Chapter 206 Plasma Turbulence

Maybe he started to explode due to his stimulation, or maybe the stuck problem was solved. In short, Fefferman completed the isometric isomorphism conjecture much faster than Xu Chuan imagined.

In less than ten days after the three-person meeting in the dormitory, Professor Fefferman had solved the equal spectral problem using his own method.

The two organized the proof process and sent it out at the same time, and submitted it to the "Annals of Mathematics". At Xu Chuan's suggestion, they posted their results on the arxiv preprint website.

As a staged proof of the NS equation, even if it is just a small step, it is a great achievement.

What's more, this staged proof also contains a world-class mathematical conjecture.

As Fefferman said, the two of them succeeded in making a big difference.

After they posted the proof paper on the arxiv preprint website, and after a period of fermentation, the entire mathematical community became lively.

Phased results of the NS equation, world-class mathematical conjectures, proved by Xu Chuan and Fefferman at the same time.

Each of these words can be said to be the focus of attention in the mathematics world, but now they appear at the same time, and for a while, the mathematics world has made waves again.

“After proving Hodge’s conjecture, Princeton’s youngest full professor Xu Chuan launched a charge on another mathematical conjecture.”

"Two top mathematicians join forces, will the NS equation be solved one day?"

"The NS equation is unsolvable, and I bet that working towards it is a waste of time."

"But people have solved it, and there are two different methods."

"First of all, these two proofs have not yet been verified to be correct. Secondly, even if the verification is successful, it is only a staged achievement. It is still far, far away from truly solving the NS equation."

"I can smell the sour smell upstairs across the Atlantic Ocean."

"Are Princeton's mathematics professors already so frightened to solve the NS equations from two completely different perspectives? These are the seven millennium problems. It may not be possible to solve a century's problem in a century."

"The Holy Land of Mathematics originally belonged to us in France, but Princeton took it from us!"

On the mathematics forum, related discussions are in full swing.

Even in the physics department next door, some people turned their attention.

After all, this is the NS equation. If it is solved, fluid mechanics will usher in a leap forward.

Under the framework of classical mechanics, the NS equation is the application of Newton's second law, and its core essence is the conservation of momentum.

Once there is a breakthrough in the N-S equation, it must be that human beings' ability to examine finer structures will be greatly improved, at least to the extent that we can distinguish equations that we thought were very similar in form to the N-S equation in the past.

This has nothing to do with whether the N-S equation is a good model in fluid mechanics. The impact it brings on the entire science will definitely include computational fluid dynamics, and its value is immeasurable.

Compared with the previously solved 'Poincaré Conjecture' and 'Hodge's Conjecture', the practical application of NS equations in human science and technology has a much larger field that can be seen.

Because fluid mechanics involves so many fields in physics and technology development.

For example, cars, airplanes, and rockets are all related to fluid mechanics.

Princeton University's Forrest Campus in New Jersey, United States.

The building of PPPL Plasma Physics Laboratory is brightly lit in the dark night, illuminating everything around it. In the huge acceleration laboratory, many scientific research staff are busy here.

"Professor Fefferman, how have you considered our invitation?"

In a bright office, Halifax Bruce, the director of the PPPL Plasma Laboratory, looked at another middle-aged and elderly man wearing an inch-shirt sitting on the sofa with a smile on his face.

Fefferman looked up at the middle-aged man and said, "I'm not interested in your invitation."

"It is very difficult to build a mathematical model for ordinary turbulence, let alone establishing a mathematical model for plasma turbulence."

Bruce: "Please believe me, we have made great progress in the turbulence model. We have been working with Purdue University since October last year and have improved the original turbulence model a lot."

Hearing this, Fefferman's eyes flashed with surprise.

Although Purdue University's ranking is not as high as that of Princeton, and its natural science department is average, its engineering department is very strong. Not only is it the first university in the United States to have its own airport, it is also the university that trains the most astronauts. Armstrong, the first man to land on the moon, graduated from Purdue University.

Moreover, more than one-third of NASA's missions involve Purdue University or Purdue alumni, especially in aircraft design, who have very rich experience.

The simulated eddy current model system used in large airlines such as Boeing and Airbus, including part of the fluid dynamics of F22, F36 and other fighters, was designed by this university.

PPPL was able to find Purdue University to cooperate. It seems that this time it is indeed serious about solving the problem of plasma turbulence.

However, he still failed to change his view. Without it, plasma turbulence would not be something that could be solved now.

Shrugging, Fefferman continued: "Then you can continue to cooperate with them. If there is nothing else, I will return to Princeton tomorrow."

Hearing this, Bruce said with some urgency: "We are doing this, but now we have encountered some troubles and need your help. The NS equation can solve many turbulence problems, and your research on the NS equation can be said to be the world's first." one person."

