## 物理代写|核物理代写nuclear physics代考|PHYS585

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear physics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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|核物理代写nuclear physics代考|Hyperfine Structure

The magnetic moment (vector) of a nucleus is proportional to its spin and is given by
$$\tilde{\boldsymbol{\mu}}_N=g_I \frac{\mu_N}{\hbar} \boldsymbol{I},$$
where $\mu_N$ is the nuclear magneton (4.6), $g_I$ is the nuclear $\mathrm{g}$-factor ${ }^3$ and $\boldsymbol{I}$ is the nuclear spin vector.
The magnetic moment of the atomic electrons is (analogously)
$$\tilde{\boldsymbol{\mu}}_e=g_J \frac{\mu_e}{\hbar} \boldsymbol{J},$$
where $\mu_e$ is the Bohr magneton
$$\mu_e \equiv \frac{e \hbar}{2 m_e} \text {, }$$
where $g_J$ is the atomic $\mathrm{g}$-factor, and $\boldsymbol{J}$ is the total electron angular momentum vector.

These two magnetic moments interact with each other, generating a hyperfine energy shift,

$$\Delta E_{\mathrm{hf}}=\frac{\mu_0}{4 \pi} \tilde{\boldsymbol{\mu}}N \cdot \tilde{\boldsymbol{\mu}}_e\left\langle\frac{1}{r_a^3}\right\rangle=\frac{\mu_0}{4 \pi \hbar^2} g_1 g_J \mu_N \mu_e \boldsymbol{I} \cdot \boldsymbol{J}\left\langle\frac{1}{r_a^3}\right\rangle,$$ where $\mu_0\left(=1 / \epsilon_0 c^2\right)$ is the permeability of the vacuum, and $r_a$ is the radial distance of the electrons from the nucleus. The nuclear and electron angular momenta combine to produce a total angular momentum with quantum number $F$, which takes possible values $$|I-J| \leq F \leq I+J,$$ and using the fact that the entire atomic state is in a simultaneous eigenstate of the operators $F^2, I^2$ and $J^2$ with eigenvalues $F(F+1) \hbar^2, I(I+1) \hbar^2$ and $J(J+1) \hbar^2$, respectively, we may write $$\boldsymbol{I} \cdot \boldsymbol{J}=\frac{\hbar^2}{2}(F(F+1)-I(I+1)-J(J+1)),$$ such that the hyperfine energy shift, $\Delta E{\mathrm{hf}}$, is
\begin{aligned} \Delta E_{\mathrm{hf}} &=\frac{\mu_0}{4 \pi} \frac{1}{2} g_I g_J \mu_N \mu_e\left\langle\frac{1}{r_a^3}\right\rangle(F(F+1)-I(I+1)-J(J+1)) \ &=\frac{\alpha}{2} g_I g_j \frac{\hbar^2}{m_p m_e c}\left\langle\frac{1}{r_a^3}\right\rangle(F(F+1)-I(I+1)-J(J+1)) \end{aligned}

## 物理代写|核物理代写nuclear physics代考|Isomeric Shift

The wavefunctions for electrons in an $s$-wave $(\ell=0)$ do not vanish at the origin, $\Psi(0) \neq 0$. This means that $s$-wave electrons have a small but non-zero probability of being inside the nucleus. When this is the case, the electrostatic potential between the nucleus and these electrons is smaller than that obtained by treating the nucleus as a point particle. It was pointed out by Richard Weiner [64] that since the effective volume of the nucleus is different for different excited states, this would lead to a

small correction to the energy of the $\gamma$-ray emitted in the transition between two nuclear states.

The shift in energy of a state due to the non-zero volume of a nucleus with charge density $\rho(\mathrm{r})$, interacting with an electron whose wavefunction is $\Psi_e(\boldsymbol{r})$, is given by
$$\Delta E_{\mathrm{vol}}=\frac{e^2}{4 \pi \varepsilon_0} \int d^3 \boldsymbol{r} \int d^3 \boldsymbol{r}^{\prime}\left|\Psi_e(\boldsymbol{r})\right|^2 \rho\left(\boldsymbol{r}^{\prime}\right)\left[\frac{1}{\left|\boldsymbol{r}-\boldsymbol{r}^{\prime}\right|}-\frac{1}{|\boldsymbol{r}|}\right]$$
Assuming that the nuclear charge density is spherically symmetric, as well as the $s$-wave electron wavefunctions, the angular integration in (8.14) can be performed to give
$$\Delta E_{\mathrm{vol}}=\frac{4 \pi e^2}{\varepsilon_0} \int r^2 d r\left|\Psi_e(\boldsymbol{r})\right|^2 \int_r^{\infty} d r^{\prime} \rho\left(r^{\prime}\right)\left[r^{\prime}-\frac{r^{\prime 2}}{r} \mid\right.$$
If we treat the nuclear charge density as being uniform inside the nuclear radius, $R$, i.e.
\begin{aligned} \rho(r) &=\frac{3 \angle e}{4 \pi R^3}, \quad(rR), \end{aligned}
the radial integrand is non-zero only for $r<R$. In that region, we can approximate the electron wavefunction by its value at the origin. Radial integration over $r$ and $r^{\prime}$ then gives
$$\Delta E_{\mathrm{vol}}=\frac{4 \pi Z \alpha \hbar c}{10}\left|\Psi_e(0)\right|^2 R^2$$

## 物理代写|核物理代写核物理学代考|超精细结构

$$\tilde{\boldsymbol{\mu}}_N=g_I \frac{\mu_N}{\hbar} \boldsymbol{I},$$

$$\tilde{\boldsymbol{\mu}}_e=g_J \frac{\mu_e}{\hbar} \boldsymbol{J},$$

$$\mu_e \equiv \frac{e \hbar}{2 m_e} \text {, }$$

$$\Delta E_{\mathrm{hf}}=\frac{\mu_0}{4 \pi} \tilde{\boldsymbol{\mu}}N \cdot \tilde{\boldsymbol{\mu}}_e\left\langle\frac{1}{r_a^3}\right\rangle=\frac{\mu_0}{4 \pi \hbar^2} g_1 g_J \mu_N \mu_e \boldsymbol{I} \cdot \boldsymbol{J}\left\langle\frac{1}{r_a^3}\right\rangle,$$ 哪里 $\mu_0\left(=1 / \epsilon_0 c^2\right)$ 真空的磁导率，和 $r_a$ 是电子到原子核的径向距离。原子核的角动量和电子的角动量结合在一起产生一个具有量子数的总角动量 $F$，它接受可能的值 $$|I-J| \leq F \leq I+J,$$ 利用整个原子状态是同时存在的算子的特征态这一事实 $F^2, I^2$ 和 $J^2$ 带有特征值 $F(F+1) \hbar^2, I(I+1) \hbar^2$ 和 $J(J+1) \hbar^2$，分别，我们可以写 $$\boldsymbol{I} \cdot \boldsymbol{J}=\frac{\hbar^2}{2}(F(F+1)-I(I+1)-J(J+1)),$$ 以至于超精细能量转移， $\Delta E{\mathrm{hf}}$，为
\begin{aligned} \Delta E_{\mathrm{hf}} &=\frac{\mu_0}{4 \pi} \frac{1}{2} g_I g_J \mu_N \mu_e\left\langle\frac{1}{r_a^3}\right\rangle(F(F+1)-I(I+1)-J(J+1)) \ &=\frac{\alpha}{2} g_I g_j \frac{\hbar^2}{m_p m_e c}\left\langle\frac{1}{r_a^3}\right\rangle(F(F+1)-I(I+1)-J(J+1)) \end{aligned}

## 物理代写|核物理代写核物理代考|同分异构体移位

$s$ -波$(\ell=0)$中的电子波函数在原点$\Psi(0) \neq 0$处不消失。这意味着$s$ -波电子在原子核内部的概率很小，但非零。在这种情况下，原子核和这些电子之间的静电势比把原子核当作点粒子得到的静电势要小。Richard Weiner[64]指出，由于不同激发态下原子核的有效体积是不同的，这将导致

$$\Delta E_{\mathrm{vol}}=\frac{e^2}{4 \pi \varepsilon_0} \int d^3 \boldsymbol{r} \int d^3 \boldsymbol{r}^{\prime}\left|\Psi_e(\boldsymbol{r})\right|^2 \rho\left(\boldsymbol{r}^{\prime}\right)\left[\frac{1}{\left|\boldsymbol{r}-\boldsymbol{r}^{\prime}\right|}-\frac{1}{|\boldsymbol{r}|}\right]$$

$$\Delta E_{\mathrm{vol}}=\frac{4 \pi e^2}{\varepsilon_0} \int r^2 d r\left|\Psi_e(\boldsymbol{r})\right|^2 \int_r^{\infty} d r^{\prime} \rho\left(r^{\prime}\right)\left[r^{\prime}-\frac{r^{\prime 2}}{r} \mid\right.$$

\begin{aligned} \rho(r) &=\frac{3 \angle e}{4 \pi R^3}, \quad(rR), \end{aligned}
，只有$r<R$的径向被积函数不为零。在这个区域，我们可以用电子波函数在原点处的值近似它。对$r$和$r^{\prime}$的径向积分得到
$$\Delta E_{\mathrm{vol}}=\frac{4 \pi Z \alpha \hbar c}{10}\left|\Psi_e(0)\right|^2 R^2$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|核物理代写nuclear physics代考|PHYS161

