反应流体的移动网格动理学格式

在移动网格上构造一种反应流的动理学格式.首先利用BGK模型推导含化学反应的流体力学方程组,并利用其积分形式构造移动网格上离散格式,再利用自适应移动网格方法得到网格速度,最后利用时间精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.一维与二维的数值实验表明这种格式同时具有高精度、高分辨率的特点.     

一维Morse势的Dirac方程的束缚态

在标量型和矢量型Morse势相等的条件下,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解.并且在求精确解时,运用一种新的自变量变换方法,使方程求解变得比较简单.     

一维时间周期势的量子隧穿

研究了一维时间周期势的量子隧穿,建立了周期势的两种物理模型,并分别在不同情况下对其进行理论研究和推导,证明了一维周期势下的量子隧穿可统一由一种模型处理.     

非线性基底势对离散非线性晶格孤波动力学性质的影响

使用一种简化的准离散多重尺度法,研究了具有非线性基底势的一维离散非线性晶格的孤波解,表明孤波能够在这种一维非线性晶格链中存在,而且非线性基底势对孤波的载波频率、群速度、振幅等动力学性质都将产生影响.另一方面,我们还对非线性动力学方程进行了数值求解,发现用简化的准离散多重尺度法得到的近似解与精确的计算机数值计算结果符合得...     

双曲函数型辅助方程构造具5次强非线性项的波方程的新精确孤波解

在辅助方程法的基础上利用两种函数变换和一种双曲函数型辅助方程，通过符号计算系统Mathematica构造了在力学当中一个重要的模型，有5次强非线性项的波方程的新三角函数型和双曲函数型精确孤波解.这种方法寻找其他具5次强非线性项的非线性发展方程的新精确解方面具有普遍意义. 关键词： 双曲函数型辅助方程 函数变换 具5次强非线性项的波方程 精确孤波解     

强激光场中H~-离子二维光电子动量谱的理论研究

选用两个模型势,利用强场近似方法研究了H-离子在线性极化强激光场中二维光电子动量谱中次外层后重散射环.研究结果表明:两个模型势中的极化势对二维光电子动量谱的影响很小;随着激光强度的增加,二维光电子动量谱中出现后重散射环的数目变多,沿着次外层后重散射环的光电子的角分布波动性变小,能够通过多项式拟合的方法从二维光电子动量谱中次外层后重散射环获得精确的电子与H原子的弹性散射截面,特别适用于激光强度较小的情况.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

倾斜入射光入射于一维非线性光子晶体中带宽加宽的二次谐波的产生(英文)

研究了置于空气中的含缺陷的一维非线性光子晶体中二次谐波的产生.由于反射的二次谐波很强而不能忽略,缓变振幅近似在系统中是不适用的.本文提出了一种不采用缓变振幅近似来处理二次谐波产生问题的方法,并应用这种方法计算相关的二次谐波转换效率.结果表明:随着入射波角度的增加,缺陷模对应的波长将变短,并且通过调整基频波入射的角度,可以产生宽带宽并且高转换效率的二次谐波.这个方法适用于任何一维非均匀系统,可以简单方便地计算出二次谐波转换效率.     

一种新型光谱表面等离子体共振二维探测方法在DNA微阵列中的应用

在此前曾提出过一种新型二维折射率探测方法——并行扫描光谱表面等离子体共振(surface plasmon resonance, SPR)成像方法。在这种方法中,使用线形光照明,CCD得到的图像包含SPR光谱信息和一维空间信息,进而通过计算可得到折射率的一维分布信息。通过一维扫描,就能够得到整个被扫描区域内的折射率二维分布信息。该方法具有高灵敏、高通量的优点,适合微阵列(microarray)的检测, 并完善了这种方法的数据处理过程,使用空气折射率作为参考,消除了无法精确控制入射角的难题。使用该方法对手工点制的军团菌mip DNA探针微阵列进行了检测,证明了这种方法高灵敏无标记地探测微阵列的可行性。我们得到的军团菌mip DNA探针制备浓度与其等效折射率的关系,这对基于SPR的微阵列技术的发展有着重要的参考意义。     

倾斜入射光入射于一维非线性光子晶体中带宽加宽的二次谐波的产生

研究了置于空气中的含缺陷的一维非线性光子晶体中二次谐波的产生.由于反射的二次谐波很强而不能忽略,缓变振幅近似在系统中是不适用的.本文提出了一种不采用缓变振幅近似来处理二次谐波产生问题的方法,并应用这种方法计算相关的二次谐波转换效率.结果表明:随着入射波角度的增加,缺陷模对应的波长将变短,并且通过调整基频波入射的角度,可以产生宽带宽并且高转换效率的二次谐波.这个方法适用于任何一维非均匀系统,可以简单方便地计算出二次谐波转换效率.     

Construction of coherent states for Morse potential: A su(2)-like approach

We propose a generalized su(2) algebra that perfectly describes the discrete energy part of the Morse potential. Then, we examine particular examples and the approach can be applied to any Morse oscillator and to practically any physical system whose spectrum is finite. Further, we construct the Klauder coherent state for Morse potential satisfying the resolution of identity with a positive measure, obtained through the solution of truncated Stieltjes moment problem. The time evolution of the uncertainty relation of the constructed coherent states is analyzed. The uncertainty relation is more localized for small values of radius of convergence.     

