I really just want to be a scholar

Chapter 382 Do you want to participate in the Mathematical Modeling Contest for College Students?

When it comes to "Zeno's Tortoise", not many people may know it, but when it comes to "Schrödinger's Cat", I believe that most people have heard of it.

In fact, the level of "Zeno's tortoise" is the same as that of "Schrödinger's cat". Together with "Laplace's monster" and "Maxwell's demon", they are called "the four great beasts of physics", It can be said to be famous in the physics world.

"Zeno's Tortoise" is also known as "Zeno's Paradox". It originally told the story of a race between God and a tortoise. We might as well change it back to the familiar race between the tortoise and the hare.

The tortoise said to the rabbit: "Although you run very fast, as long as I run first, you will never catch up with me."

The rabbit didn't believe it, and the tortoise gave an example: "For example, I ran 100 meters first, and you came to chase me. Suppose your speed is always maintained at 10 meters per second, and my speed is always maintained at 1 meter per second. After running 10 meters in 100 seconds, I walked 10 meters forward, and I was still in front of you. After 1 second, you ran another 10 meters, and I walked 1 meter, and I was still in front of you. And so on, no matter you How to approach me, but I will always be in front of you."

When the rabbit thought about it carefully, it really could never catch up with the tortoise.

So the tortoise and the hare won the race with the tortoise's mouth cannon, and the hare surrendered without fighting.

Is that really the case?Everyone knows that a rabbit can overtake a tortoise in a real run, but why is there such a paradox?
This problem is finally described in mathematical language, that is, a finite length is divided into infinitely many parts, but the sum of these infinitely many parts is not infinite.

Zhuangzi also mentioned a similar divine cudgel in "Zhuangzi · Tianxia Pian"-"A one-foot-long cudgel, take half of it in a day, and it will last forever."This is exactly the same paradox.

Hua Hong, a doctoral student, couldn't help asking: "Junior Qin Ke, I've heard of this 'Zeno's Tortoise', but does it have anything to do with our question?"

"How is the paradox 'Zeno's tortoise' solved mathematically?"

"The concept of 'limit' through calculus."

Qin Ke smiled and said: "Yes, you have used the 'maximum' and 'minimum' methods to solve the partial differential equations here, which is correct in theory, just like the assumption made by the tortoise, but the problem is The result of the final demonstration is quite different from reality, even contrary to it, is this essentially the same as "Zeno's Tortoise"?"

The eyes of Chen Licheng, Hua Hong and the others lit up at the same time. After thinking about it carefully, it was indeed so!

"The maxima-minimum method is indeed a very excellent mathematical method, but it is not suitable for this occasion. In the case of both intra-species and inter-species attraction, the solution of the Schrödinger equation in the nonlinear partial differential equation system represents the wave function. The square of the solution represents the probability density of particles appearing at a certain spatial position at a certain time point, and it is easy to cause the probability density to be distorted by the limit when using the maximin method.”

"So that's true, that's true!" Chen Licheng is also a mathematician, and he understood it after thinking about it, and then he was annoyed: "Why didn't we find this problem!"

"You are fans of the authorities, and you only want to solve this problem as quickly as possible with a sharp tool like the method of maxima and minima, but you have unknowingly fallen into a paradox similar to 'Zeno's tortoise'. "

Qin Ke found a way for everyone with a gentle tone. In fact, if a genius mathematician like Chen Licheng is not in a hurry to make the most dazzling results in the shortest time, as long as he uses different methods to study in a down-to-earth manner, Surely this puzzle can be solved within two months.

But because of the problem of mentality, it caused such a result that haste makes waste...

Hua Hong asked subconsciously: "Then what mathematical method is the most suitable?"

As soon as the words came out, several people cast strange glances at him.

It's amazing that Qin Ke can see the problem so quickly. Do you still expect him to give the correct answer?Isn't this embarrassing him so that he can't step down?

Chen Licheng coughed lightly, and was about to change the topic, but Qin Ke said thoughtfully: "If you must give me advice, you can try it from two directions."

"The first one is to use the 'difference' method to determine the parameter range in which the normalized solution exists through fine constraints, and then to prove the existence of the normalized solution."

"Another way to try the 'variational method' is to determine the existence of regular solutions by introducing 'equivalent functionals', 'mountain road lemma', and 'surrounding method'." Qin Ke took a pen on the whiteboard and roughly Wrote two directions, and then said:

"Of course, there is a third optimal method in theory, which is to start from the 'Isomorphism Theorem of Solutions' and try to combine the 'divergence' method, which may require the least amount of calculations. In three pages Solve the problem of the existence of the normal solution that you want to prove."

quiet!
The entire laboratory fell into absolute silence!
The three methods proposed by Qin Ke were like a blockbuster, which directly shocked the six people including Chen Licheng.

