Maximum error estimates for a compact difference scheme of the coupled nonlinear Schrödinger–Boussinesq equations

The coupled nonlinear Schrödinger–Boussinesq (SBq) equations describe the nonlinear development of modulational instabilities associated with Langmuir field amplitude coupled to intense electromagnetic wave in dispersive media such as plasmas. In this paper, we present a conservative compact difference scheme for the coupled SBq equations and analyze the conservative property and the existence of the scheme. Then we prove that the scheme is convergent with convergence order O(τ² + h⁴) in L_∞‐norm and is stable in L_∞‐norm. Numerical results verify the theoretical analysis.     

Conservative finite difference methods for fractional Schrödinger–Boussinesq equations and convergence analysis

In this paper, two conservative finite difference schemes for fractional Schrödinger–Boussinesq equations are formulated and investigated. The convergence of the nonlinear fully implicit scheme is established via discrete energy method, while the linear semi‐implicit scheme is analyzed by means of mathematical induction method. Our schemes are proved to preserve the total mass and energy in discrete level. The numerical results are given to confirm the theoretical analysis.     

Optimal H2‐error estimates of conservative compact difference scheme for the Zakharov equation in two‐space dimension

In this paper, a conservative compact difference scheme is proposed for the two‐dimensional nonlinear Zakharov equation with periodic boundary condition and initial condition. The proposed scheme not only conserve the mass and energy in the discrete level but also are efficient in practical experiments because the Fast Fourier transform (FFT) can be used to speed up the numerical computation. By using the standard energy method and induction argument, we can establish rigorously the unconditional and optimal H²‐error estimates. Some numerical examples are provided to support our theoretical results and show the accuracy and efficiency of the new scheme.     

棒球棒动力学分析

通过建立有限元模型, 寻找棒球的击球最佳点与棒球棒固有频率、模态振型 之间的联系. 假定棒球棒模型采用的是线弹性材料, 并且边界条件为两端自由, 这与实际是 相符合的. 接着讨论了给球棒``软木化'(在球棒头部掏出一个圆柱空腔, 在里面塞入软木 或橡胶, 然后盖上木帽) , 或者采用金属球棒都能增加``最佳点'的效果. 最后又通过实验验 证了该模型的正确性.     

The fractional dimensional theory in Lüroth expansion

It is well known that every x ∈ (0, 1] can be expanded to an infinite Lüroth series in the form of

利用比特配对来保持量子计算中的相干性

提出了一种简单高效的方案，用以克服量子计算中的消相干，该方案本质性地利用了消相干过程中的合作效应及相干保持态．文章阐明了该方案的主要思想．     

Noise of quantum solitons and their quasi-coherent states

Quantum noise of optical solitons is analysed based on the exact solutions of the quantum nonlinear Schrödinger equation (QNSE) and the construction of the quantum soliton states. The noise limits are obtained for the local photon number and for the local quadrature phase amplitude. They are larger than the vacuum fluctuation. So in the fundamental soliton states the variance of the local photon number and the local quadrature phase amplitude cannot be squeezed. The soliton states with the minimum noise are quasi-coherent states, in which the quantum dispersion effects are negligible.     

Hausdorff dimension of some kind of alternating Oppenheim series expansion

For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.     

An extension of one of the extremum principles for a Bingham solid

Summary An extension of the extremum principle concerned with velocity fields for boundary value problems of an incompressible rigid visco-plastic (Bingham) solid is derived. This extension can be used to obtain close overestimates for the rate of work of the unknown surface tractions in certain problems of visco-plastic flow.Nomenclature k yield stress in pure shear - coefficient of viscosity - _ij stress tensor referred to rectangular cartesian axes Ox _i - s _ij stress deviator tensor - T _i surface traction - J (1/2s _ijs_ij ^1/2 - F _i body force per unit volume - v _i velocity vector - _ij = rate of deformation tensor - I (2 _ijij ^1/2 - [v] magnitude of a velocity discontinuity in flow of a rigid perfectly plastic solid - S surface - V volume - S _t part of surface upon which T _iis prescribed - S _v part of surface upon which v _iis prescribed - S _d surface of velocity discontinuity in flow of a rigid plastic solid - x, y, z rectangular cartesian coordinates - u, v, w velocity components in the x, y and z directions respectively - rate of twist per unit length - T torque     

对称正则长波方程的守恒差分算法

1引言SRLW方程(?)~3u/(?)x~2(?)t-(?)u/(?)t=(?)p/(?)x u((?)u/(?)x),(1.1) (?)p/(?)t (?)u/(?)x=0(1.2)是正则长波(RLW)方程的一种对称叙述,用于描述弱非线形作用下空间电荷的等离子声