# 物理代写|光学代写Optics代考|ECOC 2022

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础
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## 物理代写|光学代写Optics代考|Free Energy in the Presence of an Applied Field

In the presence of an externally applied field (e.g. dc or low-frequency electric, magnetic, or optical electric field), a corresponding interaction term should be added to the free energy.
For an applied magnetic field $H$, the energy associated with it is
$$F_{\text {int }}=-\int_{0}^{H} \mathbf{M} \cdot d \mathbf{H}$$

where $\mathbf{M}$ is the magnetization given by
$$M_{\alpha}=\sum_{\beta} \chi_{\alpha \beta} H_{\beta}$$
Thus
$$F_{\mathrm{int}}=-\frac{1}{2} \sum_{\alpha} \chi_{a \beta}^{m} H_{\beta} H_{a}$$
Using Eq. (2.9), we can rewrite $F_{\text {int }}$ as
$$F_{\text {int }}=-\frac{1}{2} \chi_{\perp}^{m} \sum_{\alpha} H_{\alpha} H_{\beta}-\frac{1}{2} \sum_{\alpha, \beta} \Delta \chi^{m} n_{\alpha} n_{\beta} H_{\alpha} H_{\beta} .$$
The first term on the right-hand side of Eq. (2.28) is independent of the orientation of the (anisotropic) molecules, and it can therefore be included in the constant $F_{0}$.

## 物理代写|光学代写Optics代考|The Vector Field: Director Axis

In elastic continuum theory, introduced and refined over the last several decades by several workers [1-3], nematics is basically viewed as crystalline in form. An aligned sample may thus be regarded as a single crystal in which the molecules are, on average, aligned along the direction defined by the director axis $\hat{n}(\vec{r})$.
The crystal is uniaxial and is characterized by a tensorial order parameter:
$$S_{\alpha \beta}=S(\mathrm{~T})\left(n_{\alpha} n_{\beta}-\frac{1}{3} \delta_{\alpha \beta}\right) .$$
As a result of externally applied fields, stresses/constraints from the boundary surfaces, the director will also vary spatially. The characteristic length over which significant variation in the order parameter will occur, in most cases, is much larger than the molecular size. Typically, for distortions of the form shown in Figure 3.1a-c, the characteristic length is on the order of $1 \mu \mathrm{m}$, whereas the molecular dimension is on the order of at most a few tens of angstroms. Under this circumstance, as in other similar systems or media (e.g. ferromagnets), the continuum theory is valid.

The first principle of continuum theory, therefore, neglects the details of the molecular structures. Liquid crystal molecules are viewed as rigid rods; their entire collective behavior may be described in terms of the director axis $\hat{n}(\vec{r})$, a vector field. In this picture, the spatial variation of the order parameter is described by
$$S_{\alpha \beta}(\vec{r})=S(T)\left[n_{\alpha}(\vec{r}) n_{\beta}(\vec{r})-\frac{1}{3} \delta_{\alpha \beta}\right] .$$

# 光学代考

## 物理代写|光学代写Optics代考|Free Energy in the Presence of an Applied Field

$$F_{\text {int }}=-\int_{0}^{H} \mathbf{M} \cdot d \mathbf{H}$$

$$M_{\alpha}=\sum_{\beta} \chi_{\alpha \beta} H_{\beta}$$

$$F_{\text {int }}=-\frac{1}{2} \sum_{\alpha} \chi_{a \beta}^{m} H_{\beta} H_{a}$$

$$F_{\text {int }}=-\frac{1}{2} \chi_{\perp}^{m} \sum_{\alpha} H_{\alpha} H_{\beta}-\frac{1}{2} \sum_{\alpha, \beta} \Delta \chi^{m} n_{\alpha} n_{\beta} H_{\alpha} H_{\beta} .$$

## 物理代写|光学代写Optics代考|The Vector Field: Director Axis

$$S_{\alpha \beta}=S(\mathrm{~T})\left(n_{\alpha} n_{\beta}-\frac{1}{3} \delta_{\alpha \beta}\right) .$$

$$S_{\alpha \beta}(\vec{r})=S(T)\left[n_{\alpha}(\vec{r}) n_{\beta}(\vec{r})-\frac{1}{3} \delta_{\alpha \beta}\right]$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

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