本文给出一个三维标量场和向量场的视觉化方法。
A unified visualization method is presented for 3d scalar and vector fields.
对于纯标量场，存在零能量束缚态，存在分数电荷。
For a pure scalar potential the zero energy bound state does exist, and the fractional charge does exist.
对被动标量场的研究是当前湍流研究中的一个热点。
Since the 1980s, studies of passive scalar have been one of hotspots in turbulence research.
他们的解析解法对我们寻求标量场方程的解析解有着重要的启发意义。
This method is helpful for us to find the way of the analytic solution of scalar field equation.
早期的自聚焦研究是在考虑了傍轴近似和标量场近似的前提下得到的。
The early research was based on the scalar approximation and paraxial approximation.
三维标量场可视化技术不仅可以绘制等值面，而且可以模拟X线的透射效果。
Visualization techniques for 3D scalar fields can be used to display constant value surfaces as well as to simulate transmission effect of X-ray.
将标量场视为矢量场的一种特例，从亥姆霍兹定理出发导出标量场的唯一性条件。
Starting from Helmholtz's theorem, the uniqueness conditions of scalar field are obtained based on the fact that the scalar field can be regarded as a special example of vector field.
被动标量场的统计性质，在湍流理论以及湍流燃烧、污染物防治等工程领域都有非常重要的意义。
The passive scalar statistics are important in turbulence theories and engineering problems related to turbulent combustion, pollutant diffusion and others.
在论文的第一章，简单地介绍了黑洞的形成、视界的概念、黑洞的热性质以及黑洞辐射和标量场辐射等基础知识。
In the first chapters, the concepts of black hole and the event horizon, black hole radiation, the thermal properties of black hole, and scalar field radiation are introduced briefly.
针对庞大复杂的海洋数据流场，利用三维标量场的拓扑分析方法，对海洋目标水团进行提取，达到特征可视化的目的。
This paper introduces a topological simplification of 3d scalar fields for extracting water mass, and realizes the feature-based visualization.
空间中的向量场的旋度，是一个向量场，而不是一个标量函数，我必须告诉你们。
The curl of a vector field in space is actually a vector field, not a scalar function. I have delayed the inevitable.
文章主要描述了一个从标量和矢量场进行表面抽取的通用方法。
This paper mainly describes a universal method for extracting surface from scalar and vector fields.
证明了规范场不仅沿入射电子在复连通区域运动路径的积分，而且还可沿入射标量或其他旋量粒子之一在复连通区域的运动路径积分，各自都将贡献一几何相因子。
It is justified that the integral of the gauge potential along path of not only electron but also scalar particle or spinor particle will contribute a geometric phase factor.
其与形态生成场域标量栅格的几何结构的连结，使之能够与其扬升大师层面维持通讯管道。
It is the connection of the geometrical structures of the morphogenetic field scalar grids that allows for a being to attain a conduit of communication with its ascended mastery identity levels.
本文给出了平场输入和输出edg的设计方法，并利用标量衍射理论对设计的结果进行模拟，验证了平场输出EDG具有很好的分波效果。
The scalar diffraction theory is used to verify the design and the numerical results show that the designed EDG has a good performance.
根据光波导理论，推算出弱导条件下光沿光纤传输场的标量近似解，给出场的各分量表达式，以便分析讨论。
Using wave guide theory, we deduce scalar approximate solution about transmissive light through a fiber weak-guide and give the expressions of field in each component.
利用标量衍射理论，对相干光学系统中光场进行空间追踪模拟，该方法可以对光学系统中激光光场的分布进行预。
In this paper, based on scalar diffraction theory, light fields in the coherent optics system have been calculated by the spatial tracing simulation method that USES FFT.
本文采用直接数值模拟的方法，研究了颗粒惯性对均匀各向同性湍流场中被动标量混合特性的影响。
The influence of partial inertia on scalar mixing in homogeneous isotropic turbulent flows was studied using a direct numerical simulation (DNS) method.
还有计算了在弱场条件近似下引力驻波的能量密度，并给出曲率标量R和能量密度平面的数值计算。
Besides that, we presents the gravitational wave energy density under the weak field situation and gives the x - y plane numerical calculation to curvature scalar R and energy density .
在第四章，根据标量衍射理论，首先讨论了两平面波干涉场的空间分布与平行投影正弦光栅的等价性。
In chapter 4, According to the theory of scalar diffraction, firstly, the equipollence of spatial distribution of the plane-wave interferential field and parallel projective sine grating is discussed.
本文根据标量波动方程，导出了色散公式及波导色散和模场直径间的关系。
In this paper, the relation between the dipersion formula, the waveguide dipersion and the mode field diameter is derived, based on the scale wave equation.
本文根据标量波动方程，导出了色散公式及波导色散和模场直径间的关系。
In this paper, the relation between the dipersion formula, the waveguide dipersion and the mode field diameter is derived, based on the scale wave equation.
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