### 物理代写|光学代写Optics代考|PHS 2062

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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|Lyotropic Liquid Crystals

Lyotropic liquid crystals are obtained when an appropriate concentration of material is dissolved in some solvent. The most common systems are those formed by water and amphiphilic molecules (molecules that possess a hydrophilic part that interacts strongly with water and a hydrophobic part that is water insoluble) such as soaps, detergents, and lipids. Here the most important variable controlling the existence of the liquid crystalline phase is the amount of solvent (or concentration). There are quite a number of phases observed in such water-amphiphilic systems, as the composition and temperature are varied; some appear as spherical micelles, and others possess ordered structures with 1-, 2-, or 3 – $\mathrm{D}$ positional order.

Examples of these kinds of molecules are soaps (Figure 1.8) and various phospholipids like those present in cell membranes. Lyotropic liquid crystals are of interest in biological studies [7].

Polymeric liquid crystals are basically the polymer versions of the monomers discussed in Section 1.1. A good account of polymeric liquid crystals may be found in [9]. There are three common types of polymers, as shown in Figure $1.9 \mathrm{a}-\mathrm{c}$, which are characterized by the degree of flexibility. The vinyl type (Figure $1.9 \mathrm{a}$ ) is the most flexible, the Dupont Kevlar polymer (Figure 1.9b) is semirigid, and the polypeptide chain (Figure $1.9 \mathrm{c}$ ) is the most rigid. Mesogenic (or liquid crystalline) polymers are classified in accordance with the molecular architectural arrangement of the mesogenic monomer. Main-chain polymers are built by linking rigid mesogenic groups in a manner depicted schematically in Figure $1.10$; the link may be a direct bond or some flexible spacer. Liquid crystal side-chain polymers are formed by pendant side attachment of mesogenic monomers to a conventional polymeric chain, as depicted in Figure 1.10b.

## 物理代写|光学代写Optics代考|Thermotropic Liquid Crystals: Smectic, Nematic, Cholesteric

Although the molecular structures of thermotropic liquid crystals are quite complicated, they are often represented as “rigid rods” that interact with one another to form distinctive ordered structures (or phases) as a function of ascending temperature: crystals, smectic, nematic, cholesteric (including blue-phase), and the isotropic liquid phase. In smectic liquid crystals, there are several subclassifications in accordance with the positional and directional arrangement of the molecules.

As explained in greater detail in the following chapters, these mesophases are defined and characterized by many physical parameters such as long- and shortrange order, orientational distribution functions, and so on. Here we continue to use the rigid-rod model and pictorially describe these phases in terms of their molecularr arrangement.

Figure 1.11a depicts the collective arrangement of the rodlike molecules in the nematic phase schematically. These molecules are, however, directionally correlated; they are aligned in a general direction défined by a unit vector $n$, the so-called director axis, which may be regarded as the crystal axis. Nevertheless, the molecules are positionally random and exhibit flow very much like liquids; X-ray diffraction from nematics does not exhibit any diffraction peak.

Although individual molecules of nematic liquid crystal (NLC), cholesteric liquid crystal (CLC), and blue-phase liquid crystal (BPLC) may be polar, i.e. carry a permanent dipole, they tend to self-assemble themselves in such a manner that bulk liquid crystals are centrosymmetric, cf. Figure 1.12; their physical properties are the same in the $+\hat{n}$ and the optically uniaxial $-\hat{n}$ directions.

Cholesteric liquid crystals, often also called chiral nematic liquid crystals, resemble nematic liquid crystals except that the molecules assembled in a helical manner, as depicted in Figure 1.11. This property results from the addition of chiral agents to nematic constituents in the starting mixture. Owing to the spatially (helical) varying refractive index, CLCs possess special optical properties such as photonic bandgaps for transmission of circularly polarized lights. More details on CLC as well as cholesteric BPLCs obtained by increasing the concentration of the chiral constituent $[10]$ in the starting mixture are presented in Chapter 4 .

## 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。