I failed a course, and the system became my study supervisor.

Chapter 41 Self-examination

After the pros and cons were determined, the intensive training came to an end, and several teachers and a group of students left one after another.

Xu Ling kept the team members.

"Well... I think I need to reflect on the work I've been doing.

As the team leader, I didn't review the content of previous competitions, which led me to lead everyone in the wrong direction. I also made wrong decisions during the experiment, wasting a lot of everyone's time."

Xu Ling said to his team members with self-blame.

No one in the group intended to blame Xu Ling. They had always seen Xu Ling's serious attitude towards the experiment.

After listening to Xu Ling's self-examination, several people also joined in self-reflection.

"I came up with the experimental plan, I also proposed the vacuuming method, and I was mainly involved in writing the experimental report. If there are any problems, I can't escape blame."

Ji Yun said seriously.

Her words were very harsh, as if she was taking all the responsibility. Xu Ling quickly spoke to comfort her and told her not to take it too seriously.

Immediately afterwards, Liang Xiuyuan and Huang Yunfeng also conducted self-examination, which roughly meant that they were not so serious about the experiment and did not have the spirit of striving for excellence during the experimental process.

They are honest and this is indeed a problem they have.

Even Qin Qin said a few words, saying that she had not made good use of her experience and pointed out the problems to everyone.

I watched as my own self-criticism turned into a criticism meeting for all employees.

Xu Ling was at a loss for words and had a dark face.

When did everyone become so self-critical?
Xu Ling quickly stopped him: "Alright, alright, enough self-reflection, let's discuss what we should do next."

"Hmm..." Qin Qin was the first to respond. "Right now, the first thing we need to do is a theoretical analysis of the shape of the liquid surface, and then the effect of the liquid surface shape on magnification and resolution. We also need to redesign the experimental plan."

"Theoretical derivation is the big part." Xu Ling emphasized again.

"But I'm afraid I'm not very good at theoretical deduction. We're only freshmen and haven't learned much."

Huang Yunfeng said somewhat embarrassedly.

"If you haven't learned it before, just learn it now. I remember Liang Xiuyuan said he was good at looking up literature. Is that true?"

Xu Ling didn't dwell on Huang Yunfeng's question and turned to look at Liang Xiuyuan.

"I have experience in researching literature, but I'm not an expert at it."

Liang Xiuyuan scratched his head and said embarrassedly.

Xu Ling was not surprised. After all, not everyone had the experience of writing a paper in their freshman year like him.

"That's fine. First, try to find as much literature as possible. The main thing is to prove that I can do it. I have done research on fluid physics."

Xu Ling comforted him.

Liang Xiuyuan agreed deeply and nodded.

The discussion continued and finally a preliminary plan was formed.

The theoretical derivation was mainly carried out by Xu Ling and Qin Qin, while Liang Xiuyuan and Huang Yunfeng's main goal was to find references, study on their own, understand the theoretical derivation of Xu Ling and Qin Qin, and fill in some simple loopholes.

As for the experimental plan, as well as the detailed operation and experimental report of the subsequent experiments, they were all handed over to Ji Yun. Her experience in experiments was obvious to all.

After making the arrangements, Xu Ling and Qin Qin went to the library together, while the others went their separate ways to complete their tasks.

As they walked along the road, Qin Qin asked, "How is it? How does it feel? The experiment is almost starting over again."

"In the end, it's still a bit sad. I worked so hard on the experiment and wrote the report, but there are so many problems."

Xu Ling told the truth.

"It doesn't matter. The things in the previous experiments are not completely unusable. The proof of the Rayleigh criterion and the like can be directly used."

Qin Qin said seriously.

Xu Ling understood these principles. Furthermore, the new experiment had a direction and plan, and would be much more efficient than the first time. Because of this, Xu Ling wasn't feeling particularly bad at the moment, and remained confident in the upcoming experiment.

"Then let's work hard together!"

"Yeah! Come on together!"

……

For the rest of the vacation, Xu Ling and Qin Qin spent almost the entire time in the library.

As the saying goes, when men and women work together, work becomes less tiring.

Xu Ling didn't expect that it could even be applied to scientific research activities.

Xu Ling is the main expert in theoretical analysis, and Qin Qin's task is to find suitable literature for Xu Ling's reference when he needs it.

Qin Qin can always find a document in a timely manner, and that document just happens to match the problem Xu Ling encountered.

For the droplet shape, a coordinate system was established. According to the Young-Laplace equation, Xu Ling obtained:
dx/ds=cosθ
dz/ds=sinθ
dθ/ds=2/r+ρgz/γ-sinθ/x
dV/ds=πxsinθ
方程初始条件为：x(0)=z(0)=θ(0)=V(0)=0。

In the equation, γ is the surface tension coefficient.

Although this equation looks simple, it is very complicated to solve, and it is difficult for Xu Ling to solve it independently.

Qin Qin immediately discovered this problem and found a paper about using MATLAB to solve the Young-Laplace equation through numerical solution.

After taking some time to figure it out, Xu Ling easily got an image of the shape of the droplet.

What surprised Xu Ling was that Lin Yuxin did not go home during the holidays and occasionally came to the library with Qin Qin.

Sometimes, if Xu Ling and Qin Qin discussed a key point and did not have time to eat, Lin Yuxin would bring them food.

Just by starting the trend of bringing your own lunch, things got out of control.

"Do you think of me as a babysitter? You've taken care of me time and time again. It's fine if you bring me food, but now you're asking me to fetch water too!"

Lin Yuxin said angrily.

"Oh! Come on, just help your sister."

Qin Qin pursed her lips and kept pushing the cup of water to Lin Yuxin.

"Don't go!"

Lin Yuxin shook off her hand with a firm attitude.

"Let's go~"

Qin Qin grabbed Lin Yuxin's arm and shook it continuously. Her voice was not only soft but also drawn out.

"Just this once! Go by yourself next time!"

Lin Yuxin finally couldn't stand her nagging and took the cup of water.

"Can you bring me a cup too?" Xu Ling asked.

"roll!"

Lin Yuxin responded viciously.

Xu Ling shrank his neck in fear.

Forget it, go by yourself.

Xu Ling shook his head helplessly.

In addition to Lin Yuxin, Huang Yunfeng and Liang Xiuyuan would come to the library from time to time, either to look for information or to copy an analysis that Xu Ling had already completed.

If they encountered problems that they couldn't understand, they would raise them on the spot. Their diligent and thirsty expressions made Xu Ling look at them with awe.

Time passes slowly, and everything is developing steadily and positively.

(End of this chapter)