Quelques modèles diffusifs capillaires de type KortewegSome diffusive capillary models of Korteweg type.

The purpose of this Note is to propose new diffusive capillary models of Korteweg type and discuss their mathematical properties. More precisely, we introduce viscous models which provide some additional information on the behavior of the density close to vacuum. We actually prove that if some compatibility conditions between diffusion and capillarity are satisfied, some extra regularity information on a quantity involving the density is available. We obtain a non-trivial equality deduced from the special structure of the momentum equation. This Note generalizes to some extent the authors' previous works on the Korteweg model (with constant capillary coefficient) and on the shallow water equation. To cite this article: D. Bresch, B. Desjardins, C. R. Mecanique 332 (2004).     

Dynamique multi-contact d'un système de solides tridimensionnels rigidesMulti-contact dynamics of a set of three-dimensional rigid bodies

This study is in keeping with the general pattern of dynamical simulations of a set of rigid three-dimensional bodies submitted to unilateral contact constraints with dry friction. An exact formulation (respecting the contact and friction laws) of the problem of predicting the system accelerations and the contact status, in further evolution is proposed. A numerical treatment of this kind of nonlinear problem is presented. This approach is applied to a simple multi-contact example, and yields results in agreement with those of analytical and numerical type, known for this example. To cite this article: C. Le Saux et al., C. R. Mecanique 331 (2003).     

The simulation of XYZ-spin chain in coupled cavities

We simulated anisotropic XYZ-spin chain with an array of coupled cavities, each of which contains one 4-level atom. The anisotropic parameters of the effective Hamilton can be tuned by controlling the external lasers. The validity of our approximations is confirmed via a numerical simulation.     

Modeling and characterization of fiber Bragg grating for maximum reflectivity

This paper presents the modeling and characterization of an optical fiber grating for maximum reflectivity. Grating length and change in refractive index are the critical parameters in contributing to the performance of fiber Bragg grating. The wavelength chosen for analysis is from the third window to minimize the attenuation. The reflection spectra, bandwidth and side lobes strength were analyzed with different lengths and change in refractive index. The simulations are based on solving coupled mode equations by transfer matrix method that describes the interaction of guided modes.     

Diffraction errors in micromirror-array based wavefront generation

Using Laser-based Speckle-Interferometers, the shape of optically rough surfaces can be measured precisely and contactlessly from variable measuring distances even in regions of difficult access. This work is concerned with the integration of a micromirror array (MMA) into an electronic Speckle-Pattern-Interferometer. With the adaptive optics, it is intended to adapt the phasefront of a reference wave to critical surface areas of the measurement object. Yet, due to the topography of the MMA, diffraction effects occur which affect the phase and intensity of the generated wavefront. We demonstrate how these diffraction effects can be efficiently modelled by a Fraunhofer diffraction method. We compare the results of this model to theoretical data obtained by a numerical Fresnel diffraction model and to measurement data obtained from a measurement setup incorporating a multi mirror array.     

Determination of depth-of-focus in lensless in-line digital particle holography

Lensless in-line digital particle holography (DPH) can be thought of as a special case of photography, and its depth of focus (DoF) characteristics combine those of both photography and holography. The effect of important parameters such as the pixel size and the number of pixels in a charge-coupled device (CCD), the object's distance, the wavelength of the laser, and the particle diameter on the DoF of a reconstruction image in lensless in-line DPH was investigated using simulation holograms. The DoF is directly proportional to the object distance and the particle size. As the wavelength of the laser increases, the DoF decreases. The DoF is inversely proportional to the pixel size and to the number of pixels in a CCD. Instead of expressing nonspecific proportional relationships for DoF, the DoF prediction equations for typical CCD cameras were obtained using DoF data from many simulation holograms and efficient data-fitting software. Finally, the DoF prediction equations were verified using real holograms from a calibration target for several cases. Good agreement between measured and predicted values was confirmed.     

Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

Spinach--a software library for simulation of spin dynamics in large spin systems

We introduce a software library incorporating our recent research into efficient simulation algorithms for large spin systems. Liouville space simulations (including symmetry, relaxation and chemical kinetics) of most liquid-state NMR experiments on 40+ spin systems can now be performed without effort on a desktop workstation. Much progress has also been made with improving the efficiency of ESR, solid state NMR and Spin Chemistry simulations. Spinach is available for download at http://spindynamics.org.     

Analysis of two stacked cylindrical dielectric resonators in a TE₁₀₂ microwave cavity for magnetic resonance spectroscopy

The frequency, field distributions and filling factors of a DR/TE??? probe, consisting of two cylindrical dielectric resonators (DR1 and DR2) in a rectangular TE??? cavity, are simulated and analyzed by finite element methods. The TE(+++) mode formed by the in-phase coupling of the TE??(δ)(DR1), TE??(δ)(DR2) and TE??? basic modes, is the most appropriate mode for X-band EPR experiments. The corresponding simulated B(+++) fields of the TE(+++) mode have significant amplitudes at DR1, DR2 and the cavity's iris resulting in efficient coupling between the DR/TE??? probe and the microwave bridge. At the experimental configuration, B(+++) in the vicinity of DR2 is much larger than that around DR1 indicating that DR1 mainly acts as a frequency tuner. In contrast to a simple microwave shield, the resonant cavity is an essential component of the probe that affects its frequency. The two dielectric resonators are always coupled and this is enhanced by the cavity. When DR1 and DR2 are close to the cavity walls, the TE(+++) frequency and B(+++) distribution are very similar to that of the empty TE??? cavity. When all the experimental details are taken into account, the agreement between the experimental and simulated TE(+++) frequencies is excellent. This confirms that the resonating mode of the spectrometer's DR/TE??? probe is the TE(+++) mode. Additional proof is obtained from B?(x), which is the calculated maximum x component of B(+++). It is predominantly due to DR2 and is approximately 4.4 G. The B?(x) maximum value of the DR/TE??? probe is found to be slightly larger than that for a single resonator in a cavity because DR1 further concentrates the cavity's magnetic field along its x axis. Even though DR1 slightly enhances the performance of the DR/TE??? probe its main benefit is to act as a frequency tuner. A waveguide iris can be used to over-couple the DR/TE??? probe and lower its Q to ≈150. Under these conditions, the probe has a short dead time and a large bandwidth. The DR/TE??? probe's calculated conversion factor is approximately three times that of a regular cavity making it a good candidate for pulsed EPR experiments.