Research starts with PhD students

Chapter 145 Goodbye, Teacher Song, a difficult solution? Huang Weijun: This is impossible!
Academician Yan Chongwen came just for Zhang Shuo, who is a top scholar in the field of nonlinear partial differential equations.

He has published many papers in related fields, and his work has been recognized by international peers and has a certain influence in the world.

Yan Chongwen came to attend the seminar not for nonlinear partial differential equations or numerical simulation of NS equations, but for the results of the "Fermion Hubbard Model" published by Zhang Shuo.

After entering the hall together, he couldn't help but discuss related issues, "The infinite multiple discretization method of the fermion Hubbard model should also be used for other mathematical models, right?"

He then exclaimed, "There is very little research in this area in the world. Your research is truly amazing!"

Zhang Shuo said, "I haven't thought about it specifically, but some of them should be possible, right? Different mathematical models involve different splitting problems."

“Some models can be split, but some cannot. Even if they can be split, we still need to study the relationship between the modules and conduct targeted research.”

Yan Chongwen listened and nodded, "That's true. I have discussed this issue with others. Splitting is very important."

They talked for a few minutes and agreed to find time to discuss it together.

Yan Chongwen's idea was to discuss the issue after lunch and spend the entire afternoon discussing it together, but he soon found that this was impossible.

Too many people came.

Zhang Shuo is a researcher at the High Court, a student of Luo Yongjun, and one of the judges of the seminar. It is not an exaggeration to say that he is one of the organizers of the seminar.

Qi Zhixiang arranged for Zhang Shuo to entertain Yan Chongwen, but many people also came to him on their own initiative.

It is impossible for Zhang Shuo to only talk to Yan Chongwen.

The first person to come to us was Li Jianfeng from the Donggang Center for Mathematical Sciences.

Li Jianfeng brought two teams with him, all of whom were professors dual-appointed by Donggang University and the Center for Mathematical Sciences.

One of the professors looked very familiar. After Zhang Shuo saw him, he thought about it carefully and suddenly remembered that the other person was Song Xuecheng, his advanced mathematics teacher in his freshman year.

"Teacher Song!"

Zhang Shuo called out and immediately took the initiative to go over and shake hands.

There were indeed conflicts between the predecessor and Donggang University, but the conflicts involved Zhou Kaijun and the administrative management of the School of Mathematics, and had nothing to do with other faculty and staff.

Song Xuecheng was my advanced mathematics teacher in my freshman year, and we often met during the following years of study.

Song Xuecheng also knew Zhang Shuo. He warmly shook Zhang Shuo's hands with both of his own and said, "It's really different!"

He exclaimed, "You were very good when you were an undergraduate. You were one of the best in several classes. Now you are amazing!"

"Just take a look and you will know that mathematics is really a field for geniuses..."

Song Xuecheng felt quite emotional.

One thing I feel for is Zhang Shuo’s achievements. What he has accomplished is truly astonishing. He has reached this point at such a young age and is considered a strong contender for the next Fields Medal.

This is incredible.

If Zhang Shuo can win the Fields Medal next year, he will set the record for the youngest Fields Medal winner.

Before this, the youngest winner was 28 years old, French mathematician Jean-Pierre Serre, who won the award in the s.

Many people who are known as mathematical geniuses usually win the Fields Medal when they are in their early 30s.

Qiu Chengwen won the award at the age of 33.

Terence Tao won the award at the age of 31.

Peter Scholze won the award at the age of 30.

The Fields Medal is only awarded to mathematicians under the age of 40, but it is extremely difficult to win the award before the age of 30.

On the one hand, it is difficult to achieve top results before the age of 30.

On the other hand, some luck is also needed. The Fields Medal is awarded only once every four years. If a mathematician completes his research at the age of 26 and is recognized by the whole world, and the Fields Medal just happened to be awarded, the winner would be 30 years old.

If Zhang Shuo fails to break Fields' age record for winning the award, which means that he will not receive the award next year, he will most likely win the award in the next session.

By then, he will be 30 years old.

Song Xuecheng chatted with Zhang Shuo for a few words, and then talked with Li Jianfeng about the research issues of numerical simulation of NS equations.

Zhang Shuo's research bankrupted their project.

This is just one aspect.

The biggest regret of Li Jianfeng's team is that all the efforts they made on the project are not as good as Zhang Shuo's "very casual" research results.

A team's efforts for two or three years are not as good as one person's casual research...