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear physics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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|核物理代写nuclear physics代考|Radiation Modes and Selection Rules

As in the case of $\beta$-decay, the emitted photon in $\gamma$-decay can carry off angular momentum $\ell$, which permits a transition between an initial state with spin $I_i$ and a final state with spin $I_f$, provided that angular momentum is conserved, i.e. that the vector sum of $\boldsymbol{I}_f$ and the photon angular momentum, $\boldsymbol{\ell}$, must be equal to $\boldsymbol{I}_i$. The allowed values of $\ell$ are then given by
$$\left|I_i-I_f\right| \leq \ell \leq I_i+I_f .$$
The interactions responsible for $\gamma$-decay are the electromagnetic interactions (as is the case for atomic transitions). There are two types of electromagnetic transitions – electric transitions and magnetic transitions. Electric transitions with angular momentum $\ell=1,2, \ldots$ are denoted by the symbols E1, E2,… They are called “electric $2^l$-pole transitions” – “electric dipole”, “electric quadrupole” etc. Magnetic transitions with angular momentum $\ell=1,2, \ldots$ are denoted by the symbols M1, M2,… They are called “magnetic $2^l$-pole transitions” – “magnetic dipole”, “magnetic quadrupole” etc. The emitted radiation from such transitions is known as “radiation modes”.

Unlike the weak interactions, which mediate $\beta$-decay, the electromagnetic interactions are parity conserving. An electric dipole, $\boldsymbol{d}_E=e \boldsymbol{r}$, is odd under parity transformation so that electric dipole transitions are only permitted between initial and final states of opposite parity. On the other hand, a magnetic dipole is proportional to the spin, $s$, of the nucleon that makes the transition. This is an axial vector and therefore even under parity transformations, implying that magnetic dipole transitions are only permitted between initial and final states of the same parity.

More generally, for an electric transition $\mathrm{E} \ell$, the parities, $\pi$, of the initial and final states are related by
$$\pi_i=(-1)^{\ell} \pi_f,$$
whereas for a magnetic transition $\mathrm{M} \ell$, the parities of the initial and final states are related by
$$\pi_i=(-1)^{(\ell+1)} \pi_f .$$

## 物理代写|核物理代写nuclear physics代考|Decay Rates

The decay rates for different radiation modes were estimated by Victor Weisskopf [63] in 1951. A rigorous calculation of transition rates effected by electromagnetic interactions requires “Quantum Electrodynamics” (QED), but we can obtain the Weisskopf estimate for electric multipole transitions using Fermi’s golden rule (7.50), with the electric interaction Hamiltonian for the emission of a photon with energy $E_\gamma$ obtained from QED
$$H_{E_\gamma}(\boldsymbol{r})=\sqrt{\frac{2 \pi \alpha \hbar^3 c^3}{E_\gamma}} \Psi_{k_\gamma^*}(\boldsymbol{r}),$$
where $\Psi_{k_y}(\boldsymbol{r})$ is the plane-wave wavefunction for the outgoing photon (in a volume $V)$ with wave number $k_\gamma\left(=E_\gamma / \hbar c\right)$. The decay rate for an electric multipole transition $\mathrm{E} \ell$ of a nuclide with atomic mass number $A$ is then given approximately by 1
$$\lambda_{\mathrm{E} l}\left(A, E_\gamma\right) \approx \frac{2 \alpha c}{r_0} \frac{(\ell+1)}{\ell((2 \ell+1) ! !)^2}\left(\frac{3}{\ell+3}\right)^2\left(\frac{r_0 E_\gamma}{\hbar c}\right)^{(2 \ell+1)} A^{2 \ell / 3},$$
where the nuclear radius, $R$, is given by $R=r_0 A^{1 / 3}$.
The estimate of the decay rates for magnetic transitions involves the nuclear spin. We would expect the magnetic interaction Hamiltonian, $H_M$, to be proportional to the magnetic moment of the nucleon which makes the transition. ${ }^2$ Weisskopf estimated that the magnetic interaction Hamiltonian for a nucleus of radius $R$ can be approximated by $$H_M \approx \sqrt{10} \frac{\hbar}{m_p c R} H_{E_Y}$$
with $H_{E_\gamma}$ given by (8.5). The decay rate for magnetic transitions is therefore
$$\lambda_{\mathrm{M} l}\left(A, E_\gamma\right) \approx 20 \frac{\alpha \hbar^2}{r_0^3 m_p^2 c} \frac{(\ell+1)}{\ell((2 \ell+1) ! !)^2}\left(\frac{3}{\ell+3}\right)^2\left(\frac{r_0 E_\gamma}{\hbar c}\right)^{(2 \ell+1)} A^{(2 l-2) / 3} .$$

## 物理代写|核物理代写nuclear physics代考|辐射模式和选择规则

$$\left|I_i-I_f\right| \leq \ell \leq I_i+I_f .$$

“electric quadrupole”等。具有角动量的磁跃迁 $\ell=1,2, \ldots$ 用符号 M1、M2、……表示它们被称为“磁性 $2^l$ 极跃 迁”一一“磁偶极子”、“磁四极子”等。从这种跃迁发出的辐射称为“辐射模式”。

$$\pi_i=(-1)^{\ell} \pi_f,$$

$$\pi_i=(-1)^{(\ell+1)} \pi_f$$

## 物理代写|核物理代写nuclear physics代考|衰减率

$$H_{E_\gamma}(\boldsymbol{r})=\sqrt{\frac{2 \pi \alpha \hbar^3 c^3}{E_\gamma}} \Psi_{k_\gamma^*}(\boldsymbol{r}),$$

$$\lambda_{\mathrm{E} l}\left(A, E_\gamma\right) \approx \frac{2 \alpha c}{r_0} \frac{(\ell+1)}{\ell((2 \ell+1) ! !)^2}\left(\frac{3}{\ell+3}\right)^2\left(\frac{r_0 E_\gamma}{\hbar c}\right)^{(2 \ell+1)} A^{2 \ell / 3},$$

$$H_M \approx \sqrt{10} \frac{\hbar}{m_p c R} H_{E_Y}$$

$$\lambda_{\mathrm{Ml}}\left(A, E_\gamma\right) \approx 20 \frac{\alpha \hbar^2}{r_0^3 m_p^2 c} \frac{(\ell+1)}{\ell((2 \ell+1) ! !)^2}\left(\frac{3}{\ell+3}\right)^2\left(\frac{r_0 E_\gamma}{\hbar c}\right)^{(2 \ell+1)} A^{(2 l-2) / 3} .$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|核物理代写nuclear physics代考|PHYSICS404

statistics-lab™ 为您的留学生涯保驾护航 在代写核物理nuclear physics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。我们的专家在代写核物理nuclear physics代写方面经验极为丰富，各种代写核物理nuclear physics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|核物理代写nuclear physics代考|Fermi’s Golden Rule

The approximate expression for the transition rate for a system due to a perturbing potential is known as Fermi’s golden rule, although it was actually first derived by Paul Dirac [62].

If a time-independent perturbing potential, $H^{\prime}$, is applied to a quantum system in a state $|i\rangle$, energy $E_i$, at time, $t=0$, then the amplitude $a_{f i}(t)$ for the system to have made a transition to the state $|f\rangle$, with energy $E_f$, at time $t$ is given by first order time-dependent perturbation theory to be
$$a_{f i}(t)=2 e^{i \eta}\left\langle f\left|H^{\prime}\right| i\right\rangle \frac{\sin \left(\frac{1}{2}\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)},$$
where $\left\langle f\left|H^{\prime}\right| i\right\rangle$ is the matrix element of the perturbing Hamiltonian between the initial state $|i\rangle$ and final state $|f\rangle$, and $\eta$ is a phase.

