Chapter 116: Deducing physical meaning from mathematical formulas

"Um...is it gone here?"

Lin Xiao leaned on and checked, and gradually saw the last page of the draft paper.

The last page of the draft paper was left with an expression. It was probably because I encountered difficulties and did not continue.

[The existence of weak consistent attractors and strong consistent attractors in C(1H0)(Ω)*C(L)(Ω)...]

"So we just want to find out the existence of the consistent attractor?"

Lin Xiao touched his chin and started thinking.

He suddenly discovered that he seemed to be able to find a solution to this problem.

Although it is a physical problem, it is now transformed into a mathematical problem, and it must be solved using mathematical methods.

"Partial differential equations... By the way, the Fedor-Galkin approximation should be applicable to this."

After a while, Lin Xiao thought of a way to solve this problem.

So he took out his pen, pulled out a new scrap of paper, and started writing according to his own ideas.

[Suppose f satisfies equation 1.2-1.5, F(Ut) satisfies the assumption...initial value ξτ=(φ, φ)∈Cε...]

[So the existence of T0 makes there exist a Shatah-Struwe solution to the equation. 】

"Well... that should be enough here."

Lin Xiao nodded after confirming that there was no problem, but if he went back, he still had some problems.

For this kind of partial differential equation, people often like to study the existence of solutions. As for the general solution, there is no such solution, and only specific equations can be analyzed in detail.

In physics, there are especially many problems using partial differential equations. For example, the famous N-S equation is a kind of partial differential equation, and the same is true for Maxwell's equations.

When reaching a deeper level, it is necessary to have a deeper understanding of physics-related professional knowledge, and Lin Xiao does not know how to proceed.

Of course, it’s okay to simply take a look and write it down based on mathematical formulas.

So he continued to conduct simple deductions from a mathematical perspective, which was nothing more than proving the existence of solutions to partial differential equations.

In this way, he arrived at about eleven o'clock, and at this time, the sound of a key turning in the lock was heard outside the door.

Wang Wei is back.

Wang Wei came in with a tired look on his face. It was obvious that the start of school was very tiring. After all, some students might have encountered some problems and asked him as a counselor to help solve them, or there might be administrative matters in the college.

However, when he came in and saw that Lin Xiao was not sleeping yet, but was reading at the desk, he couldn't help but be surprised.

No wonder people are able to achieve this level of success. Talent and hard work are both indispensable.

"Why aren't you asleep yet?"

"Teacher Wong."

Lin Xiao finally raised his head and said hello. Then he looked at the time and was stunned for a moment: "Ah, it's already 11 o'clock?"

Wang Wei: "...Don't you even care about the time when you study?"

"I forgot to read..."

Lin Xiao said, immediately put down the pen in his hand and prepared to go to bed. After all, they would gather at six o'clock tomorrow morning.

Of course, he didn't forget to say: "Oh, by the way, Teacher Wang, I just took a look at the scratch paper you put on the table."

"Ah?" Wang Wei was stunned, walked up and saw the draft paper on the table, and then said with a smile: "Oh, this is something I studied before, just look at it, I encountered some problems in the end, so I didn't figure it out. , and now I have given up.”

"It's just to find the existence of the consistent attractor, right? I took a look and found that it can be obtained using an approximation. The result satisfies Lipschitz continuity, and then it can be figured out. The subsequent process should also be possible."

Lin Xiao had already sat on the bed and said something at the same time.

Hearing his words, Wang Wei was stunned: "What? You mean... you know how to do it? Do you also study mathematics and physics?"

"This... I haven't done any research on it."

"Then do you understand?"

"I didn't understand it at first, but after reading it I understood a little bit." Lin Xiao said: "I took a look at the formulas you wrote above, and some text explanations, and then I roughly understood what was written. What does it mean? It’s almost like deducing its physical meaning from mathematical formulas.”

"...?"

Wang Wei was stunned.

Deducing physical meaning from mathematical formulas?

Are you cheating? !

But can cheating still be done like this?

But in the end, after thinking about Lin Xiao's deeds, he gave up the idea of ​​trying to reason with such a person.

However, he was also curious about how Lin Xiao solved it, so he picked up the scratch paper and glanced at the "Fundamentals of Materials Science" that Lin Xiao was reading. He couldn't help but be surprised, Lin Xiao was still learning this thing?

"You still want to study materials science?"

"Just understand and understand."

Lin Xiao lay on the bed and took a nap.

There is no way to explain that he is doing it to gain experience.

"Then... okay, then you can go to sleep and I'll just take a look."

Wang Wei stopped thinking about it. With such geniuses, it would be difficult for ordinary people to understand what they want to do.

Then he returned to his desk, turned off the headlight first, and let Lin Xiao sleep peacefully. He just turned on the lamp on his desk.

Although as a counselor, he has to get up early on the first day of military training tomorrow, but he doesn't need military training, so he still has time to rest.

Soon, he turned directly to the page behind his draft paper and saw the difficulty he encountered at the beginning.

It was this place that he finally gave up on further research.

In fact, this question was one of the topics left by his supervisor when he was still studying for his PhD.

