A new numerical scheme for the nonlinear Schrödinger equation with wave operator

In this paper, a new compact finite difference scheme is proposed for a periodic initial value problem of the nonlinear Schrödinger equation with wave operator. This is an explicit scheme of four levels with a discrete conservation law. The unconditional stability and convergence in maximum norm with order \(O(h^{4}+\tau ^{2})\) are verified by the energy method. Those theoretical results are proved by a numerical experiment and it is also verified that this scheme is better than the previous scheme via comparison.     

Recent progress in investigations of surface structure and properties of solid oxide materials with nuclear magnetic resonance spectroscopy

In this review, some of the latest research developments on the characterization of the structure and properties of oxide materials by applying solid-state nuclear magnetic resonance spectroscopy (NMR), including the use of dynamic nuclear polarization (DNP) NMR, ¹⁷O NMR combined with surface selective labeling and ³¹P NMR coupled with phosphorous-containing probe molecules, are discussed.     

New Conservative Schemes for Regularized Long Wave Equation

In this paper, two finite difference schemes are presented for initial-boundary value problems of Regularized Long-Wave(RLW) equation. They all have the advantages that there are discrete energies which are conserved. Convergence and stability of difference solutions with order O(h2 τ2) are proved in the energy norm. Numerical experiment results demonstrate the effectiveness of the proposed schemes.     

The solving problem and the difference solving process for the shear of a bounded elastic bodies

ＩｎｔｒｏｄｕｃｔｉｏｎＡｎｅｌａｓｔｏｍｅｒ(ｃｏｍｐｒｅｓｓｉｂｌｅｏｒｉｎｃｏｍｐｒｅｓｓｉｂｌｅ)ｂｅｔｗｅｅｎｔｗｏｐａｒａｌｌｅｌｒｉｇｉｄｓｕｒｆａｃｅｓｉｓａｋｉｎｄｏｆｏｆｔｅｎｗｏｒｋｉｎｅｎｇｉｎｅｅｒｉｎｇａｎｄｔｅｃｈｎｏｌｏｇｙ.Ｔｈｅｓｔｕｄｙｆｏｒｉｔｓｄｅｆｏｒｍａｔｉｏｎｕｎｄｅｒｔｈｅｒｏｌｅｏｆｆｏｒｃｅｂｅｇａｎｍａｎｙｙｅａｒｓａｇｏ.Ｔａｒｇｅｔｓｔｕｄｉｅｄ—ｂｏｎｄｅｄｅｌａｓｔｉｃｂｏｄｙｉｓｄｉｖｉｄｅｄｉｎｔｏａｃｉｒｃｕｌａｒｃｙｌｉｎｄｒｉ…     

Linearly-Independent Quantum States Can Be Cloned by a Unitary-Reduct ion Operation

The famous quantum no-cloning theorem [Nature 299(1952)802] forbids replication of an arbitrary unknown quantum state. But it leaves open the follorc-ing question: If the state is not completely arbitrary, but secretly chosen from a certain set $ = {|Ψ₁>,| Ψ₂>,...,|Ψ_n>}, whether is the cloning possible? It is proved that the states from the set $ = {|Ψ₁>,| Ψ₂>,...,|Ψ_n>} can be faithfully cloned by a general unitary-reduction operation in a probabilistic fashion if and only if |Ψ₁>,| Ψ₂>,... and |Ψ_n> are linearly-independent.     

A second-order fast compact scheme with unequal time-steps for subdiffusion problems

Numerical Algorithms - In consideration of the initial singularity of the solution, a temporally second-order fast compact difference scheme with unequal time-steps is presented and analyzed for...     

The finite element method for the coupled Schrödinger-KdV equations

In this Letter, we employ finite element method to study a periodic initial value problem for the coupled Schrödinger-KdV equations. For the case of one dimension, this problem is reduced to a system of ordinary differential equations by using a semi-discrete scheme. The conservation properties of this scheme, the existence and uniqueness of the discrete solutions, and error estimates are presented. In numerical experiments, the resulting system of ordinary differential equations are solved by Runge-Kutta method at each time level. The superior accuracy of this scheme is shown by comparing the numerical solutions with the exact solutions.     

Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations

In this paper, we study two compact finite difference schemes for the Schrödinger-Boussinesq (SBq) equations in two dimensions. The proposed schemes are proved to preserve the total mass and energy in the discrete sense. In our numerical analysis, besides the standard energy method, a “cut-off” function technique and a “lifting” technique are introduced to establish the optimal H¹ error estimates without any restriction on the grid ratios. The convergence rate is proved to be of O(τ² + h⁴) with the time step τ and mesh size h. In addition, a fast finite difference solver is designed to speed up the numerical computation of the proposed schemes. The numerical results are reported to verify the error estimates and conservation laws.

     

生物及化学反硝化过程中N2O的产生与控制

长期以来,人们都将N2O视为一种温室气体,然而事实上N2O在航天领域是一种宝贵的能源物质,西方发达国家对N2O的制备技术相当重视。生物及化学反硝化过程都能产生大量的N2O,但将N2O作为能源气体收集利用在我国还未受到重视。本文介绍了国内外关于污水脱氮过程中N2O生成情况的研究,分析了生物脱氮过程中N2O的产生机理和影响因素,同时探讨了化学反硝化作用,尤其是Fe(Ⅱ)的还原作用对N2O生成和控制的影响,提出了对N2O进行资源化利用的途径。最后指出,可以大量积累N2O的化学反硝化过程应是今后水体脱氮的重要研究方向,尤其是化学反硝化过程中N2O的产生机理和影响因素值得进一步研究。