格林函数

In this thesis,based on the DFT+NEGF first-principles method,we construct a lead-molecule-lead sandwich system with single benzene-based molecule to investigate the relationship between the structure and properties of the molecular devices and the factors that influence properties of the molecular devices.Our computational investigations on these molecular devices are primarily concentrated on the effect of contact geometry between molecules and electrodes,the effect of side groups,the effect of different torsion angle between two phenyl rings and the effect of external electric field.This thesis consists of five chapters:In Chapter one,we mainly introduce the research background and development of the molecular electronics,including the experimental fabrication of molecular electronic components and theoretical simulation methods.Afterwards we discuss the questions that need to be solved in this area.Finally,the main contents of this thesis are listed.In Chapter two,we introduce the theoretical methods used in this thesis, including the main first-principles calculation methods,i.e.,the Density-Functionmethod and nonequilibrium Green\'s function.

本论文拟采用密度泛函理论和非平衡格林函数相结合的第一性原理计算方法，选取苯基小分子作为研究对象，构建了金属电极/有机小分子/金属电极三明治结构体系，系统地研究了苯基分子器件结构的改变与分子电输运性质之间的关系以及影响分子器件电输运性质的相关因素，其中重点研究了分子与电极间可能的接触结构改变、官能团、分子间的扭转角以及外电场对苯基分子电输运性质的影响，本论文主要包括以下五个章节的内容：第一章为综述部分，主要介绍了分子电子学产生的背景、分子器件的研究意义、当前研究分子器件的实验和主要理论方法，以及目前在研究分子器件中存在的一些问题，最后给出了本论文的主要研究内容和技术路线。

The paper aimed at resolving the question of side value of Laplace equation and Poisson equation in plane angular domain by using integral equation of the solution of mathematic physics equation.

旨在利用数学物理方程解的积分公式，去解决平面角形区域内Laplace方程和Poisson方程的边值问题，而其关键在于构造相应域内的格林函数。

By deleting integral singular point, the Green function and its far field asymptotic formula that is satisfied with radiation condition is obtained.

对兴波速度势表达式中的积分奇点进行了处理，得到满足辐射条件的格林函数和远场渐近解。

In Chapter 1, two solutions to the elliptical boundary value problem have been constructed through a monotone iterative process, and they might be identical. In Chapter 2, the author expresses the local solution to the parabolic initial boundary value problem taking advantage of Green function. In Chapter 3, the asymptotic solution to the initial value problem of Duffing equation is obtained and the method for finding the approximate solution to the inverse problem is put forward.This paper is planned with a view to the author's research means.

从研究结果看：第一章通过单调迭代过程构造出椭圆型方程的边值问题的两个解，并且指出二者可能是同一个解；第二章利用格林函数给出了抛物型方程的初边值问题的局部解的解析表达式；第三章中，先对Duffing方程的初值问题写出解的渐近展开式，再对其反问题提出一种求近似解的方法。

In the third chapter, we adopted a model in which atomic chain is connected with two reservoir and buffer Layer. Non-equilibrium Atomistic Green's Function method is adopted to study the model. And we study the influence of reservoir and buffer layer on heat transport.

第三章，我们采用了接有热库和缓冲层纳米链模型，采用非平衡原子格林函数法来研究一维链在有热库和缓冲层连接的情况下对系统热输运的影响。

Experimental study on the properties of autocorrelation function of image speckles produced by weak random screens.

随机表面散射光场的格林函数法与基尔霍夫近似的比较。

In this paper the numerical solution of Green's function of potential in 2-D arbitrary inhomogeneous media with axial symmetry has been given by using the numerical mode matching theory.

利用数值模式匹配理论，对具有轴对称的任意二维非均匀介质中位场的格林函数给出数值解。

Using a method for storing the large-scale sparse matrix with varying band width, Cholesky decomposition, Green function and normalized least square fitting inversion, the paper improved the computing accuracy and efficiency in imaging calculation.

利用有限元方法实现了井间电磁成像，为了求取散射电磁场的积分方程组，运用了处理大型对称变带宽方程组的 Cholesky 分解法，反演时使用了格林函数和最小二乘法，既提高了反演速度又提高了反演质量。

Applied Green's function, the differential equations will be transformed into the equivalent of integral equations, sufficient conditions for existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous boundary value problems with p-Lapacian operator are obtained.

文中，利用格林函数，将微分方程转化成等价解的积分方程，给出了该奇异非线性四阶p-Lapacian微分方程边值问题的正解的存在及惟一性的一个充要条件。

The property of bounded space Green's function in the neighbor domain of the singular point is studied.

研究了有界空间格林函数在奇异点邻域内的性质。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。