The probability, $T_{f i}(t)$, for such a transition to have occurred by time $t$, is then
$$T_{f i}(t)=\left|a_{f i}(t)\right|^2=4\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \frac{\sin ^2\left(\frac{1}{2}\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)^2} .$$
The transition rate, $\lambda_{f i}$, is given by the derivative of $T_{f i}$ with respect to time
$$\lambda_{f i}=\frac{2}{\hbar}\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \frac{\sin \left(\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)} .$$
To determine the total transition rate, $\lambda$, to any final state, we sum over all final states $|f\rangle$. Ilowever, if these final states are in a continuum, this discretè sum is replaced by an integral over final-state energy, $E_f$, with a Jacobian factor equal to the density of states, $\rho\left(E_f\right)$-the number of quantum states per unit energy interval. We then obtain
$$\lambda=\frac{2}{\hbar} \int d E_f\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \rho\left(E_f\right) \frac{\sin \left(\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)} .$$

## 物理代写|核物理代写nuclear physics代考|Gamma Decay

The emission of $\gamma$-rays from nuclei is the nuclear analogue of the atomic emission of photons, which occur when an electron makes a transition from an excited state either to a lower excited state or to the atomic ground state. Similarly, $\gamma$-rays are emitted when a nucleus in an excited state makes a transition to a lower state. Atomic excitation energies are typically of the order of a few electron volts ( $\mathrm{eV})$, leading to the emission of photons with wavelengths of hundreds of nanometres encompassing the visible spectrum, whereas nuclear excitations are of the order of hundreds of $\mathrm{KeV}$, emitting $\gamma$-rays with wavelengths of the order of a picometre $(1000 \mathrm{fm})$, although some nuclear excitation energies are less than $100 \mathrm{keV}$, so that the emitted photons are strictly classified as $\mathrm{X}$-rays. In contrast to atomic radiation, $\gamma$-rays are usually described in terms of their energies, $E_\gamma$, rather than their wavelengths.
Most excited states have a very short lifetime – of order $10^{-13}-10^{-10} \mathrm{~s}$. However, there are some excited states which are metastable and therefore have a much longer lifetime. An example of this is the nuclide ${ }_{27}^{58} \mathrm{Co}$, which has a metastable excited state with energy $24.9 \mathrm{keV}$ and half-life of about $9 \mathrm{~h}$. Such excited states are called “nuclear isomers” and their decays are called “isomer transitions” – often abbreviated to IT.

An excited state with decay rate $\lambda$ has a mean lifetime $\tau-1 / \lambda$ (see (5.3)). By Heisenberg’s uncertainty principle, this implies that the energy of the excited state has an uncertainty $\frac{1}{2} \hbar / \tau$, so that the spectral line of an emitted $\gamma$-ray has a halfwidth, $\frac{1}{2} \Gamma_\gamma$, which is equal to that uncertainty. The line-width is therefore given by
$$\Gamma_\gamma=\frac{\hbar}{\tau}=\hbar \lambda .$$

## 物理代写|核物理代写核物理学代考|费米黄金定律

. .

$$a_{f i}(t)=2 e^{i \eta}\left\langle f\left|H^{\prime}\right| i\right\rangle \frac{\sin \left(\frac{1}{2}\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)},$$
，其中$\left\langle f\left|H^{\prime}\right| i\right\rangle$是初始态$|i\rangle$和最终态$|f\rangle$之间的摄动哈密顿量的矩阵元，$\eta$是一个相

$$T_{f i}(t)=\left|a_{f i}(t)\right|^2=4\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \frac{\sin ^2\left(\frac{1}{2}\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)^2} .$$
$\lambda_{f i}$由的导数给出 $T_{f i}$ 关于时间
$$\lambda_{f i}=\frac{2}{\hbar}\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \frac{\sin \left(\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)} .$$

$$\lambda=\frac{2}{\hbar} \int d E_f\left|\left\langle f\left|H^{\prime}\right| i\right\rangle\right|^2 \rho\left(E_f\right) \frac{\sin \left(\left(E_i-E_f\right) t / \hbar\right)}{\left(E_i-E_f\right)} .$$

## 物理代写|核物理代写核物理学代考|伽马衰变

$$\Gamma_\gamma=\frac{\hbar}{\tau}=\hbar \lambda .$$ 给出

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|流体力学代写Fluid Mechanics代考|ENGR30002

statistics-lab™ 为您的留学生涯保驾护航 在代写流体力学Fluid Mechanics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。我们的专家在代写流体力学Fluid Mechanics代写方面经验极为丰富，各种代写流体力学Fluid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Effect of Solidity on Blade Profile Losses

Equation (5.181) exhibits a fundamental relationship between the lift coefficient, the solidity, the inlet and exit flow angle, and the loss coefficient $\zeta$. The question is, how the profile loss $\zeta$ will change if the solidity $\sigma$ changes. The solidity has the major influence on the flow behavior within the blading. If the spacing is too small, the number of blades is large and the friction losses dominate. Increasing the spacing, which is identical to reducing the number of blades, at first causes a reduction of friction losses. Further increasing the spacing decreases the friction losses and also reduces the guidance of the fluid that results in flow separation leading to additional losses. With definite spacing, there is an equilibrium between the separation and friction losses. At this point, the profile loss $\zeta=\zeta_{\text {tnctoon }}+\zeta_{\text {separaton }}$ is at a minimum. The corresponding spacing/chord ratio has an optimum, which is shown in Fig. 5.33. To find the optimum solidity for a variety of turbine and compressor cascades, a series of comprehensive experimental studies have been performed by several researchers. A detailed discussion of the results of these studies is presented in [23].

The relationship for the lift-solidity coefficient derived in the preceding sections is restricted to turbine and compressor stages with constant inner and outer diameters. This geometry is encountered in high pressure turbines or compressor components, where the streamlines are almost parallel to the machine axis. In this special case, the stream surfaces are cylindrical with almost constant diameter. In a general case such as the intermediate and low pressure turbine and compressor stages, however, the stream surfaces have different radii. The meridional velocity component may also change from station to station. In order to calculate the blade lift-solidity coefficient correctly, the radius and the meridional velocity changes must he taken into account. Detailed discussions on this and turbomachinery aero-thermodynamic topics are found in [23].

## 物理代写|流体力学代写Fluid Mechanics代考|Inviscid Potential Flows

As discussed in Chap. 4 , generally the motion of fluids encountered in engineering applications is described by the Navier-Stokes equations. Considering today’s computational fluid dynamics capabilities, it is possible to numerically solve the Navier-Stokes equations for laminar flows (no turbulent fluctuations), transitional flows (using appropriate intermittency models), and turbulent flow (utilizing appropriate turbulence models). Given today’s computational capabilities, one may argue at this juncture that there is no need to artificially subdivide the flow regime into different categories such as incompressible, compressible, viscid or inviscid ones. However, based on the degree of complexity of the flow under investigation, a computational simulation may take up to several days, weeks, and even months for direct Navier-stokes simulations (DNS). The difficulties associated with solving the Navier-Stokes equations are caused by the existence of the viscosity terms in the Navier-Stokes equations.

Measuring the velocity distributions encountered in engineering applications such as in a pipe flow, flow around a compressor or turbine blade, or along the wing of an aircraft, we find that the effect of viscosity is confined to a very thin layer called the boundary layer with a local thickness $\delta$. As we discuss in Chap. 11, comprehensive experimental investigations performed earlier by Prandtl $[26,27]$ show that the boundary layer thickness $\delta$ compared to the length $L$ of the subject under investigation is very small. In the vicinity of the wall, because of the no-slip condition, the velocity is $V_{\text {wall }}=0$. Moving away from the wall towards the edge of the boundary layer, the velocity continuously increases until it reaches the velocity at the edge of the boundary layer $V=V_\delta$. Within the boundary layer, the flow is characterized by non-zero vorticity $\nabla \times V \neq 0$. No major changes in velocity magnitude is expected outside the boundary layer, provided that the surface of the subject under investigation does not have a curvature. In case of surfaces with convex or concave curvatures, the velocity outside the boundary layer changes in lateral direction.

Outside the boundary layer, the effect of the viscosity can be neglected as long as the Reynolds number is high enough ( $\operatorname{Re}=100,000$ and above) indicating that the convective flow forces are much larger than the shear stress forces. Theoretically, the boundary layer thickness approaches zero as the Reynolds number tends to infinity. In this case, the flow can be assumed as irrotational, which is then characterized by zero vorticity $\nabla \times V=0$. Thus, as Prandtl suggested, the flow may be decomposed into two distinct regions, the vortical inner region, called the boundary layer, where the viscosity effect is predominant, and the non-vortical region outside the boundary layer.

The flow in the outer region can be calculated using the Euler equation of motion, while the boundary layer method can be applied for calculating the viscous flow within the inner region. Combining these two methods allows calculation of the flow field in a sufficiently accurate manner as long as the boundary layer is not separated. Figure $6.1$ exhibits the velocity distributions along the suction surface of an airfoil. While in case (a) the viscosity is accounted for, in case (b) it is neglected. Thus, the flow is assumed irrotational, which is characterized by $\nabla \times V=0$. As a consequence of this assumption, the velocity on the surface has a non-zero tangential component, which is in contrast to the reality. These type of flows are called potential flows which is the subject of the following sections.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|流体力学代写Fluid Mechanics代考|ZEIT2503

statistics-lab™ 为您的留学生涯保驾护航 在代写流体力学Fluid Mechanics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。我们的专家在代写流体力学Fluid Mechanics代写方面经验极为丰富，各种代写流体力学Fluid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Blade Force in an Inviscid Flow Field

