\documentclass[tikz]{standalone}
% Uncomment the following line to allow the usage of graphics (.png, .jpg)
%\usepackage[pdftex]{graphicx}
% Comment the following line to NOT allow the usage of umlauts
\usepackage{pgfgantt}
\title{Gantt chart showing PhD activity time lines over four month intervals beyond the confirmation review}
\usepackage{amsfonts}
% Start the document
\begin{document}
\definecolor{barblue}{RGB}{153,204,254}
\definecolor{groupblue}{RGB}{51,102,254}
\definecolor{linkred}{RGB}{165,0,33}
\renewcommand\sfdefault{phv}
\renewcommand\mddefault{mc}
\renewcommand\bfdefault{bc}
\setganttlinklabel{s-s}{START-TO-START}
\setganttlinklabel{f-s}{FINISH-TO-START}
\setganttlinklabel{f-f}{FINISH-TO-FINISH}
\sffamily
\begin{ganttchart}[
[
canvas/.append style={fill=none, draw=black!5, line width=.75pt},
hgrid style/.style={*1{draw=black!5, line width=.75pt}},
vgrid={*1{draw=black!5, line width=.75pt}},
today=7,
today rule/.style={
draw=black!64,
dash pattern=on 3.5pt off 6.5pt,
line width=1.5pt
},
today label font=\small\bfseries,
title/.style={draw=none, fill=none},
title label font=\bfseries\footnotesize,
title label node/.append style={below=7pt},
include title in canvas=false,
bar label font=\mdseries\small\color{black!70},
bar label node/.append style={left=2cm},
bar/.append style={draw=none, fill=black!63},
bar incomplete/.append style={fill=barblue},
bar progress label font=\mdseries\footnotesize\color{black!70},
group incomplete/.append style={fill=groupblue},
group left shift=0,
group right shift=0,
group height=.5,
group peaks tip position=0,
group label node/.append style={left=.6cm},
group progress label font=\bfseries\small,
link/.style={-latex, line width=1.5pt, linkred},
link label font=\scriptsize\bfseries,
link label node/.append style={below left=-2pt and 0pt}
]{1}{41}
\gantttitle[
]{QUARTER:\quad1}{2}
\gantttitle{2022}{12}
\gantttitle{2023}{12}
\gantttitle{2024}{12} \\
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\\
\ganttbar[
progress=100,
name=WBS1A
]{\textbf{Literature review \& thesis aims clarification }} {1}{4} \\
\ganttbar[
progress=100,
name=WBS1A
]{\textbf{To carry out a comprehensive check whether the Lagrangian self-consistently implies the correct physics via its resulting Euler-Lagrange equations}}{3}{5}\\
\ganttbar[
progress=100,
name=WBS1D
]{\textbf{to address HAVING IDENITIFIED X XANNOATE SOLUITON HODGE PR SOMEHTIGN the short-comings of the article in the BOTHEJM/B-paper}}{4}{6} \\
\ganttbar[
progress=0,
name=WBS1C
]{\textbf{Paper preperation and submission: Hodge decomposition, suggestion of a Lagrangian and computing the Euler-Lagrange equations}}{6}{8} \\
\ganttbar[
progress=100,
name=WBS1A
]{\textbf{To work out a systematic approach based on the second variation technique by which in case of compressible flow a linear acoustic model is obtained straight forwardly from an arbitrary Lagrangian}}{3}{4} \\
\ganttbar[
progress=100,
name=WBS1B
]{\textbf{To apply the forementioned approach developed in to our Lagrangian and compare with classical results }}{4}{5} \\
\ganttbar[
progress=100,
name=WBS1C
]{\textbf{to extend the analysis outlined IN TASK X? to weakly nonlinear acoustic models by amending the second variation technique by cubic terms of the respective Taylor expansion}}{4}{5} \\
\ganttbar[
progress=0,
name=WBS1D
]{\textbf{Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian}}{7}{9} \\
