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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|原子物理代写Atomic and Molecular Physics代考|MULTI-PHOTON FRAGMENTATION

We finally address in this section, as an example to illustrate the methodology extended to multi-photon ionization processes, the study of multi-photon excitation of the $\mathrm{NO}{2}$ molecule induced by the absorption of four or five photons of $400 \mathrm{~nm}$ wavelength, delivered by SLIC linearly and circularly polarized femtosecond laser sources described in section II.A, using the VC method. Although the analysis of the PADs would be simpler for a linear molecule, we first studied $\mathrm{NO}{2}$ since there is such an extensive literature on the challenging photophysics of this system. The photodynamics in $\mathrm{NO}{2}$ is complicated by numerous non-adiabatic couplings and has motivated a number of multiphoton and time-resolved studies $[46,49,106]$. In the reported experiments, three main channels producing ionic species are observed and assigned to $(i)$ four-photon ionization into the $\mathrm{NO}{2}^{+}\left(\mathrm{X}^{1} \Sigma_{\mathrm{g}}^{+}\right)$ground state, (ii) five-photon dissociative photoionization (DPI) into $\left(\mathrm{NO}^{+}\left(\mathrm{X}^{1} \Sigma^{+}, v\right)+\mathrm{O}\left({ }^{3} \mathrm{P}\right)+\mathrm{e}\right)$ and (iii) four-photon induced $\mathrm{NO}^{+}\left(\mathrm{X}^{1} \Sigma^{+}, v\right)+\mathrm{O}^{-}\left({ }^{2} \mathrm{P}\right)$ ion-pair formation. The characteristics of the ionization reactions, photoelectron energy spectra for non-dissociative ionization and $\left(E_{\mathrm{e}}, E_{\mathrm{NO}+}\right) \mathrm{KECDs}$ for dissociative photoionization, strongly differ from those observed for one-photon ionization at comparable photon excitation energies [73]. Compared to one-photon ionization, the multiphoton excitation accesses different FranckCondon factors via resonant intermediate states and changes the probability of multielectron excitation processes. In the multi-photon excitation scheme, the ion-pair formation is enhanced by one order of magnitude [107]. DPI and ion-pair formation reveal similar features such as a significant vibrational excitation of the $\mathrm{NO}^{+}\left(\mathrm{X}^{1} \Sigma^{+}, v=0-5\right)$ molecular fragment and a recoil ion fragment emission strongly aligned along the polarization axis of linearly polarized light, or preferentially emitted in the plane perpendicular to the propagation axis of circularly polarized light.

## 物理代写|原子物理代写Atomic and Molecular Physics代考|CONCLUDING REMARKS

It has been well established in the last fifteen years that the measurement of molecular frame photoemission provides one of the most effective means to study the photoionization dynamics through the determination of the complex transition dipole elements which govern the process. Meanwhile, such studies increase our knowledge of the ionized molecular orbitals including the electronic correlation within the initial neutral state, of the correlation in the continuum state between the scattered and target electrons, and of the structure of the molecular ions. Many photoionization studies have been concerned with one-photon ionization of mainly diatomic and linear molecules, taking advantage of dissociative ionization and electron-ion momentum spectroscopy to record MFPADs. In such cases it was shown that analyzing the electron-ion emission patterns while relying on a unified formalism of the MFPADs induced by linearly then elliptically polarized light provides a very efficient mean for the extraction of the dipole matrix elements or dynamical parameters.

In this chapter, we have discussed the extension of this method to non-linear molecules and to multiphoton processes. These extensions are a work in progress. Despite the increasing complexity of a general description of the MFPADs and RFPADs, which may involve a significantly increased number of one dimensional $F_{N, v}^{(L)}\left(\theta_{k}\right)$ functions, different strategies can be developed to rationalize the expression of the RFPADs and disentangle the effects of photoionization from that of fragmentation dynamics or structural properties of the parent molecule. These studies strongly benefit from a detailed comparison of cxperimental and computed photocmission observables.

# 原子物理代写

## 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。

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