WKB Wave Function of the General Time-Dependent Quadratic Hamiltonian System

We derived the WKB wave function for the general time-dependent quadratic Hamiltonian system using a unitary transformation method. We applied our research to sinusodially drived Caldirola–Kanai oscillator and confirmed that the time evolution of our approximated WKB wave function is similar to that of the exact one. This wave function can be used to analyze the interference between the probability amplitudes contributed by the area of overlap in phase space of quantum states.     

Ultraslow phonon-assisted collapse of tubular image states

We predict ultraslow collapse of “tubular image states” (TIS) on material surfaces. TIS are bound Rydberg-like electronic states formed at large distances (∼30 nm) from the surfaces of suspended circularly-symmetric nanowires, such as metallic C nanotubes. The states are formed in potential wells, resulting from a combination of the TIS-electron attraction to image charges in the nanotube and its centrifugal repulsion, caused by spinning around the tube. We demonstrate that TIS can collapse on the tube surface by passing their angular momentum l to circularly polarized flexural phonons excited in the tube. Our analysis shows that for highly detached TIS with l ? 6 the relaxation lifetimes are of the order of 10 ns-1 μs, while for l < 6 these lifetimes are reduced by several orders of magnitude.     

Numerical analysis of turbulent structure in compound meandering open channel by algebraic Reynolds stress model

The turbulent flow in a compound meandering channel with a rectangular cross section is one of the most complicated turbulent flows, because the flow behaviour is influenced by several kinds of forces, including centrifugal forces, pressure‐driven forces and shear stresses generated by momentum transfer between the main channel and the flood plain. Numerical analysis has been performed for the fully developed turbulent flow in a compound meandering open‐channel flow using an algebraic Reynolds stress model. The boundary‐fitted coordinate system is introduced as a method for coordinate transformation in order to set the boundary conditions along the complicated shape of the meandering open channel. The turbulence model consists of transport equations for turbulent energy and dissipation, in conjunction with an algebraic stress model based on the Reynolds stress transport equations. With reference to the pressure–strain term, we have made use of a modified pressure–strain term. The boundary condition of the fluctuating vertical velocity is set to zero not only for the free surface, but also for computational grid points next to the free surface, because experimental results have shown that the fluctuating vertical velocity approaches zero near the free surface. In order to examine the validity of the present numerical method and the turbulent model, the calculated results are compared with experimental data measured by laser Doppler anemometer. In addition, the compound meandering open channel is clarified somewhat based on the calculated results. As a result of the analysis, the present algebraic Reynolds stress model is shown to be able to reasonably predict the turbulent flow in a compound meandering open channel. Copyright © 2005 John Wiley & Sons, Ltd.     

对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．     

非等间距序列建模过程中存在的问题及改进

在研究非等间距序列的基础上 ,本文将非等间距累加运用于非等间距序列的建模过程中 ,使原有模型得到改进 .实例表明 ,改进后模型的精度有了很大提高     

级数小于1的亚纯函数的Borel例外值

证明了当超越亚纯函数的级小于1时，其Norel例外值最多只有一个．由于存在任何级的整函数，因此一个例外值总可达到，故所得结果不能再改进。     

半导体激光自混频干涉式传感器中的干涉与调制

应用F-P模型，阐述了半导体激光自混频干涉式传感器的干涉与调制过程，同时给出了相应的计算．     

Interpretation of the Quantum Measurement: Example of a Linearly Coupled Harmonic Oscillator

We argue that it may be possible to consistently explain the quantum measurement by assuming that the wave function is in one-to-one correspondence with objective physical reality and has no probabilistic interpretation. In the context of such approach we consider the model of a harmonic oscillator linearly coupled to a heat bath and treat the oscillator as the system being measured. Three classes of initial pure states for the bath are considered. Exact expressions for the average values and variances of the oscillator coordinate and momentum as functions of time are considered for each class of pure states. It is shown that these quantities exhibit different asymptotic behavior for different classes of initial states of the bath. In particular, if each mode of the bath is initially in a coherent state, then for an arbitrary initial state of the oscillator the variances of the oscillator coordinate and momentum asymptotically approach the same values as for a coherent state of the free oscillator, while the averages of coordinate and momentum show a Brownian-like behavior. We argue that such behavior shows several features of the quantum measurement and supports our interpretation of the wave function.     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

基于椭圆型方程的扭叶片造型方法的研究

本文以偏微分方程造型为基础,提出了一种基于椭圆型方程的扭叶片三维型面直接设计方法,详细推导了叶型曲面函数,给出了型面方程的求解及其前后缘修正。该方法具有设计叶型曲面自然光顺,设计参数少且各参数具有明显的几何意义,叶型曲面调整方便,利于采用非数值优化算法对其进行气动优化等优点。文中给出了设计实例,并通过数值实验分析了所设计叶片型面的流动特性。分析结果表明设计叶片具有良好的气动性能,同时也证明了本文提出的基于椭圆型方程的扭叶片三维型面设计方法的可靠性和实用性。