Fefferman smiled and said: "It is true that the NS equation can be applied to fluid mechanics, but if you want to use it to complete your turbulence model, it is impossible unless you can completely prove it. "

Gritting his teeth, Bruce took out his cell phone from his pocket and said, "Please wait a moment, I will make a call."

After saying that, he took his mobile phone and went out. In the office, Fefferman didn't pay attention.

Although PPPL is also a research institution of Princeton, no one stipulates that Princeton professors must work for the PPPL laboratory.

In his view, it is enough to just think about establishing a mathematical model for plasma turbulence in a controllable nuclear fusion reactor. There is no need to waste time on this.

At least for the time being, this will be the case unless the NS equations can be solved or there are huge improvements in other aspects.

Otherwise, it is almost impossible to model high-temperature plasma turbulence.

The PPPL laboratory is not the only one in the world to study this stuff. Whether it is the ITER international cooperation organization or each country's own research laboratory, they have all studied this aspect.

However, the result is that, after decades, people still cannot restrain the ultra-high temperature plasma turbulence in controllable nuclear fusion.

If the NS equation is solved, he may want to try it, but for now, it depends on the interim results he and Xu Chuan have advanced.

He suggested that it would be easier and faster to dream at night.

"Please follow me, Professor Fefferman."

Within two minutes, Bruce came back and invited Fefferman to go elsewhere.

Fefferman followed. He was also a researcher at Princeton, so he still had to give him some respect, and he also wanted to see what PPPL was doing.

The two turned several turns and entered a laboratory after passing two permission checks.

"Kyle, please bring us a copy of our latest experimental data and a data confidentiality agreement."

Entering the laboratory, Bruce gave instructions to a staff member inside.

"OK."

Not long after, a tablet was handed over and handed to Bruce's hand, along with an agreement.

"Professor Fefferman, before you look at the information in my hand, please sign your name on it."

"Of course, it's just a very normal confidentiality agreement, as long as you don't leak the information you read today."

Bruce handed over the document and pen in his hand. Fefferman frowned slightly and reached out to take the confidentiality agreement.

I have to say that Bruce really aroused his curiosity.

After browsing the confidentiality agreement in his hand and confirming that there was no problem, he signed his name in the signature column.

After handing back the confidentiality agreement, he took the tablet, opened it, and started reading.

Suddenly, as if he saw something of interest, Fefferman's eyes focused, he raised his head and asked, "Do you have manuscript paper? Please give me a copy."

Taking the manuscript paper from Bruce, Fefferman found a place to sit down, and then began to use the data on the screen to calculate.

After a long time, he put down the ballpoint pen in his hand, looked at Bruce on the side and said, "I didn't expect that you would advance the control of turbulence to this point. The temperature control of ion temperature gradient turbulence can reach nearly 10 million levels."

Hearing this, Bruce said with a smile: "This is our latest result and it will not be released for the time being, so I hope the professor will keep it secret."

"But if you want to continue pushing forward, it won't be that easy. The higher the temperature, the stronger the diffusion effect of ion turbulence will be. I am afraid that if the temperature exceeds 15 million degrees, your control system will fail."

Fefferman handed the tablet back.

Ion temperature gradient turbulence is only a part of the controllable nuclear fusion turbulence. In addition, there are various messy turbulences such as ion acoustic wave turbulence, drift wave turbulence, and Alfvén wave turbulence.

But if part of it can be solved, it will undoubtedly be a huge success.

And if the first one is solved, it can provide enough experience for other turbulences that follow, and the subsequent processing will be much simpler.

It's just that this thing is really not that easy to solve.

Even if the PPPL laboratory and Purdue University push it to a temperature level of tens of millions, it only brings a faint hope.

Of course, this glimmer of hope is enough for them to keep fighting.

Bruce grinned and said: "Yes, we have encountered a bottleneck now and need a top mathematician to help us solve this problem, and you are the most suitable."

"I believe that with your participation, we can make the control system of ion temperature gradient turbulence more perfect. At that time, the temperature will not be limited to 10 million degrees, but may be 20 million, 30 million, or even higher. "

"Maybe we can control all plasma turbulence with this?"

Fefferman smiled and said: "The data you provided makes me very excited, but I'm afraid I can't do it on my own. I need a helper. If he helps, maybe I can."

"Who?" Bruce asked quickly.

Fefferman: "The person who studied the NS equation with me, his understanding of the NS equation is not weaker than mine, and it can even be said that it is stronger than mine. He also has deep research in the field of partial differential equations. With his help, maybe we can do it."

"Xu Chuan? The rising star genius from Princeton?" Bruce reacted immediately.

Fefferman nodded: "Yeah."

Hearing this, Bruce frowned and said: "But I remember that he seems to be a Chinese? It is impossible for a Chinese to join our research, and he is only twenty years old, this age..."

Bruce did not finish his words and interrupted himself: "Of course, if you need his help, I will find a way to invite him."

Fefferman waved his hand and said: "I will ask his opinion first to see if he is interested. If he is not interested, I am afraid you can't invite him."