Gaussian Weighted Trajectory Method. IV. No Rainbow Effect in Practice

高斯加权轨迹法(GWMT)是无规随机相态近似下的经典S矩阵理论(CSMT)的实际应用. CSMT曾经是1970年代初期发展起来的第一个和最简单的半经典分子碰撞理论. 虽然GWMT非常接近于纯粹的经典描述,但GWMT在一定程度上包含了对被研究的碰撞过程中不同自由度的量子化. 尽管CSMT会得出发散的末态分布,这与弹性散射理论中的的彩虹效应有关,但GWTM却从来不会导致这种数学灾难. 本文为这一现象提供了解释.     

Relative cohomology of polynomial mappings

 Let F be a polynomial mapping from ℂ ⁿ to ℂ ^q with n>q. We study the De Rham cohomology of its fibres and its relative cohomology groups, by introducing a special fibre F ⁻¹(∞) ``at infinity' and its cohomology. Let us fix a weighted homogeneous degree on with strictly positive weights. The fibre at infinity is the zero set of the leading terms of the coordinate functions of F. We introduce the cohomology groups H ^k (F ⁻¹(∞)) of F at infinity. These groups enable us to compute all the other cohomology groups of F. For instance, if the fibre at infinity has an isolated singularity at the origin, we prove that every weighted homogeneous basis of H ^n−q (F ⁻¹ (∞)) is a basis of all the groups H ^n−q (F ⁻¹(y)) and also a basis of the (n−q) ^th relative cohomology group of F. Moreover the dimension of H ^n−q (F ⁻¹(∞)) is given by a global Milnor number of F, which only depends on the leading terms of the coordinate functions of F. Received: 12 February 2002 / Revised version: 25 May 2002 Published online: 3 March 2003     

Alternate dissociation of the screw dislocations in a (0 0 1) buried small-angle twist boundary in silicon

The square dislocation network of a (0 0 1) buried small-angle boundary in silicon was observed by dark-field transmission electron microscopy to examine the structures of more than 100 dissociated dislocation segments. Images were taken with g = (2 2 0), using a many-beam case along the reciprocal lattice row. Dissociation occurs on alternate close-packed planes without systematic rule, although a degree of ordering is taking place. Most of the dislocation segments have lengths equal to half of the square network period. Image simulation studies revealed that their experimental contrasts cannot be explained from the usual assumption of straight dislocations running in an infinite crystal. However, if these dislocations are supposed close and parallel to a nearby free surface, a reasonable agreement is found between the micrographs and the simulated images. A three-dimensional elastic model is proposed to explain the contrasts of the dislocation network.     

A new behaviour of the interstitial element H or D in solution in rare-earth metal

The study of the resistivity of the Lu-(H or D) system makes clear certain characteristics of the α phase and indicates a change for the interstitial element in the transition range 170–400°C. On both sides of this domain an appreciable difference is observed in the properties of the solid solution. The α1 phase of the domain below 170°C has a higher resistivity and a maximum hydrogen concentration independent of the temperature. For the phase α of the domain above 400°C, the expansions both with the concentration growth and with the rise in temperature are isotropic contrary to the α1 phase.The resistivity and X-ray diffraction studies, taking into account the lattice symmetry, allow us to conclude that a change may occur in the type of interstices filled by the hydrogen atoms, tetrahedral for the α phase and octahedral with H atoms associating in pairs for the α1 phase. Among the lanthanide metals, we find that only lutetium and thulium, in uniting with H or D, have the low temperature α1 phase.     

High accuracy ranging with Yb-doped fiber-ring frequency-shifted feedback laser with phase-modulated seed

This paper demonstrates that a frequency-shifted feedback laser, when seeded by a phase-modulated narrow-band radiation field, is a powerful tool for distance measurements to accuracy better than 10 μm and resolution better than 100 μm, for distances of a few meters. In such measurements the unknown distance forms one arm of a Michelson interferometer, in which the intensity of the output signal is modulated at the phase-modulation frequency of the seed. The amplitude of the output-signal modulation exhibits a resonance for every distinct signal delay, i.e. for each distinct distance within the laser spot on the target. The use of a phase-modulated input seed allows one to use a very narrow-bandwidth filter when measuring the return signal. The results reported in this paper are in excellent agreement with previous theoretical predictions [L. Yatsenko et al., Opt. Commun. 242 (2004) 581] for the resolution limit and high signal-to-noise ratio for this new technique.     

Experimental study of transient forced turbulent separation and reattachment on a bevelled trailing edge

The purpose of this experimental study is to analyze the transient processes of the separation and reattachment of a turbulent boundary layer at the trailing edge of a splitter plate. The separation is driven by a steady pneumatic injection, considered here as an actuator controlling the mixing layer. Particle image velocimetry and hot-film measurements are performed at various stages of the processes. The results highlight the behavior of each transient. Analysis of the time scale of the processes is realized by means of bi-orthogonal decomposition. This gives essential information (e.g., time scale, qualitative features) for future applications using duty cycle mode to excite instabilities of the mixing layer.     

Optical characterization of bubbly flows with a near-critical-angle scattering technique

The newly developed critical angle refractometry and sizing technique (CARS) allows simultaneous and instantaneous characterization of the local size distribution and the relative refractive index (i.e. composition) of a cloud of bubbles. The paper presents the recent improvement of this technique by comparison of different light scattering models and inversion procedures. Experimental results carried in various air/water and air/water-ethanol bubbly flows clearly demonstrate the efficiency and the potential of this technique.     

Combination of H nuclear magnetic resonance spectroscopy and mass spectrometry as tools for investigation of the thermolytic and solvolytic effects: Case of carbamates analysis

The carbamate pesticides are a well known thermo-sensible compound class. Under unfavourable conditions, these compounds are highly prone to degradation via fragmentation and/or rearrangement mechanisms. Their transformation processes are observed in consequence of two factors: structure with fragile bonds on the one hand and a stressing environment on the other hand leading to a difficult direct gas chromatography (GC) analysis, i.e. without derivatisation. In this paper, we investigated an original methodology based on the complementarity of analysis by proton nuclear magnetic resonance spectroscopy (¹H NMR) and those provided by GC hyphenated with ion-trap mass selective detection (GC–ITMS) to investigate combined effects of temperature and solvent nature affecting the behaviour of 16 carbamates. Among tested solvents, toluene and acetonitrile with 0.1% acetic acid were considered as the best solvents for storage and GC analysis respectively. Carbaryl, chlorpropham, carbofuran and N-sulfenylated compounds began to be thermodegraded with a loss equal to 1–5% even at 50 °C. An on-column injection validated as providing no degradation was used to analyse the identical solution that in ¹H NMR and it was emphasised that results of the measured degradation rates were identical at ±2%. It was highlighted that this methodology was extensible to study mechanisms and parameters with other (bio)molecules.     

Brillouin scattering study of the orientationally disordered phase of cyclohexanol

Brillouin scattering was used to measure the velocity and attenuation of longitudinal hypersonic waves in the orientationally disordered (OD) phase of a cyclohexanol single crystal and at the OD-liquid transition. Our results show that the coupling with a high-frequency relaxation mechanism, which dominates the behaviour of the hypersonic waves in the liquid, is still efficient in the OD phase.