Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.     

A model for the stabilization of atomic hydrogen centers in borate glasses

A previously proposed model describing the trapping site of the interstitial atomic hydrogen in borate glasses is analyzed. In this model the atomic hydrogen is stabilized at the centers of oxygen polygons belonging to B–O ring structures in the glass network by van der Waals forces. The previously reported atomic hydrogen isothermal decay experimental data are discussed in the light of this microscopic model. A coupled differential equation system of the observed decay kinetics was solved numerically using the Runge Kutta method. The experimental untrapping activation energy of 0.7×10⁻¹⁹ J is in good agreement with the calculated results of dispersion interaction between the stabilized atomic hydrogen and the neighboring oxygen atoms at the vertices of hexagonal ring structures.     

Time-dependent analysis of tunneling effect in the formation of ultracold molecules via photoassociation of laser-cooled atoms

The paper contains a time-dependent investigation of the tunneling effect observed in the photoassociation spectrum of Cs₂ and attributed to the 0_g ^-(6s, 6p _3/2) double well. When by photoassociation of two cold cesium atoms a vibrational level of the outer well is populated, tunneling is an efficient mechanism for transferring the population to the inner well (R < 15a ₀), where spontaneous emission may lead to formation of cold molecules in low vibrational levels of the a ³Σ⁺ _u(6s, 6s) electronic state. This tunneling effect is analyzed by wavepackets propagation, first considering the double well potential alone, and following a packet made by a superposition of states initially located at large distances. Characteristic times for the vibration dynamics, corresponding to a beating phenomenon between the two wells, to partial “revival” at large distances, and to maxima in the population localized in the inner well are reported and discussed. Second, we simulate the two-channels a ³Σ⁺ _u(6s, 6s)↦0_g ^-(6s, 6p _3/2) photoassociation at detunings around 2.9 cm^-1: the inner well can be populated either by the excitation of a vibrational level of the external well (resonant excitation), or by tuning the photoassociation laser at the energy of the inner well level which displays tunneling (“off-resonance excitation”). In the first case the photoassociation is efficient, while the tunneling probability is small; in the second, the tunneling probability is large, so that despite the poor efficiency of the photoassociation process, more population can be transferred to the inner well. This second choice is shown to be very sensitive to the laser intensity, which could be used to control the population of the inner well and hence the formation of ultracold molecules in low vibrational levels. Received 19 April 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: francoise.masnou@lac.u-psud.fr     

关于范德瓦尔斯方程对应的分子力作用模型的修正问题

证明了某文献提出的状态方程从形式到内容完全等同于范德瓦尔斯方程，其常量ａ和ｃ不能用临界参量表示，而ａ－ｃ则完全等同于范德瓦尔斯方程的常量ａ．