Starting from a given turbine cascade with the inlet and exit flow angles shown in Fig. 5.27, the blade force can be obtained by applying the linear momentum principles to the control volume with the unit normal vectors and the coordinate system shown in Fig. 5.27. Applying Eq. (5.26), the blade inviscid force is obtained from:
$$\boldsymbol{F}i=\dot{m} \boldsymbol{V}_1-\dot{m} \boldsymbol{V}_2-\boldsymbol{n}_1 p_1 s h-\boldsymbol{n}_2 p_2 s h$$ with the subscript $i$ that refers to inviscid flow, $s$ as the spacing and $h$ as the blade height that can be assumed unity. The relationship between the control volume normal unit vectors and the unit vectors pertaining to the coordinate system is given by $\boldsymbol{n}_1=-\boldsymbol{e}_2$ and $\boldsymbol{n}_2=\boldsymbol{e}_2$. The velocities in Eq. (5.153) can be expressed in terms of circumferential as well as axial components: $$\boldsymbol{F}_i=-e_1 \dot{m}\left[\left(V{u 1}+V_{u 2}\right)\right]+e_2\left[\dot{m}\left(V_{a x 1}-V_{a x 2}\right)+\left(p_1-p_2\right) s h\right]$$
with $V_{a x 1}=V_{a x 2}$ as a result of incompressible flow assumption and $V_{u 1} \not \equiv V_{u 2}$ from Fig. 5.22. Equation (5.154) rearranged as:
$$\boldsymbol{F}i=-\boldsymbol{e}_1 \dot{m}\left(V{u 1}+V_{u 2}\right)+\boldsymbol{e}2\left(p_1-p_2\right) s h=e_1 F_u+e_2 F{a x}$$
with the circumferential and axial components
$$F_u=-\dot{m}\left(V_{u 1}+V_{u 2}\right) \text { and } F_{a x}=\left(p_1-p_2\right) s h .$$
The static pressure difference in Eq. (5.156) is obtained from the following Bernoulli equation:

\begin{aligned} p_{01} &=p_{02} \ p_1-p_2 &=\frac{1}{2} \rho\left(V_2^2-V_1^2\right)=\frac{1}{2} \rho\left(V_{u 2}^2-V_{u 1}^2\right) . \end{aligned}
Inserting the pressure difference along with the mass flow $\dot{m}=\rho V_{a x} s h$ into Eq. (5.156) and the blade height $h=1$, we obtain the axial as well as the circumferential components of the lift force:
$$\left.\begin{array}{l} F_{a x}=\frac{1}{2} \varrho\left(V_{u 2}+V_{u 1}\right)\left(V_{u 2}-V_{u 1}\right) s \ F_u=-\varrho V_{a x}\left(V_{u 2}+V_{u 1}\right) s \end{array}\right}$$

## 物理代写|流体力学代写Fluid Mechanics代考|Blade Forces in a Viscous Flow Field

The working fluids in turbomachinery, whether air, combustion gas, steam or other substances, are always viscous. The blades are subjected to the viscous flow and undergo shear stresses with no-slip condition on blades, casing and hub surfaces, resulting in boundary layer developments. Furthermore, the blades have certain definite trailing edge thicknesses. These thicknesses together with the boundary layer thickness, generate a spatially periodic wake flow downstream of each cascade as shown in Fig. 5.30.
The presence of the shear stresses cause drag forces that reduce the total pressure. In order to calculate the blade forces, the momentum Eq. (5.153) can be applied to the viscous flows. As seen from Eq. (5.156), the circumferential component remains unchanged. The axial component, however, changes in accordance with the pressure difference as shown in the following relations:
\begin{aligned} F_u &=-\rho V_{a x}\left(V_{u 2}+V_{u 1}\right) s h \ F_{a x} &=\left(p_1-p_2\right) s h . \end{aligned}

The blade height $h$ in Eq. (5.169) may be assumed as unity. For a viscous flow, the static pressure difference cannot be calculated by the Bernoulli equation. In this case, the total pressure drop must be taken into consideration. We define the total pressure loss coefficient:
$$\zeta \equiv \frac{P_1-P_2}{\frac{1}{2} \varrho V_2^2}$$
with $P_1$ and $P_2$ as the averaged total pressure at stations 1 and 2 . Inserting for the total pressure the sum of static and dynamic pressures, we get the static pressure difference as:
$$p_1-p_2=\frac{\rho}{2}\left(V_2^2-V_1^2\right)+\zeta \frac{\rho}{2} V_2^2 .$$
Incorporating Eq. (5.171) into the axial component of the blade force in Eq. (5.169) yields:
$$F_{a x}=\frac{\rho}{2}\left(V_2^2-V_1^2\right) s+\zeta \frac{\rho}{2} V_2^2 s .$$
We introduce the velocity components into Eq. (5.172) and assume that for an incompressible flow the axial components of the inlet and exit flows are the same. As a result, Eq. (5.172) reduces to:
$$F_{a x}=\frac{\rho}{2}\left(V_{u 2}^2-V_{u 1}^2\right) s+\zeta \frac{\rho}{2} V_2^2 s .$$
The second term on the right-hand side exhibits the axial component of drag forces accounting for the viscous nature of a frictional flow shown in Fig. 5.31. Thus, the axial projection of the drag force is obtained from:
$$D_{a x}=\zeta \frac{\rho}{2} V_2^2 s$$

## 物理代写|流体力学代写流体力学代考|无粘流场中的叶片力

$$\boldsymbol{F}i=\dot{m} \boldsymbol{V}1-\dot{m} \boldsymbol{V}_2-\boldsymbol{n}_1 p_1 s h-\boldsymbol{n}_2 p_2 s h$$，下标$i$表示无粘流量，$s$为间距，$h$为可统一假设的叶片高度。控制体积法单位向量与坐标系中的单位向量之间的关系由$\boldsymbol{n}_1=-\boldsymbol{e}_2$和$\boldsymbol{n}_2=\boldsymbol{e}_2$给出。式(5.153)中的速度可以用周向分量和轴向分量表示:由于不可压缩流动假设，$$\boldsymbol{F}_i=-e_1 \dot{m}\left[\left(V{u 1}+V{u 2}\right)\right]+e_2\left[\dot{m}\left(V_{a x 1}-V_{a x 2}\right)+\left(p_1-p_2\right) s h\right]$$

$$\boldsymbol{F}i=-\boldsymbol{e}1 \dot{m}\left(V{u 1}+V{u 2}\right)+\boldsymbol{e}2\left(p_1-p_2\right) s h=e_1 F_u+e_2 F{a x}$$
，其中周向分量和轴向分量
$$F_u=-\dot{m}\left(V_{u 1}+V_{u 2}\right) \text { and } F_{a x}=\left(p_1-p_2\right) s h .$$

\begin{aligned} p_{01} &=p_{02} \ p_1-p_2 &=\frac{1}{2} \rho\left(V_2^2-V_1^2\right)=\frac{1}{2} \rho\left(V_{u 2}^2-V_{u 1}^2\right) . \end{aligned}

$$\left.\begin{array}{l} F_{a x}=\frac{1}{2} \varrho\left(V_{u 2}+V_{u 1}\right)\left(V_{u 2}-V_{u 1}\right) s \ F_u=-\varrho V_{a x}\left(V_{u 2}+V_{u 1}\right) s \end{array}\right}$$

## 物理代写|流体力学代写流体力学代考|叶片在粘性流场中的力

\begin{aligned} F_u &=-\rho V_{a x}\left(V_{u 2}+V_{u 1}\right) s h \ F_{a x} &=\left(p_1-p_2\right) s h . \end{aligned}

$$\zeta \equiv \frac{P_1-P_2}{\frac{1}{2} \varrho V_2^2}$$
，其中$P_1$和$P_2$为1站和2站的平均总压。将总压力插入静态压力和动态压力之和，我们得到静压差为:
$$p_1-p_2=\frac{\rho}{2}\left(V_2^2-V_1^2\right)+\zeta \frac{\rho}{2} V_2^2 .$$

$$F_{a x}=\frac{\rho}{2}\left(V_2^2-V_1^2\right) s+\zeta \frac{\rho}{2} V_2^2 s .$$

$$F_{a x}=\frac{\rho}{2}\left(V_{u 2}^2-V_{u 1}^2\right) s+\zeta \frac{\rho}{2} V_2^2 s .$$

$$D_{a x}=\zeta \frac{\rho}{2} V_2^2 s$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|流体力学代写Fluid Mechanics代考|ENGG2500

statistics-lab™ 为您的留学生涯保驾护航 在代写流体力学Fluid Mechanics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。我们的专家在代写流体力学Fluid Mechanics代写方面经验极为丰富，各种代写流体力学Fluid Mechanics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|Effect of Stage Load Coefficient on Stage Power

The stage load coefficient $\lambda$ defined in Eq. (5.139) is an important parameter which describes the stage capability to generate/consume shaft power. A turbine stage with low flow deflection, thus, low specific stage load coefficient $\lambda$, generates lower specific stage power $l_m$. To increase $l_m$, blades with higher flow deflection are used that produce higher stage load coefficient $\lambda$. The effect of an increased $\lambda$ is shown in Fig. $5.25$ where three different bladings are plotted. The top blading with the stage load coefficient $\lambda=1$ has lower deflection. The middle blading has a moderate flow deflection and moderate $\lambda=2$ which delivers the stage power twice as high as the top blading. Finally, the bottom blading with $\lambda=3$, delivers three times the stage power as the first one. In the practice of turbine design, among other things, two major parameters must be considered. These are the specific load coefficients and the stage polytropic efficiencies. Lower deflection generally yields higher stage polytropic efficiency, but many stages are needed to produce the required turbine power. However, the same turbine power may be established by a higher stage flow deflection and, thus, a higher $\lambda$ at the expense of the stage efficiency. Increasing the stage load coefficient has the advantage of significantly reducing the stage number, thus, lowering the engine weight and manufacturing cost. In aircraft engine design practice, one of the most critical issues besides the thermal efficiency of the engine, is the thrust/weight ratio. Reducing the stage numbers may lead to a desired thrust/weight ratio. While a high turbine stage efficiency has top priority in power eter for aircraft engine designers.