The gap is really too big.

The reason why Zhang Shuo's research is very casual is that he completed several studies in the middle, such as the proof of the Jebov conjecture and the study of the fermion Hubbard model. The three studies were not too far apart in time.

Li Jianfeng sighed several times in succession, and then asked some questions about Zhang Shuo's research.

Later, he asked, "Professor Zhang Shuo, what are you going to study next? I mean in the field of computational mathematics."

He even sounded a little nervous.

After the NS equation simulation calculation project went bankrupt, they were preparing to apply for a new computational mathematics project.

It would be really embarrassing if they were to encounter the same research situation with Zhang Shuo again. Li Jianfeng and everyone in the team had no confidence at all in surpassing Zhang Shuo in research.

Zhang Shuo said, "I have no research in computational mathematics for the time being."

"Recently, I have been studying the NS equations and conducting theoretical demonstrations of singularities."

Li Jianfeng heaved a sigh of relief after hearing this. If it was just a theoretical argument, it would not have much to do with computational mathematics.

This way, both parties will not conduct duplicative research.

After relaxing, he asked with interest, "Any progress? This is one of the mathematical conjectures."

Song Xuecheng also looked over.

Zhang Shuo said, "I can only say that I have a little bit of knowledge, and I have a basic direction. The research is too difficult, I think about it a little bit every day, and take my time. This kind of research cannot be completed in one go."

Song Xuecheng agreed, "We really can't be impatient. If we can achieve some results in the research process, it will be great. If it were me, I wouldn't dare to say that I would achieve any results even if I studied for 20 or 30 years."

Li Jianfeng laughed and said, "If it were me, I wouldn't even start researching. Pure mathematical proofs are too difficult."

He said and shook his head.

Song Xuecheng smiled and said, "This is a field that truly belongs to geniuses. People like us who are almost out of date don't even have to think about it."

"Haha."

Several people laughed.

Zhang Shuo talked with Li Jianfeng and others for a while, then went to entertain other people. Professors Huang Junwei and Qin Haifan from the Aerodynamics Technology Research Institute of Aviation Group came over.

Huang Junwei and Qin Haifan came for two purposes, one of which was to attend an academic seminar.

Their work involves long-term exposure to nonlinear partial differential equations, so they will also gain some academic benefits from attending the seminar.

The second, and most important, is to talk to Zhang Shuo about the problems they encountered in their research.

In fact, they wanted to invite Zhang Shuo to the Institute of Aerodynamics, but the invitation they sent was politely rejected by Soochow University, and the invitation sent to Zhang Shuo's email was also rejected.

They both found it hilarious.

The Institute of Aerodynamics also has a certain influence on the outside world. They invited a professor to give a lecture and offered him 15 yuan for the lecture, but the professor refused it directly. Generally speaking, when they send out such an invitation, even if there is no lecture fee, the university and the invited professor will be very active, because coming to give a lecture itself shows that the research is recognized.

Many universities also hope to establish good relations with aviation groups, because aviation groups have a huge influence and there are many cooperative projects between them and universities and institutions.

If you can win a project, it will be easy to get millions or tens of millions of dollars in funding.

This did not work for Zhang Shuo.

When Zhang Shuo heard about the Aerodynamics Research Institute, he also remembered the invitation and said apologetically, "I received too many invitations, including from domestic and foreign universities and many scientific research institutions, so I rejected them all."

He explained, "I went to the Second Academy of Aerospace Science and Technology, not because of the lecture fee, but because I really wanted to go to the capital."

"When I returned to Sudong, I received many invitations. It would not be good to go to one institution and not go to other institutions."

"If I go, I won't be able to make time for them all. I still have research to do..."

He said and shook his head.

Huang Junwei nodded in understanding and said with a smile, "It's okay, Professor Zhang, we are not here to call you to task."

"Besides, didn't you tell us in the email to ask the Second Academy of Aerospace Science and Technology for the video? We got the video, but there are still some problems that cannot be solved..."

Zhang Shuo asked doubtfully, "What's the problem?"

If you are researching on numerical simulation of the NS equations, you will generally be able to understand it as long as you watch the lecture video carefully.

If there are other problems, it is probably not just a matter of studying the NS equation.

Huang Junwei spoke carefully.

Different research institutions conduct different research, even in the field of aerodynamics.

The Aerospace Group's aerodynamic research is focused on rockets and rocket engines.