\ganttbar[
progress=0,
name=NONLAG
]{\textbf{ (expect intermediate results)To apply the approach developed in TASK XX OUR Lagrangian, compare the result with existing models in open literature, and to discuss the physical implications of the result}}{6}{12} \\
\ganttbar[
progress=0,
name=REL
]{\textbf{Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian}}{10}{14} \\
\ganttbar[
progress=0,name=POI]{\textbf{
To work out a stability analysis for a simple flow example (Poiseuille, Couette or film flow) based on the second variation technique with comparison to existing stability results in literature}}{14}{18} \\
\ganttbar[
progress=0,
name=FEM
]{\textbf{to figure out a FEM approach for incompressible flow based on the new Lagrangian (but without implementing a computer code for the latter) for future applications }}{16}{20} \\
\ganttbar[progress=15]{\textbf{Thesis writing / and submission}}{1}{41} \\
\ganttbar[progress=15]{\textbf{Oral Exam}}{40}{41}
\ganttlink[link type=s-s]{POI}{FEM}
%\ganttlink[link type=f-s]{NONLAG}{REL}
\ganttlink[link type=f-s]{REL}{POI}
\end{ganttchart}
\end{document}
我希望整个甘特图都有边框，包括标题区和甘特条的标签。
我想将一些甘特图条形标签放在两行上。\\ 不起作用。
我想要将标题“任务”放在甘特图条形标签上方。
请问我该怎么做？
答案1
欢迎使用 TeX.SE。条形标签是节点，因此您需要指定对齐方式才能获得换行符，如下所示，通过右对齐条形标签（感谢@Jasper）：
bar label node/.append style={left=2cm,align=right}
然后，您只需要\\在条形标签中的所需点处断线即可。
您可以像这样将每个节点标签加粗（不必\textbf在每个条形标签中使用）：
bar label font=\bfseries\small\color{black!70}, %<-- \bfseries
使用以下方法手动添加“TASKS”：
\node [text=blue,font=\Large\bfseries,anchor=east] at (-2,-1.75) {TASKS};
使用以下方法在画布周围绘制一个框：
\draw[line width=2pt,blue] ([yshift=-1cm]current bounding box.south west) rectangle
(current bounding box.north east);
使用以下方式添加标题：
\node [font=\Large\bfseries] at ([yshift=0.5cm]current bounding box.north)
{Gantt chart showing PhD activity time lines over four month intervals beyond the
confirmation review};
\myline{line thickness}{line colour}每个命令末尾都添加了“TASKS”下的行和每个条形标签\ganttbar。\myline{}{}这是对此处 hack 的改编：如何在甘特图中添加水平线？。
我还使用了我认为更令人愉悦的年份和季度标题。
祝你的论文顺利。从主题材料来看，学习 LaTeX 可能会对你有所帮助。
\documentclass[tikz,border=3pt]{standalone}
% Uncomment the following line to allow the usage of graphics (.png, .jpg)
%\usepackage[pdftex]{graphicx}
% Comment the following line to NOT allow the usage of umlauts
\usepackage{pgfgantt}
\usepackage{amsfonts}
% Start the document
\begin{document}
\definecolor{barblue}{RGB}{153,204,254}
\definecolor{groupblue}{RGB}{51,102,254}
\definecolor{linkred}{RGB}{165,0,33}
\renewcommand\sfdefault{phv}
\renewcommand\mddefault{mc}
\renewcommand\bfdefault{bc}
\setganttlinklabel{s-s}{START-TO-START}
\setganttlinklabel{f-s}{FINISH-TO-START}
\setganttlinklabel{f-f}{FINISH-TO-FINISH}
\sffamily
% Find the left edge of the bar label by measuring the width of the longest label, and add 10pt
\pgfmathsetmacro\myleft{width("To apply the forementioned approach developed in to our Lagrangian and compare with classical results")+2cm}
% Adapt \ganttnewline to draw a line from a position equal to the length of the longest label
\makeatletter
\newcommand*\myline[2][]{%
\begingroup%
\pgfmathsetmacro\y@upper{%
\gtt@lasttitleline * \ganttvalueof{y unit title}%
+ (\gtt@currentline - \gtt@lasttitleline - 1)%
* \ganttvalueof{y unit chart}%
}
\draw[#1,#2]
(-\myleft pt, \y@upper pt) -- %<-- -\myleft pt replaces 0pt, which starts the line from the left edge of the canvas.
