Numerical description of the edge mode at the beveled extremity of a plate

This paper deals with the reflection of a two-dimensional harmonic Lamb wave at the beveled end of a plate. The existence of a resonant edge mode is described by a numerical model. It is proved that the edge mode is the resonance of different complex modes. The behavior of this mode as a function of the bevel angle is studied. Its amplitude decreases and its resonance frequency shifts as the bevel angle decreases from 90 to 85 deg. An unexpected strong variation of the repartition of the reflected energy is linked to this phenomenon.     

Ultrafast reorientation of dangling OH groups at the air-water interface using femtosecond vibrational spectroscopy

We report the real-time measurement of the ultrafast reorientational motion of water molecules at the water-air interface, using femtosecond time- and polarization-resolved vibrational sum-frequency spectroscopy. Vibrational excitation of dangling OH bonds along a specific polarization axis induces a transient anisotropy that decays due to the reorientation of vibrationally excited OH groups. The reorientation of interfacial water is shown to occur on subpicosecond time scales, several times faster than in the bulk, which can be attributed to the lower degree of hydrogen bond coordination at the interface. Molecular dynamics simulations of interfacial water dynamics are in quantitative agreement with experimental observations and show that, unlike in bulk, the interfacial reorientation occurs in a largely diffusive manner.     

The madelung constant for the tetragonal distortion of the cscl lattice

The Madelung constant is calculated for the tetragonal distortion of the CsCl lattice using Ewald's method over a large $\text{c}\text{a}$ range. The results deviate considerably from the analytical expressions for the Madelung constant in the literature. As a checkpoint for our calculation, the Madelung constant for the ideal cubic AuCuI structure $\text{(}\text{c}\text{a}\text{= √2)}$ is also computed by direct lattice summation using Evjen's method.     

One-Pot synthesis of unsymmetrically substituted 2,4-dialkylisoflavenes

The trimethylsilyl derivative of formonometine reacts sequentially with two different organometallic derivatives to afford regiospecifically and with good yield 2,4-dialkylisoflavenes unsymmetrically substituted.     

Software Tools for Geometrical Problem Solving: Potentials and Pitfalls

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In this paper, we explore the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, we show how dynamic software tools can not only scaffold the solution process but also help students move from argumentation to logical deduction. However, by reference to the work of less successful students, we illustrate how software tools that cannot be programmed to fit the goals of the students may prevent them from expressing their (correct) mathematical ideas and thus impede their problem solution.This revised version was published online in September 2005 with corrections to the Cover Date.     

1,6- and 1,7-naphthyridines. I. Rearrangement of quinolinimidoacetic acid derivatives

The reaction of N-substituted quinolinimides 1a-d with sodium alkoxides afforded a mixture of 1,6-naphthyridines 2 and 1,7-naphthyridines 3 which were isolated by chromatographic methods. Structure assignment for each pair of isomers was made by comparison of their ¹H nmr spectra with those of picolinamide and nicotinamide. When esters 1a -c were treated with alkoxides from primary alcohols, other than that of the ester, total transesterification took place. Experimental results suggest that transesterification occurs in open intermediary species.     

Effective Hamiltonians for Atoms in Very Strong Magnetic Fields

 We propose rigorous statements for several properties of atoms in intense homogeneous magnetic fields. Received October 30, 2001; accepted for publication November 9, 2001