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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
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 物理代写|光学代写Optics代考|Twist and Conic Mode Relaxation Times

When the applied field is abruptly turned off, the relaxation constants depend on the kind of deformation involved. There are two distinct forms of deformation: the pure twist one discussed previously and the so-called umbrella or conic mode [1]. The first form of deformation involves fluid motion, whereas the latter does not.

The dynamics of the field-induced twist deformation in cholesterics is described by an equation analogous to the equation for nematics:
$$\gamma_1 \frac{\partial \phi}{\partial t}-K_2 \frac{d^2 \phi}{d z^2}-\Delta \chi^m H^2 \sin \phi \cos \phi=0$$
The dynamical equation for the conic distortion is much more complicated [4,5] and involves the other two elastic constants $K_3$ and $K_1$.
The corresponding relaxation times are as follows:
$$\tau_{\text {twist }}=\frac{\gamma_1}{K_2 q^2},$$
for the twist mode, and
$$\tau_{\text {conic }}=\frac{\gamma_1}{K_3 q_0^2 K_1 q^2},$$
for the conic mode, where $\vec{q}$ is the wave vector characterizing the wave vector distortion. These relaxation times are modified if an externally applied bias field is present, and they depend on the field and director axis configurations [5].

## 物理代写|光学代写Optics代考|Bragg Regime

Consider a right-handed helix whose pitch is on the order of the optical wavelength, as depicted in Figure 4.3. A normally incident right-circularly polarized light will be reflected as a right circularly polarized light, as the optical field follows the director axis rotation; that is, it follows the helix. (Note that the right-handed or left-handed circular polarization is defined by an observer looking at the incoming light).
Under the Bragg condition:
$$\frac{2 \pi}{q_0}=\lambda$$
the reflection is total, and there is no transmission.
On the other hand, an incident left circularly polarized light will be totally transmitted (see Figure 4.3b). In the case of oblique incidence, similar analysis shows that higher-order diffractions are possible. The Bragg diffraction becomes:
$$p_0 \cos \gamma=m \lambda \quad m=1,2,3$$
where $\gamma$ is the angle of the refracted light in the CLC. In this case, the polarization states are elliptical.
We shall now examine light propagation in CLC in greater detail.

# 光学代考

## 物理代写|光学代写Optics代考|Twist and Conic Mode Relaxation Times

$$\gamma_1 \frac{\partial \phi}{\partial t}-K_2 \frac{d^2 \phi}{d z^2}-\Delta \chi^m H^2 \sin \phi \cos \phi=0$$

$$\tau_{\text {twist }}=\frac{\gamma_1}{K_2 q^2},$$

$$\tau_{\text {conic }}=\frac{\gamma_1}{K_3 q_0^2 K_1 q^2},$$

## 物理代写|光学代写Optics代考|Bragg Regime

$$\frac{2 \pi}{q_0}=\lambda$$

$$p_0 \cos \gamma=m \lambda \quad m=1,2,3$$

## 有限元方法代写

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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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