(\gtt@chartwidth * \ganttvalueof{x unit}, \y@upper pt);%
\global\advance\gtt@currentline by-1\relax%
\endgroup%
}
\makeatother
\begin{ganttchart}[
[
canvas/.append style={fill=none, draw=black!5, line width=.75pt},
hgrid style/.style={*1{draw=black!5, line width=.75pt}},
vgrid={*1{draw=black!5, line width=.75pt}},
today=7,
today rule/.style={
draw=black!64,
dash pattern=on 3.5pt off 6.5pt,
line width=1.5pt
},
today label font=\small\bfseries,
title/.style={draw=black, fill=none},
title label font=\bfseries\footnotesize,
include title in canvas=false,
bar label node/.append style={left=2cm,align=right},
bar/.append style={draw=none, fill=black!63},
bar incomplete/.append style={fill=barblue},
bar progress label font=\mdseries\footnotesize\color{black!70},
link/.style={-latex, line width=1.5pt, linkred},
link label font=\scriptsize\bfseries,
link label node/.append style={below left=-2pt and 0pt}
]{1}{41}
\gantttitle{2021}{6}
\gantttitle{2022}{12}
\gantttitle{2023}{12}
\gantttitle{2024}{12} \\
\gantttitlelist{"Q3","Q4","Q1","Q2","Q3","Q4","Q1","Q2","Q3","Q4","Q1","Q2","Q3","Q4"}{3}
\myline{blue}{thick}
\ganttbar[
progress=100,
name=WBS1A
]{Literature review \& thesis aims clarification } {1}{4} \myline{thin}{blue}
\ganttbar[
progress=100,
name=WBS1A
]{To carry out a comprehensive check whether the Lagrangian self-consistently\\implies the correct physics via its resulting Euler-Lagrange equations}{3}{5} \myline{thin}{blue}
\ganttbar[
progress=100,
name=WBS1D
]{to address HAVING IDENTIFIED X XANNOATE SOLUTION HODGE PR SOMETHING \\the short-comings of the article in the BOTHEJM/B-paper}{4}{6} \myline{thin}{blue}
\ganttbar[
progress=0,
name=WBS1C
]{Paper preparation and submission: Hodge decomposition, suggestion of\\a Lagrangian and computing the Euler-Lagrange equations}{6}{8} \myline{thin}{blue}
\ganttbar[
progress=100,
name=WBS1A
]{To work out a systematic approach based on the second variation technique by which in case of\\compressible flow a linear acoustic model is obtained straight forwardly from an arbitrary Lagrangian}{3}{4} \myline{thin}{blue}
\ganttbar[
progress=100,
name=WBS1B
]{To apply the forementioned approach developed in to our Lagrangian and compare with classical results}{4}{5} \myline{thin}{blue}
\ganttbar[
progress=100,
name=WBS1C
]{to extend the analysis outlined IN TASK X? to weakly nonlinear acoustic models by amending the\\second variation technique by cubic terms of the respective Taylor expansion}{4}{5} \myline{thin}{blue}
\ganttbar[
progress=0,
name=WBS1D
]{Paper preparation and submission: second variational acoustics- linear\\(both Lagrangians), non-linear from simple Lagrangian}{7}{9} \myline{thin}{blue}
\ganttbar[
progress=0,
name=NONLAG
]{(expect intermediate results)To apply the approach developed in TASK XX OUR Lagrangian, compare\\the result with existing models in open literature, and to discuss the physical implications of the result}{6}{12} \myline{thin}{blue}
\ganttbar[
progress=0,
name=REL
]{Paper preparation and submission: second variational acoustics-\\linear (both Lagrangians), non-linear from simple Lagrangian}{10}{14} \myline{thin}{blue}
\ganttbar[
progress=0,name=POI]{
To work out a stability analysis for a simple flow example (Poiseuille, Couette or film flow) based\\on the second variation technique with comparison to existing stability results in literature}{14}{18} \myline{thin}{blue}
\ganttbar[
progress=0,
name=FEM