## 物理代写|流体力学代写Fluid Mechanics代考|Unified Description of Stage with Constant Mean Diameter

For a turbine or compressor stage with constant mean diameter (Fig. 5.27), we present a set of equations that describe the stage by means of the dimensionless parameters such as stage flow coefficient $\phi$, stage load coefficient $\lambda$, degree of reaction $r$, and the flow angles. From the velocity diagram with the angle definition in Fig. 5.27, we obtain the flow angles:
\begin{aligned} &\cot \alpha_2=\frac{U_2+W_{u 2}}{V_{a x}}=\frac{1}{\phi}\left(1+\frac{W_{u 2}}{U}\right)=\frac{1}{\phi}\left(1-r+\frac{\lambda}{2}\right) \ &\cot \alpha_3=-\frac{W_{u 2}-U_2}{V_{a x}}=-\frac{1}{\phi}\left(\frac{W_{u 3}-U}{U}\right)=\frac{1}{\phi}\left(1-r-\frac{\lambda}{2}\right) . \end{aligned}
Similarly, we find the other flow angles, thus, we summarize:
\begin{aligned} &\cot \alpha_2=\frac{1}{\phi}\left(1-r+\frac{\lambda}{2}\right), \cot \beta_2=\frac{1}{\phi}\left(\frac{\lambda}{2}-r\right) \ &\cot \alpha_3=\frac{1}{\phi}\left(1-r-\frac{\lambda}{2}\right), \cot \beta_3=-\frac{1}{\phi}\left(\frac{\lambda}{2}+r\right) . \end{aligned}
The stage load coefficient can be calculated from:
$$\lambda=\phi\left(\cot \alpha_2-\cot \beta_3\right)-1 .$$
As seen from Eq. (5.150), one is dealing with seven unknowns and only four equations. To obtain a solution, assumptions need to be made relative to the remaining three unknowns. These may include any of the following parameters: $\alpha_2, \beta_3, \phi, \lambda$, or $r$. The criteria for selecting these parameters are discussed in details in [23].
The preceding discussions that have led to Eqs. (5.150) and (5.151) deal with compressor and turbine stages with constant hub and tip diameters. These equations cannot be applied to cases where the diameter, circumferential, and meridional velocities are not constant. Examples are axial flow turbine and compressor types shown in Figs. $5.21$ and 5.22, radial inflow (centripetal) turbines, and centrifugal compressors. In these cases, the meridional velocity ratio and the diameter are no longer constant. The dimensionless parameters for these cases are summarized below:
$$\mu=\frac{V_{m 2}}{V_{m 3}}, \nu=\frac{R_2}{R_3}=\frac{U_2}{U_3}, \phi=\frac{V_{m 3}}{U_3}, \lambda=\frac{1_m}{U_3^2}, r=\frac{\Delta h^{\prime \prime}}{\Delta h^{\prime}+\Delta h^{\prime \prime}}$$

## 物理代写|流体力学代写流体力学代考|等平均直径级的统一描述

\begin{aligned} &\cot \alpha_2=\frac{U_2+W_{u 2}}{V_{a x}}=\frac{1}{\phi}\left(1+\frac{W_{u 2}}{U}\right)=\frac{1}{\phi}\left(1-r+\frac{\lambda}{2}\right) \ &\cot \alpha_3=-\frac{W_{u 2}-U_2}{V_{a x}}=-\frac{1}{\phi}\left(\frac{W_{u 3}-U}{U}\right)=\frac{1}{\phi}\left(1-r-\frac{\lambda}{2}\right) . \end{aligned}

\begin{aligned} &\cot \alpha_2=\frac{1}{\phi}\left(1-r+\frac{\lambda}{2}\right), \cot \beta_2=\frac{1}{\phi}\left(\frac{\lambda}{2}-r\right) \ &\cot \alpha_3=\frac{1}{\phi}\left(1-r-\frac{\lambda}{2}\right), \cot \beta_3=-\frac{1}{\phi}\left(\frac{\lambda}{2}+r\right) . \end{aligned}

$$\lambda=\phi\left(\cot \alpha_2-\cot \beta_3\right)-1 .$$

$$\mu=\frac{V_{m 2}}{V_{m 3}}, \nu=\frac{R_2}{R_3}=\frac{U_2}{U_3}, \phi=\frac{V_{m 3}}{U_3}, \lambda=\frac{1_m}{U_3^2}, r=\frac{\Delta h^{\prime \prime}}{\Delta h^{\prime}+\Delta h^{\prime \prime}}$$

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|傅立叶光学代写Fourier optics代考|ECE500

statistics-lab™ 为您的留学生涯保驾护航 在代写傅立叶光学Fourier 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。我们的专家在代写傅立叶光学Fourier optics代写方面经验极为丰富，各种代写傅立叶光学Fourier optics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|傅立叶光学代写Fourier optics代考|Sampling by averaging, distributions

We will now learn the important idea of the delta function that will be handy later in this book. Sampling a continuous function is a part of every measurement or digitization process. Suppose we have a signal $I(x)$ – say the intensity of ambient light along a line on a screen – that we wish to sample at discrete set of points $x_1, x_2, \ldots$. How do we go about it? Every detector we can possibly use to measure the intensity will have some finite width $2 L$ and a sample of $I(x)$ will be an average over this detector area. So we may write the intensity at point $x=0$, or $I(0)$ as:
$$I(0) \approx \frac{1}{2 L} \int_{-\infty}^{\infty} d x I(x) \operatorname{rect}\left(\frac{x}{2 L}\right) .$$
Now how do we improve this approximation so that we go to the ideal $I(0)$ ? Clearly we have to reduce the size $2 L$ over which the average is carried out. We may say that:
$$I(0)=\lim {2 L \rightarrow 0} \frac{1}{2 L} \int{-\infty}^{\infty} d x I(x) \operatorname{rect}\left(\frac{x}{2 L}\right) .$$
Notice that as the length $2 L \rightarrow 0$ the width of the function $\frac{1}{2 L} \operatorname{rect}\left(\frac{x}{2 L}\right)$ keeps reducing whereas its height keeps increasing such that the area under the curve is unity. This limiting process leads us to an impulse which is also commonly known by the name delta function. We may write:
$$\delta(x)=\lim _{2 L \rightarrow 0} \frac{1}{2 L} \operatorname{rect}\left(\frac{x}{2 L}\right) .$$
Although it is commonly referred to as the “delta function” and we will often call it that way, you will appreciate that it is not a function in the usual sense. When we say $f(x)=x^2$ we are associating a value for every input number $x$. The impulse or delta distribution is more of an idea that is the result of a limiting process. Anything that is equal to zero everywhere in the limit except at $x=0$, where it tends to infinity cannot be a function in the sense you may have learnt in your mathematics classes.

## 物理代写|傅立叶光学代写Fourier optics代考|Properties of delta function

1. Sampling property At points of continuity of a function $g(x)$ we have:
$$\int_{-\infty}^{\infty} d x g(x) \delta\left(x \quad x^{\prime}\right)=g\left(x^{\prime}\right) .$$
If at $x=x^{\prime}$ the function $g(x)$ has a finite jump discontinuity, the right hand side of the above equation is an average value of the two limits $g\left(x_{+}^{\prime}\right)$ and $g\left(x_{-}^{\prime}\right)$.
2. Derivatives of delta function All operations with delta function are to be associated with a test function under integral sign. We evaluate the integral below by parts.
\begin{aligned} \int_{-\infty}^{\infty} & d x g(x) \frac{d}{d x} \delta\left(x-x^{\prime}\right) \ &=\left.g(x) \delta\left(x-x^{\prime}\right)\right|{-\infty} ^{\infty}-\int{-\infty}^{\infty} d x \frac{d}{d x} g(x) \delta\left(x-x^{\prime}\right) \ &=-g^{\prime}\left(x^{\prime}\right) . \end{aligned}
This property applies to multiple order derivatives. So continuing along the lines of above equation we get:
$$\int_{-\infty}^{\infty} d x g(x) \frac{d^n}{d x^n} \delta\left(x-x^{\prime}\right)=(-1)^n g^{(n)}\left(x^{\prime}\right),$$
where $g^{(n)}(x)$ is the $\mathrm{n}$-th order derivative of $g(x)$.
3. Delta function with scaling First of all we note that the delta function is even: $\delta(-x)=\delta(x)$. This leads to:
\begin{aligned} \int_{-\infty}^{\infty} d x g(x) \delta(a x) &=\frac{1}{|a|} \int_{-\infty}^{\infty} d x g\left(\frac{x}{a}\right) \delta(x) \ &=\frac{1}{|a|} g(0) \end{aligned}
We may therefore write: $\delta(a x)=\frac{1}{|a|} \delta(x)$.

