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51.
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. 相似文献
52.
53.
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. 相似文献
54.
揭示非最大相干可能比最大相干产生更有效的非线性频率转换. 为此以三能级级联系统(没有最大相干)为例计算其非线性光学信号的强度, 并与三能级Λ型系统(具有最大相干)进行比较. 利用非微扰方法计算表明, 在双光子共振和相同参数的条件下, 级联系统产生的非线性光学信号的最大强度约是Λ系统的两倍. 利用缀饰态表象分析表明, 两个系统中耦合跃迁的自发辐射及其介入的不可逆三光子过程具有相反的作用. 它们在级联系统中加强非线性转换, 而在Λ系统中削弱非线性转换.
关键词:
电磁感应透明
非线性光学过程
双光子共振 相似文献
55.
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. 相似文献
56.
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。 相似文献
57.
This paper gives some global and uniform convergence estimates for a class of subspace correction (based on space decomposition) iterative methods applied to some unconstrained convex optimization problems. Some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems.
58.
针对刚性约束层、柔性约束层以及液体约束层,从激光诱导冲击波阵面状态、汽化物(包括气体和等离子体)扩散以及冲击波的反射进行分析,发现对于脉宽小于冲击波通过汽化物层的时间间隔的短脉冲激光,约束层并不能直接提高冲击波的冲量,而对于脉宽大于冲击波通过汽化层时间间隔的激光,其增强冲击效果是通过约束汽化物的扩散,提高压力幅值和由于冲击波在约束层与工件表面的多次反射而延长对工件的作用时间来实现的.刚性约束层能最大地增加冲击冲量,而柔性约束层和液体约束层的主要优点是其形状可与非平面形工件表面符合.
关键词:
激光
约束层
扩散
反射波 相似文献
59.
L. T. Ashchepkov 《Computational Mathematics and Mathematical Physics》2006,46(7):1168-1175
A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed. 相似文献
60.
Johan Helsing 《BIT Numerical Mathematics》2006,46(2):307-323
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 相似文献