]{to figure out a FEM approach for incompressible flow based on the new Lagrangian (but without\\implementing a computer code for the latter) for future applications}{16}{20} \myline{thin}{blue}
\ganttbar[progress=15]{Thesis writing / and submission}{1}{41} \myline{thin}{blue}
\ganttbar[progress=15]{Oral Exam}{40}{41} \myline{thin}{blue}
\ganttlink[link type=s-s]{POI}{FEM}
%\ganttlink[link type=f-s]{NONLAG}{REL}
\ganttlink[link type=f-s]{REL}{POI}
\node [text=blue,font=\Large\bfseries,anchor=east] at (-2,-1.75) {TASKS};
\draw[line width=2pt,blue] ([yshift=-1cm]current bounding box.south west) rectangle (current bounding box.north east);
\node [font=\Large\bfseries] at ([yshift=0.5cm]current bounding box.north) {Gantt chart showing PhD activity time lines over four month intervals beyond the confirmation review};
\end{ganttchart}
\end{document}
答案2
如果我正确理解了您的要求，这里有一种方法可以做到这一点：
广告 2，正如\ganttbar预期的文本一样，自然的做法是将标签描述放在 中\parbox。事实证明，最好定义一个新的命令\pw，它还可以处理粗体。通过选择不同于 15cm 的宽度进行调整。// 与您的标题有一些交互，请参见下文。
% put text and boldface into a new command
\newcommand\pw[1]{\parbox{15cm}{\textbf{#1}}}% adjust width by changing the 15cm
广告 1，很自然地将整个甘特图视为一些 tikz 代码，您可以将其用作节点内容。这就是为什么会出现这个额外的代码：
\tikz{% <<< TRICK: put ganttchart as node-content, draw borders of node
\node [draw] {% next follows the content
\begin{ganttchart}
...
\end{ganttchart}
};
...
}
广告 3，现在这些都是 tikz-ish，为什么不放一个保存标题的其他节点？经过对坐标的反复试验，这个似乎是合理的：
\node [draw, red] at (-19, 7) {TASKS};
为了更好地找到它，我留下了红色的框架和文字。//!! 但是，一旦调整宽度，坐标就必须改变\pw。当然有更好的方法可以做到这一点，比如使用相对放置（tikzlibrary 定位）。
\documentclass[tikz, border=5mm]{standalone}% <<< some borders
% Uncomment the following line to allow the usage of graphics (.png, .jpg)
%\usepackage[pdftex]{graphicx}
% Comment the following line to NOT allow the usage of umlauts
\usepackage{pgfgantt}
\title{Gantt chart showing PhD activity time lines over four month intervals beyond the confirmation review}
\usepackage{amsfonts}
% put text and boldface into a new command
\newcommand\pw[1]{\parbox{15cm}{\textbf{#1}}}% adjust width by changing the 15cm
% Start the document
\begin{document}
\definecolor{barblue}{RGB}{153,204,254}
\definecolor{groupblue}{RGB}{51,102,254}
\definecolor{linkred}{RGB}{165,0,33}
\renewcommand\sfdefault{phv}
\renewcommand\mddefault{mc}
\renewcommand\bfdefault{bc}
\setganttlinklabel{s-s}{START-TO-START}
\setganttlinklabel{f-s}{FINISH-TO-START}
\setganttlinklabel{f-f}{FINISH-TO-FINISH}
\sffamily
\tikz{% <<< TRICK: put ganttchart as node-content, draw borders of node
\node [draw] {% next follows the content
\begin{ganttchart}[
[
canvas/.append style={fill=none, draw=black!5, line width=.75pt},
hgrid style/.style={*1{draw=black!5, line width=.75pt}},
vgrid={*1{draw=black!5, line width=.75pt}},
today=7,
today rule/.style={
draw=black!64,
dash pattern=on 3.5pt off 6.5pt,
line width=1.5pt
},
today label font=\small\bfseries,
title/.style={draw=none, fill=none},
title label font=\bfseries\footnotesize,
title label node/.append style={below=7pt},
include title in canvas=false,
bar label font=\mdseries\small\color{black!70},
bar label node/.append style={left=2cm},
bar/.append style={draw=none, fill=black!63},
bar incomplete/.append style={fill=barblue},
bar progress label font=\mdseries\footnotesize\color{black!70},
group incomplete/.append style={fill=groupblue},
group left shift=0,
group right shift=0,
group height=.5,
group peaks tip position=0,
group label node/.append style={left=.6cm},
group progress label font=\bfseries\small,
link/.style={-latex, line width=1.5pt, linkred},
