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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|流体力学代写Fluid Mechanics代考|Material Description

Engineering fluid dynamic design process has been experiencing a continuous progress using the Computational Fluid Dynamics (CFD) tools. The use of CFD-tools opens a new perspective in simulating the complex three-dimensional (3-D) engineering flow fields. Understanding the details of the flow motion and the interpretation of the numerical results require a thorough comprehension of fluid mechanics laws and the kinematics of fluid motion. Kinematics is treated in many fluid mechanics texts. Aris [13] and Spurk [14] give an excellent account of the subject. In the following sections, a compact and illustrative treatment is given to cover the needs of engineers.
The kinematics is the description of the fluid motion and the particles without taking into account how the motion is brought about. It disregards the forces that cause the fluid motion. As a result, in the context of kinematics, no conservation laws of motion will be dealt with. Consequently, the results of kinematic studies can be applied to all types of fluids and exhibit the ground work that is necessary for describing the dynamics of the fluid. The motion of a fluid particle with respect to a reference coordinate system is in general given by a time dependent position vector $\mathbf{x}(\mathbf{t})$, Fig. $3.1$

To identify the motion of a particle or a material point labeled as $\xi^{1}$ at a certain instance of time $t=t_{0}=0$, we introduce the position vector $\xi=\boldsymbol{x}\left(t_{0}\right)$. Thus, the motion of the fluid is described by the vector:
$$\boldsymbol{x}=\boldsymbol{x}\left(\boldsymbol{\xi}, t, x_{i}=x_{i}(\xi, t)\right.$$
with $x_{i}$ as the components of vector $\boldsymbol{x}$, as explained in Chap. 2. Equation (3.1) describes the path of a material point that has an initial position vector $\xi$ that characterizes or better labels the material point at $t=t_{0}$. We refer to this description as the material description also called Lagrangian description.

## 物理代写|流体力学代写Fluid Mechanics代考|Spatial Description

The material description we discussed in the previous section deals with the motion of the individual particles of a continuum, and is used in continuum mechanics. In fluid dynamics, we are primarily interested in determining the flow quantities such as velocity, acceleration, density, temperature, pressure, and etc., at fixed points in space. For example, determining the three-dimensional distribution of temperature, pressure and shear stress helps engineers design turbines, compressors, combustion engines, etc. with higher efficiencies. For this purpose, we introduce the spatial description, which is also called the Euler description. The independent variables for the spatial descriptions are the space characterized by the position vector $\boldsymbol{x}$ and the time $t$. Consider the transformation of Eq. (3.1), where $\xi$ is solved in terms of $x$ :
$$\boldsymbol{\xi}=\boldsymbol{\xi}(\boldsymbol{x}, t), \xi_{i}=\xi_{i}\left(x_{j}, t\right)$$
The position vector $\boldsymbol{\xi}$ in the velocity of the material element $\boldsymbol{V}(\boldsymbol{\xi}, t)$ is replaced by Eq. (3.24):
$$\boldsymbol{V}(\boldsymbol{\xi}, t)=\boldsymbol{V}[\boldsymbol{\xi}(\boldsymbol{x}, t), t]=\boldsymbol{V}(\boldsymbol{x}, t) .$$
For a fixed $\boldsymbol{x}$, Eq. (3.25) exhibits the velocity at the spatially fixed position $\boldsymbol{x}$ as a function of time. On the other hand, for a fixed $t$, Eq. (3.25) describes the velocity at the time $t$. With Eq. (3.25), any quantity described in spatial coordinates can be transformed into material coordinates provided the Jacobian transformation function $J$, which we discussed in the previous section, does not vanish. If the velocity is known in a spatial coordinate system, the path of the particle can be determined as the integral solution of the differential equation with the initial condition $x\left(t_{0}\right)$ along the path $\boldsymbol{x}=\boldsymbol{x}(\xi, t)$ from the following relation:
$$\frac{d \boldsymbol{x}}{d t}-\boldsymbol{V}(\boldsymbol{x}, t), \frac{d x_{i}}{d t}-V_{i}\left(x_{j}, t\right) .$$

# 力学代考

## 物理代写|流体力学代写Fluid Mechanics代考|Material Description

$$\boldsymbol{x}=\boldsymbol{x}\left(\boldsymbol{\xi}, t, x_{i}=x_{i}(\xi, t)\right.$$

## 物理代写|流体力学代写Fluid Mechanics代考|Spatial Description

$$\boldsymbol{\xi}=\boldsymbol{\xi}(\boldsymbol{x}, t), \xi_{i}=\xi_{i}\left(x_{j}, t\right)$$

$$\boldsymbol{V}(\boldsymbol{\xi}, t)=\boldsymbol{V}[\boldsymbol{\xi}(\boldsymbol{x}, t), t]=\boldsymbol{V}(\boldsymbol{x}, t)$$

$$\frac{d \boldsymbol{x}}{d t}-\boldsymbol{V}(\boldsymbol{x}, t), \frac{d x_{i}}{d t}-V_{i}\left(x_{j}, t\right) .$$

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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
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