Analytical comparison between the surface current integral equation and the second-order small-slope approximation

This paper is the third in a series discussing a new approximate bistatic model for electromagnetic scattering from perfectly conducting rough surfaces. Our previous approach supplemented the Kirchhoff model through the addition of new terms involving linear orders in slope and surface elevation differences that arise naturally from a second iteration of the surface current integral equation. This completion of the Kirchhoff was shown to provide the correct first-order small perturbation method (SPM-1) in the general bistatic context. The agreement with SPM-1 was achieved because differences of surface heights are no longer expanded in powers of surface slope. While consistent with SPM, our previous formulation fails to reconverge toward the Kirchhoff model, at some incidence and scattered angles, when the illuminated surface satisfies the high frequency roughness condition. This weakness is also shared with the first-order small slope approximation (SSA-1) which is structurally equivalent to our previous formulation where the polarization is independent of surface roughness. The second-order small slope approximation (SSA-2), which satisfies the SPM-1 and second-order small perturbation method (SPM-2) limits by construction, was shown by Voronovich to converge toward the tangent plane approximation of the Kirchhoff model under high frequency conditions. In the present paper, we show that, in addition to the linear orders in our previous model, one must now include cross-terms between slope and surface elevation to ensure convergence toward both high frequency and small perturbation limits. With the inclusion of these terms, our new formulation becomes comparable to the SSA-2 (second-order kernel) without the need to evaluate all the quadratic order slope and elevations terms. SSA-2 is more complete, however, in the sense that it guarantees convergence toward the second-order Bragg limit (SPM-2) in the fully dielectric case in addition to both SPM-1 and Kirchhoff. Our new generalization is shown to explain correctly extra depolarization in specular conditions to be caused by surface curvature and surface autocorrelation for incoherent and coherent scattering, respectively. This result will have large repercussions on the interpretation of bistatically reflected signals such as those from GPS.     

A close analysis of metal-enhanced fluorescence of tryptophan induced by silver nanoparticles: wavelength emission dependence

In the last few years, silver nanoparticles have been proposed as a promising alternative for the label-free detection of proteins via metal-enhanced fluorescence. Generally, the aromatic amino acid tryptophan is most frequently used in this type of studies, because the intrinsic fluorescence of proteins is usually dominated by tryptophan emissions. In the present study, we evaluated the fluorescence behavior of tryptophan in the presence of a silver colloid with nanoparticles of 100 nm in diameter. The results showed that a nanoparticles concentration of 32 mg L^?1 induced maximum fluorescence enhancement. However, the metal-enhanced fluorescence was dependent on the emission wavelength of tryptophan, and this phenomenon was closely related to the metal surface reabsorption process (inner filter effect), suggesting that the plasmon resonance reabsorption effect should be taken into account in analyses involving protein studies by metal-enhanced fluorescence.     

Analysis of random nonlinear water waves: the Stokes–Woodward techniqueLa technique de Stokes–Woodward pour l'analyse de vagues aléatoires non linéaires

A generalization of the Woodward's theorem is applied to the case of random signals jointly modulated in amplitude and frequency. This yields the signal spectrum and a rather robust estimate of the bispectrum. Furthermore, higher order statistics that quantify the amount of energy in the signal due to nonlinearities, e.g., wave–wave interaction in the case of water waves, can be inferred. Considering laboratory wind generated water waves, comparisons between the presented generalization and more standard techniques allow to extract the spectral energy due to nonlinear wave–wave interactions. It is shown that our analysis extends the domain of standard spectral estimation techniques from narrow-band to broad-band processes. To cite this article: T. Elfouhaily et al., C. R. Mecanique 331 (2003).     

Laplace-Transform Based Inversion Method for Fractional Dispersion

Partial differential equations with memory are challenging models for mass transport in porous media where fluid and tracer may be stored by the solid matrix, and then released. Moreover, integral transforms (generalizing time moments) of solutions to such models are linked to the corresponding transport parameters. Inverting that link provides a method to determine model parameters on the basis of solutions. It is checked using numerically generated profiles before passing to experimental data.