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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|空气动力学代写Aerodynamics代考|Modern Topics

Hitherto, we have given the summary of so called classical and conventional aerodynamics. Starting from 1970’s, somewhat unconventional analyses based on numerical methods and high tech experimental techniques have been introduced in the literature to study the effect of leading edge separation on the very high lifting wings or on unsteady studies for generating propulsion or power extraction. Under the title of modern topics we will be studying (i) vortex lift, (ii) different sorts of wing rock, and (iii) flapping wing aerodynamics.
(i) Vortex lift: The additional lift generated by the sharp leading edge separation of highly swept wings at high angles of attack is called the vortex lift. This additional lift is calculated with the leading edge suction analogy and introduced by Polhamus, (Polhamus 1971). This theory which is also validated by experiments is named Polhamus theory for the low aspect ratio delta wings.

Now, let us analyze the generation of vortex lift with the aid of Fig. 1.10. According to the potential theory, the sectional lifting force was given in terms of the product of the density, free stream speed and bound circulation as in Eq. 1.1. We can resolve the lifting force into its chord wise component $S$ and the normal component $N$. Here, $S$ is the suction force generated by the leading edge portion of the upper surface of the airfoil. Accordingly, if the angle of attack is $\alpha$ then the suction force $S=\rho U \Gamma \sin \alpha$. Now, let us denote the effective circulation and the effective span of the delta wing, shown in Fig. $1.11, \Gamma$ and h respectively. Here, we define the effective span as the length when multiplied with the average sectional lift that gives the total lifting force of the wing. This way, the total suction force of the wing becomes as simple as S.h. Because of wing being finite, there is an induced drag force which opposes the leading edge suction force of the wing.

## 物理代写|空气动力学代写Aerodynamics代考|Boundary Conditions

Equation $2.15$ as a fundamental equation is solved with the proper boundary conditions. In general the external flow problems will be studied. Therefore, we need to impose the boundary conditions accordingly as follows.
(i) At infinity, all disturbances must die out and only free stream conditions prevail.
(ii) The time dependent boundary conditions at the body surface must be given as the time dependent motion of the body.

The equation of a surface for a 3-D moving body in Cartesian coordinate system is given as follows

$$B(x, y, z, t)=0$$
Let us take the material derivative of this surface in the flow field $\mathbf{q}=u \mathbf{i}+v \mathbf{j}+w \mathbf{k}$.
$$\frac{D B}{D t}-\frac{\partial B}{\partial t}+u \frac{\partial B}{\partial x}+v \frac{\partial B}{\partial y}+w \frac{\partial B}{\partial z}-0$$
For the steady flow it simplifies to
$$u \frac{\partial B}{\partial x}+v \frac{\partial B}{\partial y}+w \frac{\partial B}{\partial z}=0$$
The external flows studied here require to find the pressure distribution at the lower and upper surfaces of the body immersed in a free stream. For this purpose, we need to know the upper and lower surface equations of a body in a free stream in $\mathrm{x}$ direction. If we show the direction normal to the flow with $\mathrm{z}$, then the single valued surface equation, with the aid of Eq. 2.16, reads as
$$B(x, y, z, t)=z-z_a(x, y, t)=0$$

# 空气动力学代考

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## 物理代写|空气动力学代写空气动力学代考|边界条件

(i)在无穷远处，所有的扰动都必须消失，只有自由流条件存在。
(ii)体表与时间相关的边界条件必须给定为体表与时间相关的运动。 . (i)在无穷远处，所有的扰动都必须消失，只有自由流条件存在

$$B(x, y, z, t)=0$$

$$\frac{D B}{D t}-\frac{\partial B}{\partial t}+u \frac{\partial B}{\partial x}+v \frac{\partial B}{\partial y}+w \frac{\partial B}{\partial z}-0$$

$$u \frac{\partial B}{\partial x}+v \frac{\partial B}{\partial y}+w \frac{\partial B}{\partial z}=0$$

$$B(x, y, z, t)=z-z_a(x, y, t)=0$$

## 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。

assignmentutor™您的专属作业导师
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