Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

强流脉冲离子束辐照靶及其喷发的数值研究

利用拟合实测的TEMP Ⅱ型加速器磁绝缘二极管(MID)电压波形及其焦点附近束流密度曲线，建立了Gaussian分布模型，据此计算了与靶作用的离子的能量及数量，采用Monte Carlo(MC)方法计算了沉积在靶内的能量.并以此作为热源，与流体动力学(HD)模型相结合，对不同的靶状态采用相应的状态方程，模拟计算了靶内压力演化情况; 同时对烧蚀产生的等离子体采用理想气体状态方程, 结合HD方程组, 模拟计算了喷发过程中压力的空间演化过程. 关键词： 强流脉冲离子束 Gaussian模型 HD方程 数值研究     

Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

High-order accurate equations describing vibrations of thin bars

A method for deriving one-dimensional wave propagation equations in thin inhomogeneous anisotropic bars based on the mathematical homogenization theory for periodic media is used to obtain equations governing the longitudinal and transverse vibrations of a homogeneous circular bar. The equations are derived up to O(ε⁸) terms and take into account variable body forces and surface loads. Here, ε is the ratio of the bar’s typical thickness to the typical wavelength.     

Parametric oscillation at 2.1 μm in periodically poled RbTiOAsO4

An Nd:YAG laser-pumped periodically poled RbTiOAsO₄ (PPRTA) optical parametric oscillator (OPO) near degeneracy is reported. At a pump power of 3.7 W, a net conversion efficiency of 43% was obtained. These crystals were found to be phase-matchable for the higher order quasi-phase-matched second-harmonic generation (SHG) in the visible range. Detailed analyses of the phase-matching properties for these processes were made by using the published Sellmeier and thermo-optic dispersion formulas.     

两类方程亚纯解(n,1)级的上界估计

本文给出Riccati方程及另外一类具有代表性微分方程的亚纯解（n,1)级的上界估计，在一定条件下确立了文[2]中的猜测的正确性。     

不连续不可逆二维映象的动力学特性

总结两个保守映象不可逆地分段连续链接(称为类耗散系统)以及一个保守映象与一个耗散映象不可逆地分段连续链接(称为半耗散系统)情况下得到的五项共同动力学特征：不连续边界象集构成的随机网成为唯一的混沌轨道；由于某些相点具有两个逆象而导致的相空间塌缩(类耗散)；由于系统的不连续不可逆性质而出现的胖分形禁区网；在具有吸引子共存时占据不连续边界象集随机网和胖分形禁区网区域的点滴状吸引域以及由此导致的吸引子不可预言性；即使在传统强耗散存在的情况下点滴状吸引域仍由类耗散机制主宰.以一个累积-触发电路为例，说明这五项系统动 关键词： 随机网 禁区网 点滴状吸引域     

Approximate Inverse Preconditioners for Some Large Dense Random Electrostatic Interaction Matrices

A sparse mesh-neighbour based approximate inverse preconditioner is proposed for a type of dense matrices whose entries come from the evaluation of a slowly decaying free space Green’s function at randomly placed points in a unit cell. By approximating distant potential fields originating at closely spaced sources in a certain way, the preconditioner is given properties similar to, or better than, those of a standard least squares approximate inverse preconditioner while its setup cost is only that of a diagonal block approximate inverse preconditioner. Numerical experiments on iterative solutions of linear systems with up to four million unknowns illustrate how the new preconditioner drastically outperforms standard approximate inverse preconditioners of otherwise similar construction, and especially so when the preconditioners are very sparse. AMS subject classification (2000) 65F10, 65R20, 65F35, 78A30     

Numerical solution of the three‐dimensional parabolic equation with an integral condition

Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank‐Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040     

解奇异非光滑方程组的牛顿法和不精确牛顿法

本文主要解决奇异非光滑方程组的解法。应用一种新的次微分的外逆，我们提出了牛顿法和不精确牛顿法，它们的收敛性同时也得到了证明。这种方法能更容易在一引起实际应用中实现。这种方法可以看作是已存在的解非光滑方程组的方法的延伸。