半直线上随机环境中的随机游动的常返性

本文讨论半直线上随机环境中的随机游动的常返性。在独立环境下，主要通过强大数定律，找到了非常返和正常返的一个充分条件下，并将这一结果推广到一些特殊情情形。在一般的随机环境下，主要通过数列的有界性，给出了常返与零常返的一个充分条件。     

Massively time-parallel,approximate simulation of loss queueing systems

A time-parallel simulation obtains parallelism by partitioning the time domain of the simulation. An approximate time-parallel simulation algorithm named GG1K is developed for acyclic networks of loss FCFSG/G/1/K queues. The GG1K algorithm requires two phases. In the first phase, a similar system (i.e. aG/G/1/ queue) is simulated using the GLM algorithm. Then the resultant trajectory is transformed into an approximateG/G/1/K trajectory in the second phase. The closeness of the approximation is investigated theoretically and experimentally. Our results show that the approximation is highly accurate except whenK is very small (e.g. 5) in certain models. The algorithm exploits unbounded parallelism and can achieve near-linear speedup when the number of arrivals simulated is sufficiently large.     

Variations on a theme by Mark Kac

Mark Kac's theorem on the mean recurrence time in a stationary stochastic process in discrete time with discrete states is taken as the starting point for a series of variations, most of which are formulated in terms of 0–1 processes. Whereas the original theorem deals with the mean recurrence time of a given state under the condition that the state is realized at time 0, this condition is dropped in part of the variations; two others refer to the variance of the recurrence time and two to the Poincaré cycle of a dynamical system. Most variations consist in inequalities and formal identities for the mean first-arrival time and subsequent recurrence times for the given state.     

The dynamics of one-dimensional random quantum XY system with Dzyaloshinskii-Moriya interaction

In this paper,the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied.By means of the recurrence relation method in the high-temperature limit,we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution.It is found that when the standard deviation of random exchange coupling δJ(or the standard deviation of random external field δB) is small,the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one.However,when δJ(or δB) is large,the crossover vanishes,and the system shows a central-peak behavior or the most disordered one.We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions.Our results show that for all the cases considered,the dynamics of the above system is similar to that of the one-dimensional random XY model.     

Analytical study of a flattened Gaussian beam through multi-apertured optical imaging systems of B = 0

By using the methods of the matrix decomposition and expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expressions for a flattened Gaussian beam (FGB) through multi-apertured optical imaging systems of B = 0 are derived and illustrated with numerical examples. Comparisons with the straightforward numerical integration of the Collins formula and with the previous work are made. It is shown that the main advantages of our methods and results are the more accuracy and great reduction of computer time.     

周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.     

快速数值差分递推改进算法在超宽连续谱模拟中的应用研究

对快速数值差分递推公式进行了改进,使之能够求解带有脉冲自陡峭项和脉冲内喇曼散射项的非线性薛定谔方程.通过与传统孤子解析结果及分步傅里叶方法数值结果的对比分析表明,快速数值差分递推改进算法是一种快速而准确的数值计算方法,它不仅能够同步考虑光学媒质中的群速色散作用和非线性克尔作用,而且将所有高阶非线性项对光脉冲传输的影响也...     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

电场中里德伯原子动力学性质的半经典理论研究

利用闭合轨道理论和Poincaré截面两种方法研究了鞍点附近电场中高里德伯态Li原子的动力学性质.由于原子实的作用,体系是混沌的,闭合轨道和周期轨道在混沌体系中并存,但二者在Poincaré截面上的反映是不同的.讨论了两种半经典理论在研究混沌体系时的联系,得到了仅靠闭合轨道理论得不到的信息. 关键词： Poincaré截面 回归谱 Stark效应     

东亚北部地区气温的冬季-冬季再现特征研究

对东亚北部(40—50°N,100—130°E)区域1953—2012年大气温度的冬季-夏季-次年冬季(简称冬季-冬季)的季节变化特征进行了初步研究.结果表明:2008年以来,该区域的气温从低层至高层(1000—400 h Pa)连续三年出现冬季偏冷-夏季偏暖-次年冬季偏冷的典型特征,20世纪50—60年代亦有类似情况;而20世纪90年代则出现了与此相反的冬季偏暖-夏季偏冷-次年冬季偏暖的变化特征.将这种典型的气温季节变化特征定义为一种新的变化机理:冬季-冬季再现(WWR).根据1953—2012年的历年变化情况将这60年划分为四种不同的类型:负(正)冬季-冬季再现(negative/positive WWR)型和负(正)冬季-冬季非再现(negative/positive non-WWR)型.其中,气温表现为WWR型的年份共计23年,出现概率近40%,并且该WWR特征是相对独立于El Nio-南方涛动指数的变化而存在的.对不同类型年份的位势高度场、垂直速度场及其850 h Pa风场进行的合成分析表明:对于WWR型,高层(500 h Pa)至低层(1000 h Pa)的大气内部动力过程具有与气温相匹配的冬季-冬季的再现特征;而non-WWR型则没有出现类似的特征,从而在一定程度验证了WWR存在的可能性.WWR的提出为进一步开展当前全球增暖背景下冬季低温事件的频发提供了一个新的思路.