Time dependence in quantum mechanics

It is shown that the time-dependent equations (Schr?dinger and Dirac) for a quantum system can be derived from the time-independent equation for the larger object of the system interacting with its environment, in the limit that the dynamical variables of the environment can be treated semiclassically. The time which describes the quantum evolution is then provided parametrically by the classical evolution of the environment variables. The method used is a generalization of that known for a long time in the field of ion-atom collisions, where it appears as a transition from the full quantum mechanical perturbed stationary states to the impact parameter method in which the projectile ion beam is treated classically. Received 25 October 1999     

Restoring entanglement in atomic collisions: A gedanken experiment

A new type of collision experiments is discussed, where observations of two successive collisions of the same pair of particles would be possible. When such technology is available, a surprising restoring of entanglement, normally considered broken in usual collision experiments, could be observed. As an illustration the collision partners He⁺ and He⁺⁺ in a collision regime where the resonant charge transfer is dominating are considered. In the analysis it is shown that in such experiments, two spatially widely separated ion paths, corresponding in fact to two different charge states, would contribute coherently to the final amplitudes, describing which of the ions emerges as singly charged, i.e. which carries the single electron involved. The double collision experiments are not trivial, since their overall cross-sections are extremely small. Development of relevant experimental techniques will decide if the proposed phenomena remain in the field of gedanken experiments or enter the world of real experimental physics. Received 2 December 1999 and Received in final form 12 May 2000     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

基于拓扑优化的新型蜂窝结构设计

可变体飞行器若要实现机翼后掠角、面积和前后缘弯度等参数的大幅度变化,机翼蒙皮需要具有光滑的气动外形、大变形、高承载以及驱动力小的特点。针对柔性蒙皮的需求,本文利用拓扑优化方法设计了一种新型零泊松比蜂窝结构,通过有限元仿真与U形蜂窝结构和余弦形蜂窝结构进行对比,验证其变形和承载等性能。以最大应变2%为基准,比较了三种蜂窝结构的变形能力。结果表明,新型蜂窝结构的拉伸变形量高达75%,分别是U形蜂窝结构和余弦形蜂窝结构的1.7倍和2.1倍。在最大位移量相同时,所需驱动力分别是U形蜂窝结构和余弦形蜂窝结构的0.51倍和0.28倍,表明新型蜂窝结构具有很大的易变形能力。当蜂窝结构的橡胶蒙皮受到相同压强载荷且处于初始未拉伸状态/拉伸状态时,新型蜂窝结构橡胶蒙皮的最大法向位移量分别是U形蜂窝橡胶蒙皮和余弦形蜂窝橡胶蒙皮的0.4倍/0.56倍和0.29倍/0.42倍,表明新型蜂窝结构具有良好的面外承载能力。另外,通过适当增加壁厚,可以提高新型蜂窝结构本身的抗弯曲能力。分析结果表明,本文设计的新型蜂窝结构具备大变形、高承载以及驱动力小的优点。     

基于交叉降阶取样的改进响应面方法

针对经典响应面法和加权响应面法存在的计算精度不高和稳定性不强的问题,提出一种新的样本点选择策略,即交叉降阶思想,并基于此发展出一种新的改进响应面方法。该方法以均值点加上0.5倍的标准差作为初始迭代点。在Bucher试验设计的基础之上,将n维坐标系降阶为n个一维坐标系。然后,依据样本点的重要性,筛选出n+1个靠近真实失效面的优秀样本点,并用这些样本点去拟合线性响应面函数。最后依据样本中心间的距离与上一次迭代得到的设计点的范数之商作为其收敛准则。通过5个数值算例与工程算例,验证了交叉降阶响应面法具有较高的精度、效率、稳定性和一定的工程适用性。     

流对波边界层湍流运动的影响

采用大涡模拟方法和Smagorinsky亚格子模型,求解三维Navier-Stokes方程,研究了波流边界层中的湍流特性．将大涡模拟结果与相应的直接数值模拟结果和实验数据进行比较,吻合较好．获得了不同波雷诺数,不同波流比情况下的大涡模拟数据库,并由此分析了波流边界层中各种湍流统计量,如速度廓线、剪应力、湍流强度等的变化规律．     

