Numerical Approaches to Compute Spectra of Non-Self Adjoint Operators and Quadratic Pencils

In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators. This leads to solve nonlinear eigenvalue problems. We begin with a review of theoretical results for the spectra of quadratic operators, especially for the Schrödinger pencils. Then we present the numerical methods developed to compute the spectra: spectral methods and finite difference discretization, in infinite or in bounded domains. The numerical results obtained are analyzed and compared with the theoretical results. The main difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are very unstable.     

Local strong solution for the incompressible Korteweg model

We consider a Navier–Stokes type system with a Korteweg stress tensor, coupled with a concentration equation without diffusion. We give a result concerning the local in time existence (and uniqueness) of strong solution for any data (and the global in time existence defined in a interval $(0,T)$ for $T<+\infty$ fixed if data are small enough), in the case of a bounded domain $\Omega ?{\mathbb{R}}^3$. To cite this article: M. Sy et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Homogenization near resonances and artificial magnetism from dielectrics

The homogenization of periodic dielectric structures in harmonic regime usually leads to an effective permittivity tensor ${?}^{\mathrm{eff}}$. It has been observed by Bouchitté and Felbacq [Waves Random Media 7 (1997) 245–256], that in the high contrast case (high conductivity fibers), this tensor depends on the angular frequency ω. In this Note, we enlight a new effect induced by microscopic resonances which leads in parallel to a possibly negative effective permeability ${\mu }^{\mathrm{eff}}(\omega )$ (although the original medium is assumed to be nonmagnetic i.e. $\mu =1$). To cite this article: G. Bouchitté, D. Felbacq, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

The fractal dynamics of self-esteem and physical self

The aim of this paper was to determine whether fractal processes underlie the dynamics of self-esteem and physical self. Twice a day for 512 consecutive days, four adults completed a brief inventory measuring six subjective dimensions: global self-esteem, physical self-worth, physical condition, sport competence, attractive body, and physical strength. The obtained series were submitted to spectral analysis, which allowed their classification as fractional Brownian motions. Three fractal analysis methods (Rescaled Range analysis, Dispersional analysis, and Scaled Windowed Variance analysis) were then applied on the series. These analyses yielded convergent results and evidenced long-range correlation in the series. The self-esteem and physical self series appeared as anti-persistent fractional Brownian motions, with a mean Hurst exponent of 0.21. These results reinforce the conception of self-perception as the emergent product of a dynamical system composed of multiple interacting elements.     

Noisy inflows cause a shedding-mode switching in flow past an oscillating cylinder

Vortex streets formed behind oscillating bluff bodies consist of arrays of groups of two, three, or four vortices classified as 2S, P+S, and 2P shedding modes, respectively. The prevailing dominant mode depends primarily on the amplitude and the frequency of the oscillation and on the Reynolds number. We investigate the effect of noise at the inflow on the stability of these vortex modes in laminar flow past a circular cylinder. We employ stochastic simulations based on a new polynomial chaos method to study the shedding-mode switching from a P+S pattern to a 2S mode in the presence of noise.     

BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals

It is common knowledge that in an infinite periodic medium, for instance, an infinite photonic crystal, the direction of propagation of a monochromatic wave packet is given by the normal to the isofrequency diagram. We show that this is no longer true in a finite size medium, due to the existence of evanescent waves near the interfaces of the photonic crystal. We derive a renormalized isofrequency diagram giving the correct direction. We give a physical interpretation, showing that this phenomenon can be considered as a generalized Goos-H?nchen effect.     

Supported choline hydroxide (ionic liquid) as heterogeneous catalyst for aldol condensation reactions

Choline hydroxide was used as a basic catalyst for aldol condensation reactions to produce new C-C bonds between several ketones and aldehydes. Choline supported on MgO exhibits higher TOF values than other well known basic catalysts in these reactions.     

广义基的多重散射理论

提出了任意函数基表象中的多重散射理论. 基于这个框架, 一组新基的多重散射计算表明其收敛性比传统的球谐函数基的要好, 从而可以实现更快和更节省物理内存的计算. 另外, 将多重散射矩阵分为传播矩阵和散射矩阵, 很好地描述了散射性质和减小了多重散射计算中块矩阵的尺寸.