Research starts with PhD students

Chapter 115: Fields-level achievements, the first in computational mathematics!
"A mathematician spent a lot of computing power to verify that a Mersenne number happened to be a Mersenne prime number... Could it be a coincidence?"

"It can't be a coincidence!"

"It must have been analyzed. However, Mersenne primes are extremely rare and have no regular pattern. How did you analyze them?"

"You'll have to ask Zhang Shuo himself..."

There was a lot of discussion in the media, and many people did ask Zhang Shuo about the last question.

For example, Dong Hao, Liu Haibin, and other professors in the school.

They are very interested in this. Mersenne primes have no regularity at all, so how were they analyzed?
The only one who didn't speak was Luo Yongjun, he still felt like he was dreaming.

You used to feel bad about spending 10 yuan, but now you earn 10 yuan, get great honor and a bonus of 15 US dollars?
He was not the one who spent the money, nor was he the one who made the money, but his mood still experienced huge ups and downs!

Sun Xingli felt complicated because his dream would never come true. The 'billion-digit prime number' had been detected, and he only had one chance to be the 'first'.

Although he had given up long ago without Zhang Shuo, he still felt complicated!

Zhang Shuo was surrounded by a large group of people. He explained, "I was just lucky. I analyzed 30 numbers, but because the calculations were too huge, I finally chose one."

He didn't want to say anything more.

If he were asked to find another prime number with 15 million digits, he would be able to find it, but without the honor of being the "first" and the $ prize, there would be no point in looking for it again.

"Even if we analyze thirty numbers and one of them corresponds to a Mersenne prime, it would be amazing."

"It's not luck!"

"How did you analyze it? I want to analyze it too..."

During a discussion among a group of people, Dong Hao suddenly remembered something. There was indeed a lot of numbers on the paper that Zhang Shuo took at the beginning.

Later, most of it was crossed out, leaving only one number.

So are there any other numbers that correspond to Mersenne primes?

"That piece of paper might still be in the office, or it might have been thrown into the wastebasket? Or maybe it was dumped into the trash can?"

"Don't get taken away by the garbage truck!"

Dong Hao suddenly became extremely anxious. He stepped back from the crowd and ran towards the laboratory.

……

Everyone is talking about Mersenne prime numbers, there has been a lot of coverage in the media, and many reporters have come to interview.

The school will deal with any issues regarding public opinion.

Zhang Shuo returned to his office and finally had some peace and quiet. He opened his mailbox and saw the email from Curtis.

Curtis wanted to know the story behind the discovery of Mersenne primes.

Zhang Shuo briefly explained the situation, for example, he is a researcher at the Institute for Advanced Studies of Soochow University.

These can be found in the media.

In the reply email, he briefly talked about his feelings and mentioned that he had borrowed computing power from the Computer Structure Laboratory.

That's enough.

At the end of the email, Zhang Shuo also asked about the bonus issue.

The Electronic Frontier Foundation is now offering a prize for the discovery of Mersenne primes through GIMPS calculations. They have announced that they will offer a $3000 prize for each Mersenne prime discovered and a $150000 prize for the discovery of the first million-digit prime.

The Electronic Frontier Foundation is a nonprofit international legal organization headquartered in San Francisco, with offices in Toronto and Brussels.

Their purpose is to protect Internet freedom and safeguard the challenges of intellectual property, personal privacy and innovation brought about by Internet convenience.

Zhang Shuo carefully learned the information and waited for professors Liu Jian, Zhang Chunyang and Xu Jun to arrive.

Xu Jun and his two companions stayed in the hotel for one night, and today they waited for a long time on the first floor of the High Court before they finally "queued up" to meet Zhang Shuo.

Wang Duoju also walked in. She helped with a brief introduction and then looked at Zhang Shuo with admiration.

Zhang Shuo is the treasure of the School of Mathematics, and he always achieves great results.

After completing the Gerbov conjecture, many people thought he would be quiet for a while, but he discovered the Mersenne primes, which caused heated discussions at home and abroad.

Now, is it the study of NS equations again?
Wang Duoju didn't know the specific situation, but she knew that the three professors came on behalf of the Science, Technology and Industry Bureau, and Zhang Shuo's research related to the NS equation was under the young scholars funding supported by the school.

In other words, this study is a youth project supported by the school.

An inconspicuous youth project caused the Science, Technology and Industry Bureau to make a big fuss, and even sent three professors to communicate with Zhang Shuo.

unimaginable!

All Wang Duoju could do was sigh.

The three professors sat on the sofa, and Xu Jun spoke first, "We are here on behalf of the Science and Technology Industry Bureau. We want to learn about the research progress of the numerical simulation of the NS equation."

"Where did you get the news from?"

Zhang Shuo was a little curious because he had never revealed his research. Everyone else only knew that he was doing research but didn't know the specific progress.

Xu Jun and the other two looked at each other and said, "There's nothing to hide. It's Academician Zhou from the Second Academy of Aerospace Science and Technology. He said that your research has made great progress."

Zhang Shuo suddenly understood.

Before he left, he said that the research was almost completed, but it was just talk and he didn't think the other party would believe it.