The Aviation Group Aerodynamics Research Institute mainly focuses on aircraft engines and aircraft.

Although aerospace is the exploration of space, in fact, the research in the field of aerodynamics has higher requirements in the aviation field, because rockets are only launched into space and the aerodynamics in space can be ignored.

Aircraft and aircraft engines are different.

Among them, the most demanding are fighter jets, or to put it bluntly, fighter planes. The highest-end fighter planes can easily fly at speeds exceeding the speed of sound, and must be able to perform a variety of flexible maneuvers during normal flight.

For example, a large corner, or looking up into the sky.

For example, the rotation of the fuselage in the air.

and many more.

"The design of the new generation of aircraft requires greater flexibility, and the calculation of air flow caused by the movement of the fuselage and the power generated by the aircraft engine must be more precise."

"For these problems, we want to ask, is there a more accurate method to calculate?"

Zhang Shuo listened carefully and said, "I have never done any application work, so I still don't quite understand what kind of calculation it is. Can you give me some specific questions?"

Huang Junwei and Qin Haifan looked at each other.

Qin Haifan thought about it, then took out a piece of paper and started writing on the table, saying, "This is a problem we encountered when studying the corner resistance of the aircraft. It is related to the design of the wing."

“This set of equations needs to be calculated with values ​​as close as possible to make the design more perfect, which can improve the performance of the aircraft on the one hand and improve safety on the other.”

He wrote out a system of equations as he explained.

Zhang Shuo took a quick look and found that it was indeed very complicated, including the NS equations and several other types of equations.

Such a complex system of equations is generally difficult to solve.

The NS equations alone are very complicated. Add in other unknown variables and a few more conditional settings, and it becomes ridiculously difficult to evaluate them, let alone calculate more precise values.

Of course, the most important thing is to find the direction and the starting point.

Zhang Shuo stared at the equations for a long time, and then simply created a system task -

【Task 2】

[Research project name: Finding numerical solutions to partial differential equations (difficulty assessment: D).]

【Progress: 0.094%.】

(The task can be canceled. Currently, the number of scientific research coins required to cancel the task is 0.)
(The remaining progress requires 10 scientific research coins.)
“It’s really difficult!”

Zhang Shuo was emotional. He had used the system task function to solve many complex equations and systems of equations. The difficulty of the tasks he established was basically at level E or F.

This shows that the research is not innovative.

The difficulty of solving the current system of equations has increased to level D, which is obviously not solvable by conventional methods.

He thought about it carefully, and then spent a research coin -

【Scientific research coin - 1.】

[Task 10, progress +%. ]

"The speed of krypton coins is really fast!"

Zhang Shuo sighed, and a clear idea of ​​how to solve the problem came to his mind. He did not directly state his idea or start calculating, but asked, "Have you done any research on the calculation of this system of equations?"

Huang Junwei smiled bitterly and said, "More than a dozen of us have been researching for more than half a month, and we have only solved a set of values ​​using a very unstable method, but we have no idea of ​​its accuracy."

"We can only verify the accuracy through experiments, but the experimental deviation is large. In particular, we cannot simulate the rotation of large wings under high-speed flight."

Zhang Shuo nodded and continued, "Can you tell me how you solved it?"

"This one……"

Qin Haifan hesitated for a moment.

Huang Junwei said generously, "There is nothing to hide. The values ​​we obtained can be detected by experiments. The deviation is too large. It is the same whether we solve it or not..."

After he finished speaking, he began to explain seriously.

Zhang Shuo listened carefully and found that the task progress was indeed increasing, and it increased by several points each time.

This is probably because D-level research is relatively easy.

After Huang Junwei finished his explanation, the research progress had even reached '93%'.

Although there is still '7%' left, compared with the D-level research, it can be said that there is no difficulty anymore.

Zhang Shuo also knew what to do next.

Follow the method and solve the problem normally.

While Huang Junwei and Qin Haifan were puzzled, Zhang Shuo stood up and walked outside, saying, "Come with me to my office. To solve this system of equations, we need computing software."

"It will be quick. About ten minutes will be enough."

"..."

Huang Junwei and Qin Haifan looked at each other, and for a moment they were a little confused.

What does it mean?
Does Zhang Shuo already know how to solve the problem and then go do the calculations?

Unlikely?
The team worked together for more than half a month, but they only roughly calculated a numerical value group with unknown deviations...

(End of this chapter)