Meson spectra governed by the Fermi-Breit potential

We calculate the meson mass spectra in a quark potential model by using the complete Fermi-Breit potential including the terms of orbit-orbit interaction, spin-orbit coupling, and tensor force interaction. We find that these terms give nontrivial contributions to the calculated meson spectra. The orbit-orbit coupling term may lead to an instability of the solution of the Schrodinger equation and should be regularized.     

Evaluation of eigenvalues of a smooth potential via Schroedinger transmission across multi-step potential

In a one-dimensional quantal solution of Schroedinger equation, the general expressions for reflection and transmission coefficients are derived for a potential constituting n number of rectangular wells and barriers. These expressions are readily used for the estimation of eigenvalues of a smooth potential which is simulated by a multi-step potential. The applicability of this method is demonstrated with success in potentials with different forms including the most versatile Ginocchio potential where the widely used numerical method like Runge-Kutta integration algorithm fails to yield the result. Accurate evaluation of eigenvalues free from numerical problem for any form of potentials, whether analytically solvable or not, is the highlight of the present multi-step approximation method in the theory of potential scattering.      

Spectra of electron pair under harmonic and Debye potential

Two electron systems confined by harmonic potential is known as harmonium. Such a system has been studied for many reasons in the literature. In this work we study harmonium under Debye potential. We use higher order finite difference method for the solution of Schrodinger equation. Complete energy spectrum of harmonium and harmonium under Debye potential is studied. Debye screening length shows considerable effect on the energy levels and the radial matrix elements. The results are analysed in the light of existing results and the comparison with available results shows remarkable agreement.     

The equivalent dipole potential of water for the electronic structure of threonine

The equivalent potential of water for the electronic structure of threonine (Thr) in solution is constructed by the first-principles, all-electrons, ab initio calculations. The main process of calculation consists of three steps. First, the geometric structure of the cluster containing Thr and water molecules is calculated by the free cluster calculation. Then, based on the obtained geometric structure, the electronic structure of Thr with the potential of water molecules is calculated using the self-consistent cluster-embedding method. Finally, the electronic structure of Thr with the potential of dipoles is calculated. The results show that the major effect of water on the electronic structure of Thr is to raise the occupied molecular orbitals near the Fermi level by about 0.01 Ry on average, and its energy gap is almost not changed. The effect of water on the electronic structure of Thr can be simulated by dipoles potential.     

积与积减原理

文章分析了重力势能、引力势能、电荷势能、化学势能、热量势能、质量积、动量积等多种势能,发现它们均可表达为一种守恒广延量和对应的强度量的乘积,因此可将其统一定义为"积".基于积这一概念,文章得到了孤立系统内守恒广延量传递过程的积减原理,即孤立系统内进行的守恒广延量传递过程中系统的积总是减小的.进一步,文章还基于积的概念发展了孤立系统和封闭系统的势平衡判据,发现孤立系统达到势平衡状态时,系统的积达到最小值(最小积原理);当封闭系统达到势平衡状态时,系统的准自由积达到最小值(最小准自由积原理).上述结论应用于传热学中即可得到热量传递过程的(火积)减原理及相应的热平衡判据.与热力学中的核心概念熵相对应,由于物理量(火积)可以描述传热过程的不可逆性,作为传热过程的优化准则,度量系统的无序度,并给出系统的热平衡判据,因此(火积)是传热学中的核心概念. 关键词： 势能 积 积减原理 平衡判据     

The infinite-volume ground state of the Lennard-Jones potential

We consider a finite chain of particles in one dimension, interacting through the Lennard-Jones potential. We prove the ground state is unique, and approaches uniform spacing in the infinite-particle limit.Research supported in part by NSF grant MCS 78-01520.     

Equivalent potentials for a nonsymmetric non-local interaction

Scattering formalisms which incorporate antisymmetrization of the projectile with respect to identical particles in the target result in a nonsymmetric non-local interaction. Such an interaction constraints the relative wavefunctions to be orthogonal to redundant states forbidden by the Pauli principle. Concentrating on the nonsymmetric non-local kernel of Saito we try to visualize the mechanisms by which a potential can ensure the required orthogonality. We achieve this by replacing the Saito kernel by an effective symmetric non-local potential. The constructed symmetric potential is found to be phase-equivalent only but not off-shell equivalent to the original kernel. This difference in the off-shell behaviour is attributed to the dynamical origin simulating the redundant states. In close analogy with one of our recent works we also derive an energy-momentum dependent equivalent to the local potential. Our solution of the pseudo inverse problem is exact and provides a basis for writing the phase—and quasiphase—equations. We present numerical results in support of this.     

Controlling the collision between two solitons in the condensates by a double-barrier potential

We present an analytical solution of two solitons of Bose-Einstein condensates trapped in a double-barrier potential by using a multiple-scale method.In the linear case,we find that the stable spots of the soliton formation are at the top of the barrier potential and at the region of barrier potential absence.For weak nonlinearity,it is shown that the height of the barrier potential has an important effect on the dark soliton dynamical properties.Especially,in the case of regarding a double-barrier potential as the output source of the solitons,the collision spots between two dark solitons can be controlled by the height of the barrier potential.     

The bound state solution for the Morse potential with a localized mass profile

We investigate an analytical solution for the Schr o¨dinger equation with a position-dependent mass distribution, with the Morse potential via Laplace transformations. We considered a mass function localized around the equilibrium position.The mass distribution depends on the energy spectrum of the state and the intrinsic parameters of the Morse potential. An exact bound state solution is obtained in the presence of this mass distribution.