Qin Ke actually pointed out the direction to solve this problem!

Even if it's just the direction, it's incredible enough, because Qin Ke only read the relevant information for 3 minutes!
This is simply unbelievable, but Qin Ke easily pointed out the performance of the problem just now, which indeed made it impossible for several people to underestimate his suggestion!

Chen Licheng murmured: "Is the 'difference' method a widely praised new mathematical method published on ANN MATH the year before last? I never thought of trying this method at all..." He took a few steps forward, excited He firmly held Qin Ke's hand: "Thank you, Junior Brother Qin! You just awakened the dreamer with your words. If it weren't for you, our project would have stalled for another two months before we could find out the problem!"

What Chen Licheng said was two months. In fact, he knew in his heart that as long as he survived for another half a month, the team would basically fall apart. It is not difficult to judge from the fierce quarrel among the team members before they came in. ending.

After all, long-term research on a topic with no hope in sight is too much a test of people's will and mentality, let alone this is a new team that has not been established for a long time and the running-in period has not yet ended.

So this time, Chen Licheng was really grateful to Qin Ke from the bottom of his heart, and at the same time, he was also reflecting that he was really too impatient.

He sighed in his heart, after all, he is still young and vigorous... On the road of cultivating his mind, he still has a lot to learn.

Qin Ke hurriedly said: "Senior Chen, you are too polite. I am just a bystander. If I were in your position, I might not be able to get around this paradox for half a year."

Qin Ke's lack of credit and humility made several doctoral students in Chen Licheng's team like it even more. Even the two doctoral students who were silent before and somewhat rejected Qin Ke took the initiative to shake hands with Qin Ke and thank him.

Chen Licheng tried again and again to invite Qin Ke to join his scientific research team, but Qin Ke politely declined.

He knew that this project was very important to Chen Licheng, and when he estimated the results, it was when his paper on the proof of the twin prime number conjecture was published.

At that time, I was afraid that my reputation would skyrocket, far surpassing Chen Licheng. If I was in this scientific research team, would outsiders put all the scientific research achievements on my head, and there would be a scene of overwhelming the host?As soon as he thought about this, Qin Ke knew that even if he was interested in this subject, he couldn't join it.

Everyone in the research room expressed deep regret. Chen Licheng could only say that he would thank Qin Ke for his help in the final acknowledgments of the thesis, and made an appointment to have a good meal in a hotel outside to thank Qin Ke.

Qin Ke shook his head and said: "Senior Chen, I see that you are all gearing up to try to solve the current difficulty from a new direction, so I won't take up your time. And there is a special training for the school basketball team in the evening, and I have to participate. Alright, I won’t bother you anymore, I’m going back to class at about the same time.”

Several people personally sent Qin Ke out of the scientific research center before waving goodbye reluctantly.

Looking at Qin Ke's back as he walked away, Chen Licheng said with emotion: "The mathematics world in the next few decades will probably belong to this junior Qin."

Hua Hong and other graduate students nodded in agreement.

……

Hua Hong sent a WeChat message to his sister at night:
"Sister, I met your male god Qin Ke today."

"Wow, really? Handsome or not, God or not?"

"Handsome is really handsome, and god is also really god. Didn't you say before that our research has encountered a big problem, the whole project has been stagnant for a month because of this problem, we are going to despair, what do you think of the result?"

"How so?"

"Your male god came over as a guest, watched for 3 minutes, and then found the problem, and pointed us to the three directions with the highest probability of success. Since the afternoon, we have been experimenting separately. From the results so far It is inferred that these three directions may be correct. No wonder you call God and God all day long. Brother Qin Ke is a god, and I am completely convinced. Originally, our team leader wanted to give him a bonus, but he thought it was just a matter of effort , would not accept it at all.”

"Wow! My male god is so handsome and powerful! Brother, you have to work hard to become friends with him and introduce him to me!"

"You? Just forget it. You are three years older than him, and you are not beautiful. Brother Qin Ke has a girlfriend like Ning Qingyun."

"Woo... the stinky old man is ignoring you!"

Hua Hong's sister burst into tears.

But soon, she cut off the front part of the conversation (cutting off the part that says she is not beautiful), and then sent it to Qin Ke's fan group "Ke Ke God who will always protect us", causing a blockbuster scream.

