Electromagnetic theory; Vector wave function space; Vector partial differential operator; helmholtz
电磁场理论；矢量波函数空间；矢量偏微分算子；亥姆赫兹定理
This paper includes two parts: theory and simulation. The theory part is based on an enclosure model. In order to consider structural-acoustic coupling of the enclosure, two formulas are deduced. One is used to describe the amplitude of sound pressure that can be gained by combining Green function of fluid, Helmholtz equation and boundary conditions. The other is used to describe the amplitude of velocity that is obtain by combining Green function of structure, vibration equation of a panel and boundary conditions.
以封闭声腔为模型，在考虑流固祸合作用的基础上，结合流体格林函数和Helmholtz方程及其边界条件，导出了各阶声压模态对应的声压振幅响应公式；结合结构格林函数和板的振动方程及其边界条件，导出了各阶板模态对应的速度振幅响应公式。
Based on a bulk Helmholtz free energy of mixing and a simple weighting procedure, a Helmholtz free energy function containing both local and nonlocal contribution are constructed.
在均相混合Hemholtz自由能和简单加权方法的基础上，构建了一个包含局域和非局域贡献的Hemholtz自由能泛函。
By introducing effective chain-insert on probability into the excess entropy and adopting wohl expression for the excess internal energy, a new Helmholtz function of mixing based on lattice theory with several universal constants has been established. Those universal constants are determined by Monte Carlo simulation data and referring to the Freed theory. This molecular thermodynamic model can be used to calculate the phase equilibria of multicomponent systems containing both small molecules and macromolecules.
在格子模型基础上，通过引入有效链插入几率，并采用Wohl式表达过量内能，经过统计力学推导，得到了密堆积格子上含待定普适性常数的混合亥氏函数表达式，利用Monte Carlo计算机模拟数据并参考严格的非平均场Freed格子场理论求取了哪些未知普适性常数，最后得出了形式简单、适合于工程计算、可应用于多组分小分子、高分子混合物相平衡计算的分子热力学模型-S-H-L模型。
In this paper, the Helmholtz integral surface is replaced by a number of interconnected flat triangular elements and flat quadrilateral elements with linear plotted function. The element surface integration is performed by means of two-dimensional Gaussion quadrature.
文中首先利用边界元方法对Helmholtz积分方程进行离散化，其中采用了线性插值的平面三角形单元和四边形单元，每个单元上的表面积分采用二维高斯积分。
In other words, now I know how to tell how the Helmholtz free energy changes as a function of temperature.
换句话说，我现在知道如何写出亥姆赫兹，自由能作为温度的函数。
So it becomes interesting, then, to figure out, how can we write the Helmholtz free energy in terms of the canonical partition function?
这就让我们开始思考，要怎么来表示亥姆霍兹自由能，用正则配分函数？
Both a free volume approach for Helmholtz free energy and a theoretically-based fitted formula for radial distribution function (rdf) of hard sphere solid were employed to describe the Helmholtz free energy of Lennard-Jones (LJ) solid in the framework of first order thermodynamic perturbation theory.
结合描述硬球固体Helmholtz自由能的自由体积方法与描述硬球固体径向分布函数的拟合的分析表达式与一阶热力学摄动理论，用于描述LennardJones（LJ）固体的Helmholtz自由能。
The Helmholtz free energy expansion of the Rochelle salt crystal is obtained by the basis function of the irreducible representations ofthe paraelectric phase group D2.
利用罗息盐晶体顺电相所属晶体点群-D2群不可约表示的基函数，构造出该晶体亥姆霍兹自由能展开式。
The equations of motion for the free vibration of the coupling system are derived by the use of Kennard's thin shell theory and Helmholtz equation and the coupling conditions on the surface of the shell as well as Dirac - δ function.
基于Kennard薄壳理论、Helmholtz方程以及壳壁外表面的运动协调条件，并借助Diracδ函数引进肋骨对壳体的作用，从而建立耦合系统的运动方程。
The rational form of Helmholtz theorem for electromagnetic field vector E and B is discussed. The solving problem for rotational field equation transforming a scalar field equation is given, and then a new method for solving dyadic Green's function of electromagnetic wave field is given.