link label font=\scriptsize\bfseries,
link label node/.append style={below left=-2pt and 0pt}
]{1}{41}
\gantttitle[
]{QUARTER:\quad1}{2}
\gantttitle{2022}{12}
\gantttitle{2023}{12}
\gantttitle{2024}{12} \\
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\\
% --- replace \textbf by \pw in \ganttbar --------
\ganttbar[
progress=100,
name=WBS1A
]{\pw{Literature review \& thesis aims clarification }}{1}{4} \\
\ganttbar[
progress=100,
name=WBS1A
]{\pw{To carry out a comprehensive check whether the Lagrangian self-consistently implies the correct physics via its resulting Euler-Lagrange equations}}{3}{5}\\
\ganttbar[
progress=100,
name=WBS1D
]{\pw{to address HAVING IDENITIFIED X XANNOATE SOLUITON HODGE PR SOMEHTIGN the short-comings of the article in the BOTHEJM/B-paper}}{4}{6} \\
\ganttbar[
progress=0,
name=WBS1C
]{\pw{Paper preperation and submission: Hodge decomposition, suggestion of a Lagrangian and computing the Euler-Lagrange equations}}{6}{8} \\
\ganttbar[
progress=100,
name=WBS1A
]{\pw{To work out a systematic approach based on the second variation technique by which in case of compressible flow a linear acoustic model is obtained straight forwardly from an arbitrary Lagrangian}}{3}{4} \\
\ganttbar[
progress=100,
name=WBS1B
]{\pw{To apply the forementioned approach developed in to our Lagrangian and compare with classical results }}{4}{5} \\
\ganttbar[
progress=100,
name=WBS1C
]{\pw{to extend the analysis outlined IN TASK X? to weakly nonlinear acoustic models by amending the second variation technique by cubic terms of the respective Taylor expansion}}{4}{5} \\
\ganttbar[
progress=0,
name=WBS1D
]{\pw{Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian}}{7}{9} \\
\ganttbar[
progress=0,
name=NONLAG
]{\pw{(expect intermediate results)To apply the approach developed in TASK XX OUR Lagrangian, compare the result with existing models in open literature, and to discuss the physical implications of the result}}{6}{12} \\
\ganttbar[
progress=0,
name=REL
]{\pw{Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian}}{10}{14} \\
\ganttbar[
progress=0,name=POI]{\pw{
To work out a stability analysis for a simple flow example (Poiseuille, Couette or film flow) based on the second variation technique with comparison to existing stability results in literature}}{14}{18} \\
\ganttbar[
progress=0,
name=FEM
]{\pw{to figure out a FEM approach for incompressible flow based on the new Lagrangian (but without implementing a computer code for the latter) for future applications }}{16}{20} \\
\ganttbar[progress=15]{\pw{Thesis writing / and submission}}{1}{41} \\
\ganttbar[progress=15]{\pw{Oral Exam}}{40}{41}
\ganttlink[link type=s-s]{POI}{FEM}
%\ganttlink[link type=f-s]{NONLAG}{REL}
\ganttlink[link type=f-s]{REL}{POI}
\end{ganttchart}
};
% HEADER
\node [draw, red] at (-19, 7) {TASKS};
}
\end{document}
附言：仍然不确定您想要的结果会是什么样子，但这里有 2 条进一步修改的建议，只是为了说明您原则上可以做什么。最后：
% HEADER
\node at (-19, 7) {\underline{TASKS}};% underline text
\draw [blue] (-20, 6.3) to (-4, 6.3) to (-4, -8.35);% draw some lines
答案3
假设您想在报告中提供甘特图，并结合缩短标签的想法，这里有另一种方法。也许它不是一个解决方案，而是一个概念的说明。
基本步骤：
- 使用文章类
- 显示标题
- 删除所有定义和图表选项（存在一些模糊的交互）
- 保留
\gantttitles季度，但删除年份（我的经验不足） - 将
\gantbar代码转换为更紧凑的形式，以提高编辑器的可读性 - 介绍简短的标签，并在图表后进行解释
%\documentclass[tikz, border=5mm]{standalone}% <<< some borders
%\documentclass[landscape]{article}% <<< other class
\documentclass[a4]{article}% <<< other class
\usepackage{tikz, pgfgantt}
\usepackage{amsfonts}