## 物理代写|傅立叶光学代写傅里叶光学代考|通过平均采样，分布

$$I(0) \approx \frac{1}{2 L} \int_{-\infty}^{\infty} d x I(x) \operatorname{rect}\left(\frac{x}{2 L}\right) .$$

$$I(0)=\lim {2 L \rightarrow 0} \frac{1}{2 L} \int{-\infty}^{\infty} d x I(x) \operatorname{rect}\left(\frac{x}{2 L}\right) .$$

$$\delta(x)=\lim _{2 L \rightarrow 0} \frac{1}{2 L} \operatorname{rect}\left(\frac{x}{2 L}\right) .$$

## 物理代写|傅立叶光学代写傅里叶光学代考|函数的性质

1. 采样性质在函数的连续性点上 $g(x)$ 我们有:
$$\int_{-\infty}^{\infty} d x g(x) \delta\left(x \quad x^{\prime}\right)=g\left(x^{\prime}\right) .$$
如果at $x=x^{\prime}$ 函数 $g(x)$ 有一个有限跳跃不连续，上面方程的右边是两个极限的平均值 $g\left(x_{+}^{\prime}\right)$ 和 $g\left(x_{-}^{\prime}\right)$
2. δ函数的导数所有关于δ函数的运算都与积分符号下的测试函数相关联。我们用分部计算下面的积分。
\begin{aligned} \int_{-\infty}^{\infty} & d x g(x) \frac{d}{d x} \delta\left(x-x^{\prime}\right) \ &=\left.g(x) \delta\left(x-x^{\prime}\right)\right|{-\infty} ^{\infty}-\int{-\infty}^{\infty} d x \frac{d}{d x} g(x) \delta\left(x-x^{\prime}\right) \ &=-g^{\prime}\left(x^{\prime}\right) . \end{aligned}
此属性适用于多个阶导数。所以继续沿着上面的等式，我们得到:
$$\int_{-\infty}^{\infty} d x g(x) \frac{d^n}{d x^n} \delta\left(x-x^{\prime}\right)=(-1)^n g^{(n)}\left(x^{\prime}\right),$$
where $g^{(n)}(x)$ 是 $\mathrm{n}$的-阶导数 $g(x)$.
3. 带缩放的函数首先我们注意到函数是偶的: $\delta(-x)=\delta(x)$。这将导致:
\begin{aligned} \int_{-\infty}^{\infty} d x g(x) \delta(a x) &=\frac{1}{|a|} \int_{-\infty}^{\infty} d x g\left(\frac{x}{a}\right) \delta(x) \ &=\frac{1}{|a|} g(0) \end{aligned}因此，我们可以这样写: $\delta(a x)=\frac{1}{|a|} \delta(x)$.

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。

## 物理代写|傅立叶光学代写Fourier optics代考|ECE502

statistics-lab™ 为您的留学生涯保驾护航 在代写傅立叶光学Fourier 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。我们的专家在代写傅立叶光学Fourier optics代写方面经验极为丰富，各种代写傅立叶光学Fourier optics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|傅立叶光学代写Fourier optics代考|Fourier transform as a limiting case of Fourier series

We will now consider the limiting case of the Fourier series as the period $T$ goes to $\infty$. It is clear that the function $g(x)$ is no more periodic. We denote the discrete frequencies as:
$$f_{x n}=\frac{n}{T},$$
The difference between the consecutive discrete frequencies is given by $\Delta f_x=f_{x(n+1)}-f_{x n}=1 / T$. Further we define:
$$G\left(f_{x n}\right)=\int_{-\infty}^{\infty} d x g(x) \exp \left(-i 2 \pi f_{x n} x\right) .$$
We may write the Fourier series expansion as:
\begin{aligned} g(x) &=\sum_{n=-\infty}^{\infty} G_n \exp \left(i 2 \pi f_{x n} x\right) \ &=\sum_{n=-\infty}^{\infty}\left[\frac{1}{T} \int_{-T / 2}^{T / 2} d x^{\prime} g\left(x^{\prime}\right) \exp \left(-i 2 \pi f_{x n} x^{\prime}\right)\right] \exp \left(i 2 \pi f_{x n} x\right) . \end{aligned}
In the limit $T \rightarrow \infty$ we have:
\begin{aligned} g(x) & \rightarrow \sum_{n=-\infty}^{\infty} G\left(f_{x n}\right) \exp \left(i 2 \pi f_{x n} x\right) \Delta f_x \ & \rightarrow \int_{-\infty}^{\infty} d f_x G\left(f_x\right) \exp \left(i 2 \pi f_x x\right) \end{aligned}

## 物理代写|傅立叶光学代写Fourier optics代考|Fourier transform of the rectangle distribution

The Fourier transform of the rect function may be evaluated as:
\begin{aligned} G\left(f_x\right) &=\int_{-L}^L d x \exp \left(-i 2 \pi f_x x\right) \ &=\left[\frac{\exp \left(-i 2 \pi f_x x\right)}{-i 2 \pi f_x}\right]{-L}^L \ &=2 L \frac{\sin \left(2 \pi f_x L\right)}{\left(2 \pi f_x L\right)} \ &=2 L \operatorname{sinc}\left(2 L f_x\right) \end{aligned} Here the sinc-function is as defined in Eq. (2.21). Note that although $\operatorname{rect}(x)$ has a discontinuity, its transform is continuous. Further it is somewhat surprising to know that $\left|\operatorname{sinc}\left(f_x\right)\right|$ is not absolutely integrable to have a Fourier transform or Fourier inverse in the conventional sense required by the Dirichlet sufficiency conditions. To show this consider the intervals along $f_x$ axis where $\left|\sin \left(\pi f_x\right)\right| \geq$ $0.5$. These intervals are given by $f_x \in[n+1 / 6, n+5 / 6]$. We therefore have: $$\int{-\infty}^{\infty} d f_x\left|\operatorname{sinc}\left(f_x\right)\right|>2 \frac{1}{2 \pi} \sum_{n=0}^{\infty} \frac{2 / 3}{n+5 / 6} \rightarrow \infty$$
The series on the right hand side diverges and as a result the absolute integral of $\operatorname{sinc}\left(f_x\right)$ does not exist. Functions such as spikes, steps and even ever extending sines and cosines do not have a Fourier transform in traditional theory. Defining Fourier transforms for such functions is however a practical necessity when representing images as $2 \mathrm{D}$ matrices in digital form. In fact edges or spikes contain most important visual information in images. The traditional Fourier transform theory must therefore be extended to take these cases into account. We will study the important case of the Dirac delta function in this context. This class of functions (spikes, steps, etc) with no Fourier transform in conventional theory is known by the name generalized functions. We will not deal with theory of generalized functions in detail but study some specific cases of interest starting with the Dirac delta function.

## 物理代写|傅立叶光学代写傅立叶光学代考|傅立叶变换作为傅立叶级数的极限情况

$$f_{x n}=\frac{n}{T},$$

$$G\left(f_{x n}\right)=\int_{-\infty}^{\infty} d x g(x) \exp \left(-i 2 \pi f_{x n} x\right) .$$

\begin{aligned} g(x) &=\sum_{n=-\infty}^{\infty} G_n \exp \left(i 2 \pi f_{x n} x\right) \ &=\sum_{n=-\infty}^{\infty}\left[\frac{1}{T} \int_{-T / 2}^{T / 2} d x^{\prime} g\left(x^{\prime}\right) \exp \left(-i 2 \pi f_{x n} x^{\prime}\right)\right] \exp \left(i 2 \pi f_{x n} x\right) . \end{aligned}

\begin{aligned} g(x) & \rightarrow \sum_{n=-\infty}^{\infty} G\left(f_{x n}\right) \exp \left(i 2 \pi f_{x n} x\right) \Delta f_x \ & \rightarrow \int_{-\infty}^{\infty} d f_x G\left(f_x\right) \exp \left(i 2 \pi f_x x\right) \end{aligned}

