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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|统计物理代写Statistical Physics of Matter代考|Thermodynamic Properties of Water

Liquid water has many properties that are distinct from other liquids. One of water’s most well-known anomalies is that it expands when cooled, contrary to ordinary liquids. At atmospheric pressure, when ice melts to form liquid water at $0^{\circ} \mathrm{C}$, the density increases discontinuously, and then the liquid density continues to increase until it reaches a maximum at $4^{\circ} \mathrm{C}$ (Fig. 6.1a). This behavior leads to a well-known consequence that a lake freezes top-down from the surface, on which the ice floats, whereas the bottom of the lake remains at $4{ }^{\circ} \mathrm{C}$. Children skate on the icy surface while fishes swim over the watery bottom.

The phase diagram (Fig. 6.1b) shows how the ice, vapor, and water liquid phases exist as functions of temperature $T$ and pressure $p$. The curved solid lines indicate coexistence of the different phases at equilibrium. They meet at the triple point (about $0.01{ }^{\circ} \mathrm{C}$ and $0.008$ atmospheric pressure (atm)), where the three phases coexist. The coexistence line of liquid and vapor terminates at the critical point $(T=378 \mathrm{~K}, p=218 \mathrm{~atm})$. Near this point the interfaces of coexisting liquid and vapor become unstable and fluctuate widely. showing a variety of divergent response behaviors called the critical phenomena. The critical phenomena that occur in diverse matter have been one of central problems in modern statistical physics, but are beyond the scope of this book.

In Fig. 6.1b each of phase-coexistence (solid) lines is given by the Clausius-Clapeyron equation
$$\frac{d p}{d T}=\frac{\Delta s}{\Delta v}$$

物理代写|统计物理代写Statistical Physics of Matter代考|The Interactions in Water

The remarkable properties of water discussed above derive from its unique molecular structure, and to hydrogen bonding (HB) among water molecules. In a water molecule an oxygen atom is covalent-bonded with two hydrogen atoms by sharing electrons. But the oxygen atom has much greater affinity for electrons than the hydrogen atoms, making the molecule polar with a high dipole moment (Fig. 6.2a). HB is the electrostatic attraction between hydrogen containing polar molecules in which electropositive hydrogen in one molecule is attracted to an electronegative atom such as oxygen in another molecule nearby (Fig. 6.2b).
The HB in water has strength of a few $\mathrm{kJ} /$ mole, which is much weaker than covalent or ionic bonds, but much stronger than the generic (non-HB) bonds between small molecules. This is the reason why the heat of vaporization, boiling point, and surface tension are relatively high in water. Furthermore, in water, HB forms a network with large orientation fluctuations of the molecules that can be correlated over a long range. The large fluctuations and long-range correlation hint at water’s high response functions (susceptibilities) such as high dielectric constant and high heat capacity, somewhat likened to the phenomena near the critical point. HBs occur in both inorganic molecules and biopolymers like DNA and proteins.

统计物理代考

物理代写|统计物理代写Statistical Physics of Matter代考|Thermodynamic Properties of Water

$$\frac{d p}{d T}=\frac{\Delta s}{\Delta v}$$

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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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