颗粒在大涡结构中的弥散

气相采用大涡模拟方法,颗粒相采用轨道模型研究了三维后台阶气粒两相湍流流动的大尺度涡结构的瞬时演变过程以及颗粒的瞬时弥散规律.比较了不同入流速度的颗粒在大涡结构中的瞬时弥散特性,尤其研究了高速释放大颗粒的弥散特性.三维流动中大尺度涡结构具有明显的脱离、发展、合并和破碎过程.小颗粒的分布受大涡结构的控制,其空间的弥散过程与流体 大涡结构的空间发展相一致,但是由于三维流动中大涡边缘和中心区的压力差,颗粒在大尺度 涡的边缘出现密集.而大颗粒在流场中的分布受其惯性控制,对气相的涡结构不敏感.高速释放到流场中的大颗粒受惯性影响最大,保持在其原有动量方向上运动.     

Identification of local extinction topology in axisymmetric bluff‐body diffusion flames with a reactedness‐mixture fraction presumed probability density function model

The effects of finite‐rate chemistry, such as partial extinctions and re‐ignitions, are investigated in turbulent non‐pre‐mixed reacting flows stabilized in the wake of an axisymmetric bluff‐body burner. A two‐dimensional large‐eddy simulation procedure is employed that uses a partial equilibrium/two‐scalar reactedness mixture fraction probability density function (PDF) combustion sub‐model, which is applied at the sub‐grid scale (SGS) level. An anisotropic sub‐grid eddy–viscosity and two equations for the SGS turbulence kinetic and scalar energies complete the SGS closure model. The scalar covariances required in the joint PDF formulation are obtained from an extended scale‐similarity assumption between the resolved and the sub‐grid fluctuations. Extinction due to strong turbulence/chemistry interactions is recognized with the help of a ‘critical’, locally variable, turbulent Damkohler number criterion, while transient localized extinctions and re‐ignitions are treated with a Lagrangian transport equation for a reactedness progress variable. Comparisons with available experimental data suggested that the formulated approach was capable of identifying the effects of large‐scale vortex structure activity, which were inherent in the reacting wake and dominant in the counterpart isothermal flows that otherwise would have been obscured if a standard time‐averaged procedure had been used. Additionally, the post‐extinction and re‐ignition behaviour and its time‐varying interaction with the large‐scale structure dynamics were more appropriately addressed within the context of the present time‐dependent method. Copyright © 2001 John Wiley & Sons, Ltd.     

On the effect of selection in genetic algorithms

To study the effect of selection with respect to mutation and mating in genetic algorithms, we consider two simplified examples in the infinite population limit. Both algorithms are modeled as measure valued dynamical systems and are designed to maximize a linear fitness on the half line. Thus, they both trivially converge to infinity. We compute the rate of their growth and we show that, in both cases, selection is able to overcome a tendency to converge to zero. The first model is a mutation‐selection algorithm on the integer half line, which generates mutations along a simple random walk. We prove that the system goes to infinity at a positive speed, even in cases where the random walk itself is ergodic. This holds in several strong senses, since we show a.s. convergence, L^p convergence, convergence in distribution, and a large deviations principle for the sequence of measures. For the second model, we introduce a new class of matings, based upon Mandelbrot martingales. The mean fitness of the associated mating‐selection algorithms on the real half line grows exponentially fast, even in cases where the Mandelbrot martingale itself converges to zero. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 18: 185–200, 2001     

Sharp Bounds for the Ratio of q – Gamma Functions

Let Γ_q (0 < q ≠ 1) be the q–gamma function and let s ∈ (0, 1) be a real number. We determine the largest number α = α(q, s) and the smallest number β = β(q, s) such that the inequalities hold for all positive real numbers x. Our result refines and extends recently published inequalities by Ismail and Muldoon (1994).