弱耦合映射系统在周期窗口内的行为

通过解析讨论及数值计算的验证,发现弱耦合映射系统的周期窗口只存在于耦合强度极小的范围内(对于3周期窗口大约为10^-3),这个范围可以定义为周期窗口的深度。在周期窗口内耦合映射的行为可以通过讨论少数几个模(相对简单的耦合三映射,实质是一维映射)而确定。耦合映射的第一Lyapunov指数随耦合强度增大的变化曲线呈锯齿形状。 关键词：     

THE INHOMOGENEOUS PERIODIC STATES IN A COUPLED MAP LATTICE

Numerical method is used to study the inhomogeneous periodic states in a coupled map lattice, and some scaling relations are obtained. The statistical language is proven to be suitable to describe the inhomogeneous periodic states because of its sensitive dependence on the initial conditions.     

弱耦合满迭代中的标度行为

本文研究由一维单峰满迭代以很弱的耦合组成的系统的Lyapunov指数,以有力的数值证据表明第一Lyapunov指数与耦合常数之间有普适的标度关系。 关键词：     

THE INHOMOGENEOUS PERIODIC STATES IN A COUPLED MAP LATTICE

Numerical method is used to study the inhomogeneous periodic states in a coupled map lattice, and some scaling relations are obtained. The statistical language is proven to be suitable to describe the inhomogeneous periodic states because of its sensitive dependence on the initial conditions.     

H2(X1∑g+)—H2(E1∑g+)系统的相互作用

采用显含电子对相关坐标的波函数,在微扰论的框架下计算了E^l∑_g⁺态氢分子与基态氢分子取cross构型时的中长程相互作用。结果表明,该相互作用在分子间距6.5α₀附近存在着一个活化能势垒,在4.5α₀附近显示出较强的化学键行为。 关键词：     

基态氢分子之间的相互作用波函数显含电子相关坐标的微扰计算

本文采用Weinbaum波函数与显含电子相关坐标的Jastrow相关因子的乘积作为氢分子的变分波函数,在微扰论的框架下计算了Cross构型的H_2-H_2系统在van der Waals极小值附近的势能曲线。     

H_2(X~1∑_g~ )—H_2(E~1∑_g~ )系统的相互作用

采用显含电子对相关坐标的波函数,在微扰论的框架下计算了E~l∑_g~ 态氢分子与基态氢分子取cross构型时的中长程相互作用。结果表明,该相互作用在分子间距6.5α_0附近存在着一个活化能势垒,在4.5α_0附近显示出较强的化学键行为。     

ONE-DIMENSIONAL SANDPILE MODEL WITH STOCHASTIC SLIDE

A new kind of theoretical one-dimensional sandpile model is proposed. In contrast to the models studied previously, the sliding process in this model is assumed to be of stochastic nature. Numerical simulations show that the behavior of this model is apparently closer to the reality of true sandpile than the models considered previously. The universality and sealing of this model is also discussed.