Soon, the screenshot of this conversation was reposted everywhere, and someone even reposted it to the bib and @ several well-known media, causing a sensation on the Internet.

[I saw the news of my male god again, as expected of my male god! 】

[Mathematics depends too much on talent. I guess Qin Shen's math talent should be the ceiling among young people, right? 】

[Qin Shen is sincere, willing to help others, and doesn't ask for anything in return, ahhh, I like him more and more! 】

[If you don’t, you won’t for a lifetime, but if you know it, you can see it at a glance. That’s right, I’m talking about mathematics. 】

[Someone asked if it was true or false?Can this be fake?Looking at this style, this strength is absolutely true. 】

[Only geniuses can reach the peak, and I look forward to the day when Qin Shen will reach the peak of mathematics. 】

[Basic exercises, Qin Ke can single-handedly beat mathematicians all over the world, what is a mere scientific research problem? 】

[Speaking of which, this is the second hot search related to God Qin today. God Qin is too popular, but I suggest not to consume him too much, let him study with peace of mind. 】

【That is, I hope the reporter will stop disturbing Qin Shen. 】

……

Qin Ke didn't notice that there was another hot search of his on the scarf. He returned to the new study room and continued to tutor Ning Qingyun's "To Ning Qingyun II".

This new study room has nearly [-] square meters. When you open the window, you can see the Jinchun Garden. You can see the lotus pond in the moonlight. The scenery is beautiful and the air is fresh. It is a study room in the VIP position.

Ning Qingyun didn't pay much attention to Qin Ke's talk about Chen Licheng's subject. She was used to Qin Ke's mathematics level. After all, they were attacking Polignac's conjecture. Can it be more difficult than this?
After Ning Qingjun finished studying the contents of "To Ning Qingjun II", he did exercises by himself, while Qin Ke continued to ponder his thesis on fluid mechanics physics.

Although Qin Ke is proficient in all sub-subjects of mathematics, his relatively strongest sub-subject is functional analysis, especially the solution of nonlinear partial differential equations.

He has studied the first, second, and second parts of "The Exploration and Detailed Explanation of the Nonlinear Partial Differential Equation "Navier-Stokes Equation"" for a long time, and he has completely digested and absorbed 70% of the mathematics part. The countless methods of linear partial differential equations can be said to be clear and easy to grasp. In this respect, he is completely comparable to or even surpassed many professors who specialize in functional analysis.

That's why he was able to easily point out the correct solution to the difficulties in Chen Licheng's project this time.

However, compared to mathematics that has reached the professional level, Qin Ke's professional-level physics is only at the undergraduate level. Although it is at the top undergraduate level, it is difficult to digest and absorb the difficult and profound S-level knowledge.

Therefore, in the physical part of "Exploration and Detailed Explanation of the Nonlinear Partial Differential Equation "Navier-Stokes Equation"", Qin Ke only completed the digestion and absorption of about 30% of the knowledge.

Of course, it is more than enough to write three academic papers with sufficient depth.

The only problem is how to combine this knowledge with suitable and reasonable topics and transform it into formal thesis results.

Physics papers are not like mathematics papers, which can be written purely with a pen and thinking.

Even if it is a thesis in the professional direction of "theoretical physics", it must be supported by sufficient simulation data or experimental results.

The task of the system also limited the direction of the thesis to fluid mechanics, which made it even more difficult to write the thesis. Although Qin Ke had the right to use the various physics laboratories of the school according to the enrollment contract he signed at the beginning, but he really wanted to conduct experiments. It will take at least a year and a half to produce results.

So Qin Ke decided to write his first physics paper in the direction of "computational fluid dynamics" after careful consideration.This is a result of the rapid development of computers, an interdisciplinary subject between mathematics, fluid mechanics and computers.

It uses computer and numerical methods to solve the control equations of fluid mechanics, and establishes mathematical models to simulate and analyze fluid mechanics problems with the computing power of computers.

Computational fluid dynamics is more theoretical than experimental, which is very suitable for Qin Kelai, who is also good at mathematics, physics, and computer informatics, to play freely.

Qin Ke just wrote an idea, and Ning Qingyun's phone vibrated. She picked it up to watch the meeting, then turned to Qin Ke: "Qin Xiaoke, Yan Fei asked me if I want to join her in mathematics modeling for college students. Contest. What do you think?"

　If Wei Shen was reading this novel, he would definitely say:? ? ?
　　Thanks for the reward of "you can eat meat"!

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(End of this chapter)