\begin{aligned} G\left(f_x\right) &=\int_{-L}^L d x \exp \left(-i 2 \pi f_x x\right) \ &=\left[\frac{\exp \left(-i 2 \pi f_x x\right)}{-i 2 \pi f_x}\right]{-L}^L \ &=2 L \frac{\sin \left(2 \pi f_x L\right)}{\left(2 \pi f_x L\right)} \ &=2 L \operatorname{sinc}\left(2 L f_x\right) \end{aligned}这里的since函数定义在式(2.21)中。注意，尽管$\operatorname{rect}(x)$具有不连续性，但它的转换是连续的。此外，有些令人惊讶的是，知道$\left|\operatorname{sinc}\left(f_x\right)\right|$不是绝对可积的具有传统意义上的狄利克雷充分性条件要求的傅里叶变换或傅里叶反变换。为了说明这一点，考虑沿着$f_x$轴的间隔，其中\left|\sin \left(\pi f_x\right)\right| \geq$$0.5。这些间隔由f_x \in[n+1 / 6, n+5 / 6]给出。因此我们有:$$ \int{-\infty}^{\infty} d f_x\left|\operatorname{sinc}\left(f_x\right)\right|>2 \frac{1}{2 \pi} \sum_{n=0}^{\infty} \frac{2 / 3}{n+5 / 6} \rightarrow \infty $$右边的级数发散，因此\operatorname{sinc}\left(f_x\right)的绝对积分不存在。像尖峰函数，阶跃函数，甚至是不断扩展的正弦和余弦函数在传统理论中都没有傅里叶变换。然而，当以数字形式将图像表示为2 \mathrm{D}矩阵时，为这样的函数定义傅里叶变换是实际需要的。事实上，边缘或尖刺包含了图像中最重要的视觉信息。因此，传统的傅里叶变换理论必须加以推广，以考虑到这些情况。我们将在此背景下研究狄拉克函数的重要情况。这类在传统理论中没有傅里叶变换的函数(峰值函数、阶跃函数等)被称为广义函数。我们将不详细讨论广义函数的理论，而是从狄拉克函数开始研究一些感兴趣的具体情况 统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## 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。 ## 物理代写|傅立叶光学代写Fourier optics代考|EE238 如果你也在 怎样代写傅立叶光学Fourier optics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 傅里叶光学是利用傅里叶变换（FTs）对经典光学的研究，其中所考虑的波形被认为是由平面波的组合或叠加组成的。 statistics-lab™ 为您的留学生涯保驾护航 在代写傅立叶光学Fourier 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。我们的专家在代写傅立叶光学Fourier optics代写方面经验极为丰富，各种代写傅立叶光学Fourier optics相关的作业也就用不着说。 我们提供的傅立叶光学Fourier optics及其相关学科的代写，服务范围广, 其中包括但不限于: • Statistical Inference 统计推断 • Statistical Computing 统计计算 • Advanced Probability Theory 高等概率论 • Advanced Mathematical Statistics 高等数理统计学 • (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|傅立叶光学代写Fourier optics代考|Fourier Series A periodic function g(x) with period T such that$$ g(x)=g(x+T), \quad-\infty<x<\infty $$may be represented as a Fourier series:$$ g(x)=\sum_{n=-\infty}^{\infty} G_n \exp (i 2 \pi n x / T) . $$This is a very important idea as we shall see when studying linear systems. The question of when such an expansion exists is addressed in the Dirichlet sufficiency conditions: 1. The function g(x) must be absolutely integrable over one period. 2. The function g(x) must be piecewise continuous. A finite number of finite discontinuities is allowed.The function g(x) must have finite number of extrema in one period. Something like \sin (1 / x) near x=0 is not allowed. 3. The co-efficient G_n may be determined using the following orthogonality relation: 4.$$ 5. \begin{aligned} 6. \int_{-T / 2}^{T / 2} d x \exp [i 2 \pi(m-n) x / T] &=\left[\frac{\exp [i 2 \pi(m-n) x / T]}{i 2 \pi(m-n) / T}\right]{x=-T / 2}^{T / 2} \ &=T \frac{\sin [\pi(m-n)]}{\pi(m-n)} \ &=T \delta{m, n} 7. \end{aligned} 8. $$9. The coefficients G_n can therefore be obtained as: 10.$$ 11. G_n=\frac{1}{T} \int_{-T / 2}^{T / 2} d x g(x) \exp (-i 2 \pi n x / T) . 12. $$13. If g(x) has a (finite) discontinuity at x=x_0, the series expansion converges to: 14.$$ 15. g\left(x_0\right)=\left[\frac{g\left(x_{0-}\right)+g\left(x_{0+}\right)}{2}\right] . 16. $$## 物理代写|傅立叶光学代写Fourier optics代考|Gibbs phenomenon We note a peculiar phenomenon which arises near the discontinuity of a periodic function that is being represented by means of the Fourier series. We rewrite the Fourier series representation for the square wave considered in the illustration earlier.$$ \begin{aligned} g(x) &=\frac{1}{2}+\frac{2}{\pi} \sin \left(\frac{2 \pi x}{T}\right)+\frac{2}{3 \pi} \sin \left(\frac{6 \pi x}{T}\right)+\ldots \ &=\frac{1}{2}+\frac{2}{\pi} \sum_{n=0}^{\infty} \frac{1}{(2 n+1)} \sin \left[\frac{2 \pi(2 n+1) x}{T}\right] \end{aligned} $$When a finite number of terms is included in the summation above, the left hand side has a discontinuity while the right hand side is a sum of continuous functions. The convergence of the series sum to the periodic square wave is therefore not a point-wise convergence (near the discontinuity one observes undershoot and overshoot) but uniform convergence. In fact the overshoot and undershoot do not die out as the number of terms in the partial series sum increases. This interesting feature is known by the name of Gibbs phenomenon. The under and overshoot get closer to the discontinuity with increasing number of terms such that the area under them tends to zero. In other words they do not contribute to the energy in the function. This type of convergence is termed as uniform convergence or “almost everywhere” convergence (convergence everywhere except on sets of measure zero). Figure 2.2 shows a region near the discontinuity of the square wave in Fig. 2.1 to illustrate the behaviour of the Fourier series representation as the number of terms increases. We may express the uniform convergence property as follows:$$ \lim {N \rightarrow \infty}\left|g(x)-\frac{1}{2}-\sum{n=0}^N \frac{1}{(2 n+1)} \sin \left[\frac{2 \pi(2 n+1) x}{T}\right]\right|^2=0 \text {. (2.14) } $$The notation above for the L2-norm square is to be understood as:$$ |g(x)|^2=\int_{-\infty}^{\infty} d x|g(x)|^2 . $$## 傅立叶光学代考 ## 物理代写|傅立叶光学代写傅立叶光学代考|傅立叶级数 周期为T的周期函数g(x)，使得$$ g(x)=g(x+T), \quad-\infty<x<\infty $$可以表示为傅立叶级数:$$ g(x)=\sum_{n=-\infty}^{\infty} G_n \exp (i 2 \pi n x / T) . $$这是一个非常重要的思想，我们将在学习线性系统时看到。在狄利克雷充分性条件 中解决了何时存在这种展开的问题 函数g(x)必须在一个周期内是绝对可积的。函数g(x)必须分段连续。有限数量的有限不连续是允许的。函数g(x)在一个周期内必须有有限个极值。不允许在x=0附近使用\sin (1 / x)之类的内容。系数G_n可以用以下的正交关系确定:$$\begin{aligned}\int_{-T / 2}^{T / 2} d x \exp [i 2 \pi(m-n) x / T] &=\left[\frac{\exp [i 2 \pi(m-n) x / T]}{i 2 \pi(m-n) / T}\right]{x=-T / 2}^{T / 2} \ &=T \frac{\sin [\pi(m-n)]}{\pi(m-n)} \ &=T \delta{m, n}\end{aligned}$$因此，系数G_n可以得到为:$$G_n=\frac{1}{T} \int_{-T / 2}^{T / 2} d x g(x) \exp (-i 2 \pi n x / T) .$$如果g(x)在x=x_0处有(有限)不连续，级数展开收敛为:$$g\left(x_0\right)=\left[\frac{g\left(x_{0-}\right)+g\left(x_{0+}\right)}{2}\right] .$$## 物理代写|傅立叶光学代写傅里叶光学代考|吉布斯现象 我们注意到一个奇特的现象，它出现在周期函数的不连续附近，这个周期函数是用傅立叶级数表示的。我们重写前面图解中考虑的方波的傅立叶级数表示。$$ \begin{aligned} g(x) &=\frac{1}{2}+\frac{2}{\pi} \sin \left(\frac{2 \pi x}{T}\right)+\frac{2}{3 \pi} \sin \left(\frac{6 \pi x}{T}\right)+\ldots \ &=\frac{1}{2}+\frac{2}{\pi} \sum_{n=0}^{\infty} \frac{1}{(2 n+1)} \sin \left[\frac{2 \pi(2 n+1) x}{T}\right] \end{aligned} $$当上面的和式中包含有限数量的项时，左边是不连续的，而右边是连续函数的和。因此，级数和对周期方波的收敛不是逐点收敛(在不连续处附近观察到的过冲和过冲)，而是一致收敛。事实上，超调和过调并不会随着部分级数和中项数的增加而消失。这个有趣的现象被称为吉布斯现象 随着项数的增加，下限和超调越来越接近不连续，以至于它们下面的面积趋于零。换句话说，它们对函数的能量没有贡献。这种类型的收敛称为一致收敛或“几乎处处”收敛(除测度为0的集合外处处收敛)。图2.2显示了图2.1中方波的不连续附近的区域，以说明随着项数的增加，傅立叶级数表示的行为。$$ \lim {N \rightarrow \infty}\left|g(x)-\frac{1}{2}-\sum{n=0}^N \frac{1}{(2 n+1)} \sin \left[\frac{2 \pi(2 n+1) x}{T}\right]\right|^2=0 \text {. (2.14) } $$上面l2范数平方的符号可以理解为:$$ |g(x)|^2=\int_{-\infty}^{\infty} d x|g(x)|^2 . $$统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。 ## 金融工程代写 金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。 ## 非参数统计代写 非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。 ## 广义线性模型代考 广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。 术语 广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。 ## 有限元方法代写 有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。 有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。 tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。 ## 随机分析代写 随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。 ## 时间序列分析代写 随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。 随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。 ## 回归分析代写 多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。 ## 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。 ## 物理代写|分析力学代写Analytical Mechanics代考|PHY225 如果你也在 怎样代写分析力学Analytical Mechanics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。 分析力学是理论力学的一个分支，是对经典力学的高度数学化的表达。 statistics-lab™ 为您的留学生涯保驾护航 在代写分析力学Analytical Mechanics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。我们的专家在代写分析力学Analytical Mechanics代写方面经验极为丰富，各种代写分析力学Analytical Mechanics相关的作业也就用不着说。 我们提供的分析力学Analytical Mechanics及其相关学科的代写，服务范围广, 其中包括但不限于: • Statistical Inference 统计推断 • Statistical Computing 统计计算 • Advanced Probability Theory 高等概率论 • Advanced Mathematical Statistics 高等数理统计学 • (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|分析力学代写Analytical Mechanics代考|Virtual Work The importance of introducing the notion of virtual displacement stems from the following observation: if the surface to which the particle is confined is ideally smooth, the contact force of the surface on the particle, which is the constraint force, has no tangential component and therefore is normal to the surface. Thus, the work done by the constraint force as the particle undergoes a virtual displacement is zero even if the surface is in mótion, differently from thé work donne during a reeal displaccement, which does nôt necessarily vanish. In most physically interesting cases, the total virtual work of the constraint forces is zero, as the next examples attest. Example 1.10 Two particles joined by a rigid rod move in space. Let \mathbf{f}_1 and \mathbf{f}_2 be the constraint forces on the particles. By Newton’s third law \mathbf{f}_1=-\mathbf{f}_2 with both \mathbf{f}_1 and \mathbf{f}_2 parallel to the line connecting the particles. The virtual work done by the constraint forces is$$ \delta W_v=\mathbf{f}_1 \cdot \delta \mathbf{r}_1+\mathbf{f}_2 \cdot \delta \mathbf{r}_2=\mathbf{f}_2 \cdot\left(\delta \mathbf{r}_2-\delta \mathbf{r}_1\right) . $$Setting \mathbf{r}=\mathbf{r}_2-\mathbf{r}_1, the constraint equation takes the form (1.38), namely r^2-l^2=0. In terms of the variable \mathbf{r}, the situation is equivalent to the one discussed in Example 1.9. Taking f(\mathbf{r}, t)=r^2-l^2, Eq. (1.51) reduces to \mathbf{r} \cdot \delta \mathbf{r}=0. Since \mathbf{f}_2 and \mathbf{r} are collinear, there exists a scalar \lambda such that \mathbf{f}_2=\lambda \mathbf{r}, hence \delta W_v=\lambda \mathbf{r} \cdot \delta \mathbf{r}=0. Inasmuch as a rigid body consists of a vast number of particles whose mutual distances are invariable, one concludes that the total virtual work done by the forces responsible for the body’s rigidity is zero. Example 1.11 A rigid body rolls without slipping on a fixed surface. As a rule, in order to prevent slipping, a friction force between the fixed surface and the surface of the body is needed, that is, the surfaces in contact must be rough. Upon rolling without slipping, the body’s particles at each instant are rotating about an axis that contains the body’s point of contact with the surface. Thus, the friction force acts on a point of the body whose velocity at each instant is zero, because it is on the instantaneous axis of rotation. Virtual displacements are such that the body does not slip on the surface, that is, \delta \mathbf{r}=0 at the point of contact between the body and the fixed surface. Therefore, the virtual work done by the constraint force is \delta W_v=\mathbf{f} \cdot \delta \mathbf{r}=0 because \delta \mathbf{r}=0, even though \mathbf{f} \neq 0. ## 物理代写|分析力学代写Analytical Mechanics代考|Principle of Virtual Work Newton’s formulation of mechanics is characterised by the set of differential equations$$ m_i \ddot{\mathbf{r}}_i=\mathbf{F}_i, \quad i=1, \ldots, N, $$where \mathbf{F}_i is the total or resultant force on the i th particle, supposedly a known function of positions, velocities and time. This system of differential equations determines a unique solution for the \mathbf{r}_i(t) once the positions and velocities are specified at an initial instant. { }^{10} In the presence of constraints, it is patently clear how inconvenient the Newtonian formulation is. First of all, it usually requires the use of more coordinates than are necessary to specify the configuration of the system. When the constraints are holonomic, for instance, the positions \mathbf{r}_1, \ldots, \mathbf{r}_N are not mutually independent, making the Newtonian approach uneconomical by demanding the employment of redundant variables. Furthermore, the total force on the i th particle can be decomposed as$$ \mathbf{F}_i=\mathbf{F}_i^{(a)}+\mathbf{f}_i, $$where \mathbf{F}_i^{(a)} is the applied force and \mathbf{f}_i is the constraint force. In the case of the double pendulum in Example 1.4, \mathbf{F}_1^{(a)} and \mathbf{F}_2^{(a)} are the weights of the particles, whereas \mathbf{f}_1 and \mathbf{f}_2 are determined by the tensions on the rods or strings. The difficulty here lies in that one does not a priori know how the constraint forces depend on the positions and velocities. What one knows, in fact, are the effects produced by the constraint forces. One may also argue that the applied forces are the true causes of the motion, the constraint forces merely serving to ensure the preservation of the geometric or kinematic restrictions in the course of time. No less important is the fact that Newton’s laws – the second law together with the strong version of the third law – turn out to be incapable of correctly describing the motion of certain constrained systems (Stadler, 1982; Casey, 2014). For all these reasons, it is highly desirable to obtain a formulation of classical mechanics as parsimonious as possible, namely involving only the applied forces and employing only independent coordinates. We shall soon see that this goal is achieved by the Lagrangian formalism when all constraints are holonomic. As an intermediate step towards Lagrange’s formulation, we shall discuss d’Alembert’s principle, which is a method of writing down the equations of motion in terms of the applied forces alone, the derivation of which explores the fact that the virtual work of the constraint forces is zero. ## 分析力学代考 ## 物理代写|分析力学代写分析力学代考|虚拟功 . 引入虚位移概念的重要性来源于以下观察结果:如果质点所受限制的表面是理想光滑的，则表面对质点的接触力，即约束力，没有切向分量，因此垂直于表面。因此，当粒子经历虚位移时，约束力所做的功为零，即使表面在mótion，这与真实位移时所做的thé功不同，真实位移时所做的功nôt必然消失。在大多数物理上有趣的情况下，约束力的总虚功为零，正如下面的例子所证明的 两个由刚性杆连接的粒子在空间中运动。设\mathbf{f}_1和\mathbf{f}_2是对粒子的约束力。根据牛顿第三定律\mathbf{f}_1=-\mathbf{f}_2$$\mathbf{f}_1和$\mathbf{f}_2$都平行于连接粒子的直线。约束力所做的虚功为
$$\delta W_v=\mathbf{f}_1 \cdot \delta \mathbf{r}_1+\mathbf{f}_2 \cdot \delta \mathbf{r}_2=\mathbf{f}_2 \cdot\left(\delta \mathbf{r}_2-\delta \mathbf{r}_1\right) .$$

