Rapid convergence of a Galerkin projection of the KdV equation

In this Note, it is shown that a Fourier Galerkin approximation of the Korteweg–de Vries equation with periodic boundary conditions converges exponentially fast if the initial data can be continued analytically to a strip about the real axis. To cite this article: H. Kalisch, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Differential effects of synchronous and asynchronous multifinger coactivation on human tactile performance

Background  

Repeated execution of a tactile task enhances task performance. In the present study we sought to improve tactile performance with unattended activation-based learning processes (i.e., focused stimulation of dermal receptors evoking neural coactivation (CA)). Previous studies show that the application of CA to a single finger reduced the stationary two-point discrimination threshold and significantly increased tactile acuity. These changes were accompanied by an expansion of the cortical finger representation in primary somatosensory cortex (SI). Here we investigated the effect of different types of multifinger CA on the tactile performance of each finger of the right hand.     

Development of m-plane GaN anisotropic film properties during MOVPE growth on LiAlO2 substrates

The anisotropic film properties of m-plane GaN deposited by metal organic vapour phase epitaxy (MOVPE) on LiAlO₂ substrates are investigated. To study the development of layer properties during epitaxy, the total film thickness is varied between 0.2 and 1.7 μm. A surface roughening is observed caused by the increased size of hillock-like features. Additionally, small steps which are perfectly aligned in (1 1 −2 0) planes appear for samples with a thickness of ∼0.5 μm and above. Simultaneously, the X-ray rocking curve (XRC) full width at half maximum (FWHM) values become strongly dependent on incident X-ray beam direction beyond this critical thickness. Anisotropic in-plane compressive strain is initially present and gradually relaxes mainly in the [1 1 −2 0] direction when growing thicker films. Low-temperature photoluminescence (PL) spectra are dominated by the GaN near-band-edge peak and show only weak signal related to basal plane stacking faults (BSF). The measured background electron concentration is reduced from ∼10²⁰ to ∼10¹⁹ cm⁻³ for film thicknesses of 0.2 μm and ∼1 μm while the electron mobilities rise from ∼20 to ∼130 cm²/V s. The mobilities are significantly higher in [0 0 0 1] direction which we explain by the presence of extended planar defects in the prismatic plane. Such defects are assumed to be also the cause for the observed surface steps and anisotropic XRC broadening.     

Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy.The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.     

Wave breaking in Boussinesq models for undular bores

A nonlinear dispersive model equation is used to study the onset of breaking in long waves behind the front of an undular bore. According to experiments conducted by Favre (1935) [1], weak bores have a smooth, but oscillatory structure, with undulations appearing behind the bore front. With increasing bore strength, the amplitude of these oscillations grows until one or several of them start breaking. The change in type from the purely undular bore occurs at a sharply defined depth ratio which is under review in this article. A convective breaking criterion is put forward, and numerical computations are used to compare the predictions of this model to Favre?s wavetank experiments. It appears that the numerical results underpredict the appearance of breaking waves, but are in good qualitative agreement with the experiments. The results are interpreted with the aid of exact solitary-wave solutions, and it is found that the transition from purely undular to breaking bore may be recast with the help of a breaking criterion for solitary waves.