex aerodynamic flows at high Reynolds numbers. They also reflect the limitations of TBLE-based wall models.     

Designing liquid-crystalline dendronised hexa-adducts of [60]fullerene via click chemistry

ABSTRACT

Liquid-crystalline [60]fullerodendrimers were constructed via click chemistry based on the reaction between hexa-adducts of [60]fullerene (C₆₀) bearing 12 azide groups and alkyne-terminated cyanobiphenyl dendrons of first- and second-generation. The structure of all the new compounds was confirmed by IR, UV, ¹H and ¹³C NMR spectroscopies and mass spectrometry. The mesomorphic properties were studied by polarised optical microscopy, differential scanning calorimetry and small-angle X-ray scattering. The hexa-adduct of C₆₀ functionalised with the first-generation dendrons gave rise to the formation of a smectic A phase and a rectangular columnar phase (c2mm symmetry) while the hexa-adduct of C₆₀ decorated with the second-generation dendrons displayed only a rectangular columnar phase (c2mm symmetry). Our results show that the hexa-adduct of C₆₀ is a unique synthetic platform for the design of fullerodendrimers and dendronised materials.