讨论了电磁场矢量E和B的Helmholtz定理的合理形式，提出了将旋量场方程化为一个标量场方程求解的问题，然后给出了求解电磁波场并矢格林函数的新方法。
The scalar Helmholtz equation in cylindrical coordinate is constructed, using the method of separating variable, and fourier transform, and residue theory, and the Green's function and field of the transverse electric mode associated with the electric diple are also obtained.
用分离变量法、傅氏变换和留数定理求解Helmholtz方程，获得电偶极子激励的Green函数及其场。
The Helmholtz function and compressibility factor of associated mixture includes two contributions, physical interaction and chemical association.
缔合流体及其混合物的亥氏函数和压缩因子可表示为物理相互作用的贡献和化学缔合作用的贡献两部分之和。
With constructing the generalized Lagrangian function of the system by the integral manifolds of the system, the paper studies the inverse problem of Helmholtz Dynamics System. Also, two examples are given to illustrate the application of the - method.
研究了Helmholtz系统动力学逆问题，即用已知系统的积分流形来构造系统的广义La－grange函数.最后举例说明该方法的应用。
The linearized Navier Stokes equation of 2 D viscous incompressible fluid is transformed into resolving the corresponding potential function and stream function in Laplace domain, while the former satisfies the Laplace equation and the latter satisfies the Helmholtz equation.
在拉氏变换域内将线性化的Navierstokes方程转化为求解相应的势函数和流函数，前者满足拉普拉斯方程，后者满足Helmholtz方程。
The strain energy density function equals the Helmholtz.
应变能密度函数等于亥姆霍兹函数。
The generalized Helmholtz's equation is solved by the dyadic method, the analytic expression for dyadic Green's function of the equation is given combining with Fourier's transformation, theorem of residues, etc.
运用并矢法求解广义Helmholtz方程，结合Fourier变换、留数定理等数学处理，给出方程的并矢Green函数解析表达式；
First, in virtual of identification of flaws is a typical of inverse problems, proceeding from time-harmonic electromagnetic Maxwell's equation and Helmholtz equation, the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given. Second, the uniqueness and existence of inverse scattering problems and the theory of ill-posed integral equation are briefly looked back upon. Finally, indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects, meanwhile, the proof of possibility for near-field measurements and numerical simulation are given.
由于缺陷的识别是一类典型的反问题，因而首先从时谐电磁Maxwell方程和Helmholtz方程出发，具体地阐述了求解的存在性唯一性；随后对逆散射问题的理论作了简短的回顾，包括解的唯一性以及非线性不适定积分方程的处理等；然后对均匀介质和非均匀介质的逆散射问题建立了在各种边界条件下的边界识别的指示函数方法，鉴于近场数据获得的重要性，对近场测试时边界识别的方法给予了相应的证明，并且实现了数值模拟。
First, in virtual of identification of flaws is a typical of in-verse problems, proceeding from time-harmonic electromagnetic Maxwell's equa-tion and Helmholtz equation, the uniqueness and existence of direct scattering problems including the numerical algorithms of diverse of boundary conditions is given. Second, the uniqueness and existence of inverse scattering problems and the theory of ill-posed integral equation are briefly looked back upon. Finally, indicator function method for boundary identification is set up under all kinds of boundary conditions for inverse scattering of homogenous and inhomogenous objects, meanwhile, the proof of possibility for near-field measurements and nu-merical simulation are given.
由于缺陷的识别是一类典型的反问题，因而首先从时谐电磁Maxwell方程和Helmholz方程出发，具体地阐述了求解正散射问题的有关方法，包括各种边界条件下的数值解法，就解的存在性唯一性给予了肯定的回答；随后对逆散射问题的理论作了简短的回顾，包括解的唯一性以及非线性不适定积分方程的处理等；然后对均匀介质和非均匀介质的逆散射问题建立了在各种边界条件下的边界识别的指示函数方法，鉴于近场数据获得的重要性，对近场测试时边界识别的方法给予了相应的证明，并且实现了数值模拟。
A mixing Helmholtz function model based on Flory - Huggins lattice
Flory-Huggins格子上的混合亥氏函数模型