His doctoral supervisor was Academician Tang Qing from the School of Mathematical Sciences at Peking University. Academician Tang Qing was accomplished in mathematics and mathematical physics, so Wang Wei followed him into the area of ​​mathematical physics.

However, when choosing a topic at that time, Tang Qing told him that the difficulty of this problem was the most difficult one among the topics given to him, and he was allowed to choose on his own. At first, he acted according to his ability, so he gave up on this topic and chose something else that was relatively simple. subject.

Although he has graduated now, he remembered this problem again some time ago and wondered whether he should try this most difficult subject. Unexpectedly, he encountered difficulties before proceeding very far and had to give up in the end.

However, for such a question that made him unable to continue writing, now Lin Xiao told him that he had no research on mathematical physics, how could he still write about something that he couldn't figure out at the beginning?

He felt a little incomprehensible.

However, when he opened Lin Xiao's draft paper and the following steps, he was stunned.

"Fedo Galkin is approaching? What method is this?"

He suddenly realized that he didn't know what this method was called.

This is probably from a related paper, right?

In fact, Lin Xiao learned about this method when he attended a report at the International Congress of Mathematicians. Then he remembered the general theory. When he looked at the problem Wang Wei encountered just now, he thought of this method. , so I deduced it based on the previous impression and used it here.

However, Wang Wei naturally does not know these things. Now he can only admire Lin Xiao's knowledge in his heart. At the same time, he also wants to ask Lin Xiao where the original paper is. He wants to know more about it, but he just sees Lin Xiao. Xiao already fell asleep, so he could only give up.

Then, he turned his head and looked at Lin Xiao's steps. The approaching Fedor Galkin 'approached' this difficulty into an easy-to-understand form, which suddenly made him enlightened. After that, Lin The Lipschitz continuum that Xiao used was already known to him. Doctors who study partial differential equations should basically know it anyway.

In this way, after ten minutes of reading, he finished reading all Lin Xiao's steps, and then put down the scratch paper.

At this time, he could only marvel in his heart, because next, as long as he followed the steps that Lin Xiao took to get here, he could continue this project again.

Although there is no guarantee that he will encounter problems later, for now, Lin Xiao has solved the biggest problem he faced.

With a wry smile, he murmured: "Is it true that a student in my class has become my corresponding author?"

Generally speaking, the corresponding author is the mentor of the first author of the paper or the person in charge of the project. He is responsible for the reliability of the article. Of course, he will also be responsible for guidance during the research process.

Obviously, Lin Xiao provided Wang Wei with guidance.

Wang Wei couldn't laugh or cry for a moment.

It's hard to say, but this can be regarded as Lin Xiao's compensation for living here?

"If it happens later, I have to leave a place for Lin Xiao as the second author."

After thinking about it for a while, as for the position of the corresponding author, of course it cannot be given casually, but based on the help Lin Xiao provided him, the second work will definitely be fine.

Wang Wei stopped thinking about it, turned off the desk lamp, and prepared to sleep.

…

The next day, military training began as usual. Although it was hard, it was essential for every student.

Lin Xiao felt that it was acceptable. After swallowing a health capsule, his body has been in great shape since then, just like military training, which is just a bit tired.

The only thing that made the students feel uncomfortable was the extremely hot weather in Beijing in September.

When tigers come out of the mountains in autumn, most people complain endlessly.

Of course, there are some interesting activities during military training, which can be regarded as a time for students to relax their bodies and minds. One day, they were taken to the army training ground to try out target shooting. This is also part of the military training at Peking University. kind of welfare.

However, time passed so quickly, and fifteen days later, the military training ended.

In the cheers of the students, the torturous life was finally over, and it was time for Lin Xiao to leave Wang Wei's dormitory.

"Are you leaving?"

"Um."

Lin Xiao nodded and put his toothbrush and cup into his schoolbag, preparing to carry them back to Yanbeiyuan.

Although I have lived here for half a month, I have become somewhat accustomed to it, but it is Wang Wei's dormitory after all. If he really lived here, even if Wang Wei didn't say anything on the surface, he would definitely complain a few words in his heart.

What's more, Lin Xiao felt that it was a pity to leave the more than 5 million house without living in it.

Wang Wei stepped forward, helped Lin Xiao tidy up, and then said: "By the way, I'm going to write a paper on the last question."

"what is the problem?"

Lin Xiao was stunned.

"It was the night before the military training, the mathematical physics problem I encountered, the weakly damped wave equation."

Lin Xiao finally remembered at this time, and then said with a smile: "That's pretty good, has it been solved?"

"That's not true."

Wang Wei shook his head: "I only have this plan temporarily. I am still studying it recently, but it will be done in about half a month."

"Which one do you plan to post at that time?"

""MATHEMATICAL-METHODS-IN-THE-APPLIED-SCIENCES", from District 2."

"sure."

Lin Xiao nodded. Being able to send it to Area 2 shows that the value of the paper is still great.

"I will put your name on the second work when the time comes, I hope you don't mind."

At this time, Wang Wei said with a smile again.

Please give me a monthly pass! !