微分求积法的特性及其改进

微分求积法已在科学和工程计算中得到了广泛应用。然而,有关时域微分求积法的数值稳定性、计算精度即阶数等基本特性,仍缺乏系统性的分析结论。依据微分求积法的基本原理,推导证明了微分求积法的权系数矩阵满足V-变换这一重要特性;利用微分求积法和隐式Runge-Kutta法的等值性,证明了时域微分求积法是A-稳定、s级s阶的数值方法。在此基础上,为进一步提高传统微分求积法的计算精度,利用待定系数法和Padé逼近,推导出了一类新的s级2s阶的微分求积法。数值计算对比结果验证了所提出的新微分求积法比传统的微分求积法具有更高的计算精度。     

非周期波浪与直墙作用的非线性数值研究

基于时域高阶边界元方法,建立了完全非线性二维数值波浪水槽,对非周期波浪与直墙的相互作用问题进行了模拟和研究.自由表面满足完全非线性自由水面运动学和动力学边界条件,采用混合欧拉-拉格朗日方法追踪瞬时自由面流体质点,采用四阶Runge-Kutta法对下一时间步的波面和自由面速度势进行更新.采用加速度式法求解直墙表面速度势的时间导数,对瞬时物体湿表面上的水动力压强积分,得到作用在物体上的瞬时波浪力.首先,将全非线性与Serre-Green-Naghdi(SGN)模型的结果进行了对比分析,发现对于大幅值双入射波问题,仅满足弱色散关系的SGN模型大大低估了最大波浪爬高;其次,研究了双入射波与直墙的非线性作用问题,发现线性预报对波浪最大爬高有较大低估,而波浪的非线性成分不只导致了自由面爬高的异常增大,也引起了局部自由面的高频振荡,该物理过程中,直墙所受的波浪载荷,也展示出了与波浪爬高相似的非线性特性;最后,对波浪爬升和波浪力的时间历程进行了频谱分析,发现入射主频波的部分能量传递给了更高频的波浪成分,反映出该问题具有典型的非线性特性.     

非均匀束团在储存环高频腔中产生的高次模功率

通过分析束流频谱与高频腔高次模的相互作用,提出了计算单束流和双束流储存环中非均匀束团产生的高频腔高次模功率的方法,推导出了这两种情况下的一般通用公式,并对所得到的解析结果进行了比较和讨论.     

Approximating Scheduling Unrelated Parallel Machines in Parallel

We show how to approximate in NC the problem of scheduling unrelated parallel machines, for a fixed number of machines in which the makespan C _max is the objective function to minimize. We develop an approximate NC algorithm which finds a schedule whose length is at most (1+o(1))(C^* _max + 3 C^* _maxln(2n(n-1)/)), where C*_max denotes the optimal schedule, n the total number of jobs and a small positive constant. Our approach shows how to relate the linear program obtained by relaxing the integer programming formulation of the problem with a linear program formulation that is positive and in the packing/covering form. The established relationship enables us to transfer approximate fractional solutions from the later formulation that is known to be approximable in NC. Then, we show how to obtain an integer approximate solution, i.e. a schedule, from the fractional one, using the randomized rounding technique. We stress that our analysis assumes that the length of the schedule is (ln n) and that the min p _ij and max p _ij values are not too disparate (where p _ij is the time to run job j on machine i).Finally, we show that the same technique can be applied to the general assignment problem with a fixed number of machines and makespan T.     

Development of the Hubbell Rectangular Source Integral

The integral

耦合高阶非线性薛定谔方程及其光孤波解

从色散关系出发,推导了描述超短光脉冲不同偏振分量在双折射光纤中传输特性的耦合高阶非线性薛定谔方程(CHNLS),在一定参量下得到了亮亮、暗暗、亮暗孤波解析解,包括一种非常特殊的"W"型孤波解,并对这些孤波解的特性进行了分析.     

Momentum distribution of relativistic nuclei with Hartree-Fock mesonic correlations

The impact of Hartree-Fock correlations on the nuclear momentum distribution is studied in a fully relativistic one-boson-exchange model. Hartree-Fock equations are exactly solved to first order in the coupling constants. The renormalization of the Dirac spinors in the medium is shown to affect the momentum distribution, as opposed to what happens in the non-relativistic case. The unitarity of the model is shown to be preserved by the present renormalization procedure. Received: 7 June 2002 / Accepted: 24 September 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: juan@nucle.us.es Communicated by G. Orlandini     

Microscopic structure of superdeformed states in Th, U, Pu and Cm isotopes with Gogny force

The structure properties of the even-even nuclei ^{226, 228, 230, 232, 234}Th, ^{230, 232, 234, 236, 238, 240}U, ^{240, 242, 244, 246}Pu, and ^{242, 244, 246, 248}Cm have been investigated at normal and superdeformed shapes in microscopic mean-field calculations based on Gogny force. Collective levels are predicted from constrained Hartree-Fock-Bogoliubov and configuration mixing calculations. Two quasiparticle states are also predicted from blocking calculations for neutron and proton configurations. Predictions are shown and compared with experimental data at superdeformed shapes. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: michel-g.girod@cla.tr     

第Ⅰ类两态叠加多模叠加态光场的非线性高阶压缩特性研究

本文在文献20的基础上进一步提出了多模辐射场的N-Y最小测不准态、N-H最小测不准态、N-Y压缩最小测不准态以及N-H压缩最小测不准态等的定义.构造了由多模(q模)相干态|{Z_j}>_q及其相反态|{-Z_j}>_q的线性叠加所组成的第Ⅰ类两态叠加多模叠加态光场|ψ₁⁽²⁾>_q,利用文献20新近提出的有关多模辐射场的两种非线性高阶压缩的定义,首次对态|ψ₁⁽²⁾>_q的N次方Y压缩及N次方H压缩效应进行了详细研究.结果表明,1)当N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-Y最小测不准态;当N为奇数时,态|ψ₁⁽²⁾>_q在一定条件下可呈现出周期性变化的、任意阶的N次方Y压缩效应.2)当q·N为偶数时,态|ψ₁⁽²⁾>_q恒处于N-H最小测不准态;当q·N为奇数时,在另外的条件下,态|ψ₁⁽²⁾>_q则可呈现出周期性变化的、任意阶的N次方H压缩效应.3)N次方Y压缩及N次方H压缩效应的压缩深度与腔模总数q、压缩参数R_j以及压缩阶数N等非线性相关,后者与上述参量的非线性关联程度要比前者的更强.