## 物理代写|分析力学代写分析力学代考|虚功原理

$$m_i \ddot{\mathbf{r}}_i=\mathbf{F}_i, \quad i=1, \ldots, N,$$
，其中$\mathbf{F}_i$是作用在第$i$个粒子上的总力或合力，应该是位置、速度和时间的已知函数。这个微分方程组确定了$\mathbf{r}_i(t)$的唯一解，一旦在初始瞬间指定了位置和速度。${ }^{10}$

$$\mathbf{F}_i=\mathbf{F}_i^{(a)}+\mathbf{f}_i,$$
，其中$\mathbf{F}_i^{(a)}$为施加力，$\mathbf{f}_i$为约束力。在例1.4中的双摆的情况下，$\mathbf{F}_1^{(a)}$和$\mathbf{F}_2^{(a)}$是粒子的重量，而$\mathbf{f}_1$和$\mathbf{f}_2$是由杆或弦上的张力决定的。这里的困难在于，我们不能先验地知道约束力如何依赖于位置和速度。事实上，我们所知道的是约束力所产生的效应。人们也可以争辩说，施加的力是运动的真正原因，约束力仅仅是为了确保在时间过程中几何或运动限制的保存。同样重要的是，牛顿定律——第二定律和第三定律的强版本——被证明不能正确描述某些受约束系统的运动(Stadler, 1982;Casey, 2014)。

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。