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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写光学Optics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写光学Optics代写方面经验极为丰富，各种代写光学Optics相关的作业也就用不着说。

• 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|MOLECULAR THEORIES AND RESULTS

Among the various theories developed to describe the order parameter and phase transitions in the liquid crystalline phase, the most popular and successful one is the theory first advanced by Maier and Saupe and corroborated in studies by others [8]. In this formalism, Coulombic intermolecular dipole-dipole interactions are assumed. The interaction energy of a molecule with its surroundings is then shown to be of the form [6]:
$$W_{\text {int }}=-\frac{A}{V^{2}} S\left(\frac{3}{2} \cos ^{2} \theta-1\right),$$
where $V$ is the molar volume $(V=M / p), S$ is the order parameter, and $A$ is a constant determined by the transition moments of the molecules. Both $V$ and $S$ are functions of temperature. Comparing Eqs. (2.11) and (2.1) for the definition of $S$, we note that $W_{\text {int }} \approx S^{2}$, so this mean-field theory by Maier and Saupe is often referred to as the $S^{2}$ interaction theory [1]. This interaction energy is included in the free enthalpy per molecule (chemical potential) and is used in conjunction with an angular distribution function $f(\theta, \phi)$ for statistical mechanics calculations.

## 物理代写|光学代写Optics代考|Nonequilibrium and Dynamical Dependence of the Order Parameter

While the equilibrium statistical mechanics of the nematic liquid crystal order parameter and related physical properties near $T_{c}$ are now well understood, the dynamical responses of the order parameter remain relatively unexplored. This is probably due to the fact that most studies of the order parameter near the phase transition point, such as the critical exponent, changes in molar volume, and other physical parameters, are directed at understanding the phase transition processes themselves and are usually performed with temperature changes occurring at very slow rates.

The temperature of the nematics can be abruptly raised by very short laser pulses $[11,12]$. The pulse duration of the laser is in the nanosecond or picosecond time scale, which, as we shall see, is much shorter than the response time of the order parameter. As a result, the nematic film under study exhibits delayed signals.
Figure $2.3 \mathrm{a}$ and $\mathrm{b}$ shows the observed diffraction from a nematic film in a dynamic grating experiment [11]. As explained in more detail in Chapter 9 , the diffracted signal is a measure of the dynamical change in the refractive index, $\Delta n(t)$,following an instantaneous (delta function like) pump pulse.

# 光学代考

## 物理代写|光学代写Optics代考|MOLECULAR THEORIES AND RESULTS

$$W_{\text {int }}=-\frac{A}{V^{2}} S\left(\frac{3}{2} \cos ^{2} \theta-1\right),$$

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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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师