Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

用不确定度评价测量结果中的有效自由度的作用

论述了有效自由度的计算方法及有效自由度量值在分析测量结果中的应用。     

大学物理实验中分类教学的探索和研究

本文对大学物理实验课程的教学现状进行了分析,提出了对大学物理实验课程进行分类教学改革的指导思想和遵循的原则及采取的措施。     

On Quantum Team Games

Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied.     

仓库容量有限条件下的随机存贮管理问题的评注

给出2005年全国部分高校研究生数学建模竞赛D题的研究背景,对参赛论文作了简要评注,并提供了一种参考解答.     

Irregularities of distribution with respect to strips

Summary A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry.     

Schrödinger Uncertainty Relations and Physical Features of Correlated-Coherent States

We show that the difference between the Schrödinger uncertainty relations (UR) and the Heisenberg UR is fundamental. We propose a modified version of stochastic mechanics that allows clearly demonstrating that the contributions from the anticommutator and the commutator to the Schrödinger UR are equally important. A classification of quantum states minimizing the Schrödinger UR at an arbitrary instant is proposed. We show that the correlation of the coordinate and momentum fluctuations in such correlated-coherent states (CCS) is largely determined by the contributions from not only the commutator but also the anticommutator of the corresponding operators. We demonstrate that the character of this correlation changes qualitatively in time from the antiphase correlation typical for the Heisenberg UR to the inphase correlation for which the contribution from the anticommutator is decisive. We comparatively analyze properties of a free microparticle and a quantum oscillator in CCS and show that the CCS correspond to traveling-standing de Broglie waves in both models.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

拆边法求最短路径

本文利用局部比较法 ,在图中定义子图、无效路径、以及可去边 .利用推导的有关定理 ,拆去可去边 ,利用最短路径相同的等价性 ,达到化简图 ,从而求出最短路径     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.