Zhou Yongchang can say this because he must have studied the manuscript on analyzing the pogo problem. The above-mentioned latest transformation methods will enable the NS equation to obtain more accurate numerical solutions.

Zhang Shuo nodded and asked, "What do you want to know?"

"Progress." Xu Jun said two words, and then said, "I want to know how far the research has progressed."

"finished."

"finished?"

Xu Jun and the other two looked at each other, obviously very surprised.

Zhang Shuo said, "My research is about numerical simulation of the NS equations. One part of my research is about numerical methods of the equations, and the other part is about computational simulation."

"Because the method is relatively complicated and involves a lot of calculations, it is impossible to simulate the equation without any boundary restrictions or approximations."

Liu Jian asked doubtfully, "Similar to DNS?"

DNS, or Direct-Numerical-Simulation, solves the control equations directly without any approximate processing.

This is a high-precision solution method that mathematically solves the system of equations directly without involving approximations or simplifications, making it possible to provide a very detailed and accurate description of fluid behavior.

However, the practicality is very low.

The DNS method has two unsolvable flaws. One is that direct numerical simulation requires a lot of computing power, which means that the calculation will be very expensive. With the current level of computing technology, the computing power required is simply unaffordable.

In addition, the DNS method is calculated step by step, and the subsequent calculations must refer to the previous results. Therefore, there will be a very large deviation at the end of the calculation, and it can even be said that the result will be completely opposite.

This is because when performing numerical calculations, errors due to discretization and rounding errors in calculations are inevitable.

Even if the error is relatively small, as the error accumulates, it will lead to very large differences in the results.

This is the butterfly effect and chaos theory in mathematical calculations.

Therefore, the DNS method is only used in the field of basic research. It is currently unrealistic to use it in engineering calculations.

Zhang Shuo also knew the DNS method. He shook his head and said, "It's different from DNS. The difference is that each part of the calculation is done separately, and there will be no error accumulation."

“Second, the computational requirements are not that high.”

He simply elaborated, "When I say the method is complicated, I mean direct computational simulation, but if the conditions are set, for example, for some individual engineering fields, numerical simulation can also be done, and even displayed on the computer like computer graphics."

"However, due to the particularity of the NS equation, the graph will be very complicated."

He added, "If you only intercept a part, you can still do it."

Now Xu Jun and the other two understood.

The NS equation is very complex, and many conditions need to be set for numerical calculations. For calculations in individual engineering fields, there will be certain conditions, that is, restrictions on parameters.

It can perform numerical simulations in a separate field or capture a part of it...

It’s amazing too!
The three of them looked at each other, and Liu Jian stepped forward and said, "Professor Zhang Shuo, can you give us some information, such as a part of the manuscript, or a general introduction to the research?"

"We need to take it back for research. The Science, Technology and Industry Bureau attaches great importance to your research and may apply for a large-scale scientific research project in the future."

"Ok."

Zhang Shuo agreed readily.

The Bureau of Science, Technology and Industry is related to national defense technology. It is a very important department in the country and its department level is also very high.

For example, the Bureau of Science, Technology and Industry is the superior unit of the Space Administration. The research, projects and development of the Space Administration are all managed and supervised by the Bureau of Science, Technology and Industry.

Zhang Shuo knew what the other party needed. The manuscript materials he found were all introductions to the overall plan. Then he asked, "Are there any restrictions on the publication of the results?"

"Not this one."

Liu Jian said, "When you publish a paper, you only introduce the general direction, not the specific calculation method, so the impact is not great."

"This is all your own research. The NS equations involve many engineering applications. We hope to make more accurate calculations in various application directions based on your results."

this is very important.

The NS equations have a wide range of applications, for example, in the aerospace field.

In the field of aerospace, the NS equations are used to simulate the aerodynamic characteristics of aircraft and rockets flying in the air.

If more precise calculations can be made, security will be greatly improved.

Another example is weather forecast.

Meteorological forecasting uses the NS equation more directly. Computer simulation of atmospheric circulation and prediction of weather changes require the elliptic NS equation.

……

Xu Jun carefully put the information given by Zhang Shuo into his briefcase, and the three of them left the office together and walked out of the research institute building.

After they got outside, the three of them seemed a little silent.

They gained a lot from this trip. They witnessed the discovery of billion-digit prime numbers with their own eyes, and also saw the media's bombardment of reports.

But the surprise brought by the billion-digit prime numbers is far less than the research progress in numerical simulation of the NS equations.

The former is just a numerical study, which has no practical significance, while the latter...

It's their field!
Their research areas are all related to the engineering applications of partial differential equations. This is why it is clear how important Zhang Shuo's research is.

If everything is as Zhang Shuo said, the research will definitely shock the world when it is published and will be the greatest achievement of applied mathematics research in the new century.

At the same time, it will be a result at the level of Fields and Albert.

If he can win international awards such as Fields and Albert for his research in applied mathematics and computational mathematics, Zhang Shuo will become the number one in the field of applied mathematics and computational mathematics.

No doubt!
(End of this chapter)