\title{Gantt chart showing PhD activity time lines over four month intervals beyond the confirmation review}
% put text and boldface into a new command
%\newcommand\pw[1]{\parbox{15cm}{\textbf{#1}}}% adjust width by changing the 15cm
\newcommand\pw[1]{\textbf{#1}}% simpler layout
% Start the document
\begin{document}
\maketitle% Title at beginning
\begin{ganttchart}[%removed all definitions for clarity
expand chart=\textwidth% tame the drawing
]{1}{41}
% removed ganttiltle, as there is something strange about it
\gantttitle{}{1}% a missing leading month
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\gantttitle{Q1}{4}
\gantttitle{Q2}{4}
\gantttitle{Q3}{4}
\gantttitle{Q4}{4}
\ganttnewline
% ~~~ made entries more readable in the editor ~~~~~~~~~~~~
\ganttbar[progress=100, name=WBS1A] {\pw{A}}{1}{4} \\
\ganttbar[progress=100, name=WBS1A] {\pw{B}}{3}{5} \\
\ganttbar[progress=100, name=WBS1D] {\pw{C}}{4}{6} \\
\ganttbar[progress=0, name=WBS1C] {\pw{D}}{6}{8} \\
\ganttbar[progress=100, name=WBS1A] {\pw{E}}{3}{4} \\
\ganttbar[progress=100, name=WBS1B] {\pw{F}}{4}{5} \\
\ganttbar[progress=100, name=WBS1C] {\pw{G}}{4}{5} \\
\ganttbar[progress=0, name=WBS1D] {\pw{H}}{7}{9} \\
\ganttbar[progress=0, name=NONLAG] {\pw{I}}{6}{12} \\
\ganttbar[progress=0, name=REL] {\pw{J}}{10}{14} \\
\ganttbar[progress=0, name=POI] {\pw{K}}{14}{18} \\
\ganttbar[progress=0, name=FEM] {\pw{L}}{16}{20} \\
\ganttbar[progress=15] {\pw{M}}{1}{41} \\
\ganttbar[progress=15] {\pw{N}}{40}{41}
\end{ganttchart}
\newpage% start new page
Some more details:
\vspace{2em}% typesetting: put some vertical space
\begin{tabular}{p{1cm}p{11cm}}
A: & Literature review \& thesis aims clarification\\
B: & To carry out a comprehensive check whether the Lagrangian self-consistently implies the correct physics via its resulting Euler-Lagrange equations\\
C: & to address HAVING IDENITIFIED X XANNOATE SOLUITON HODGE PR SOMEHTIGN the short-comings of the article in the BOTHEJM/B-paper\\
D: & Paper preperation and submission: Hodge decomposition, suggestion of a Lagrangian and computing the Euler-Lagrange equations\\
E: & To work out a systematic approach based on the second variation technique by which in case of compressible flow a linear acoustic model is obtained straight forwardly from an arbitrary Lagrangian\\
F: & To apply the forementioned approach developed in to our Lagrangian and compare with classical results\\
G: & to extend the analysis outlined IN TASK X? to weakly nonlinear acoustic models by amending the second variation technique by cubic terms of the respective Taylor expansion\\
H: & Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian\\
I: & (expect intermediate results)To apply the approach developed in TASK XX OUR Lagrangian, compare the result with existing models in open literature, and to discuss the physical implications of the result\\
J: & Paper preperation and submission: second variational acoustics- linear (both Lagrangians), non-linear from simple Lagrangian\\
K: & To work out a stability analysis for a simple flow example (Poiseuille, Couette or film flow) based on the second variation technique with comparison to existing stability results in literature\\
L: & to figure out a FEM approach for incompressible flow based on the new Lagrangian (but without implementing a computer code for the latter) for future applications\\
M: & Thesis writing / and submission\\
N: & Oral Exam
\end{tabular}
\end{document}
另外，这些排除的语句会导致一些麻烦，我暂时还没有解决。
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