The top student must be diligent.

Chapter 206: Physical Transport of Hard Drive

Obviously, from the perspective of results, simply improving Greenwald's limits is not that important compared to proving one of the seven major problems of the millennium.
After all, it is one of the most important core problems in the field of mathematics, and it is also the last problem in classical physics. Its applications in reality are countless. It can play a very important role in any problem related to fluids.

The other one is just a slightly important issue in the field of nuclear fusion. For nuclear fusion, the more important issues are the major material issues. Only by solving these material problems can controlled nuclear fusion be realized. As for the Greenwald limit problem, its application will only be meaningful after controlled nuclear fusion is officially realized.

Therefore, solving the smoothness problem of the NS equation in order to solve a Greenwald limit problem can really be regarded as making dumplings for a plate of vinegar.

"Um……"

Xiao Yi thought for a moment, and then thought: "Let's see if there is any other way to solve it."

Then he put this problem aside for the time being and began to study from other angles how to combine the NS equations and the multi-fluid model.

In this way, time passed quietly for a long time.
It was almost evening when he raised his head again and sighed helplessly.

"It looks like it won't work."

For nearly half a day, he considered at least four different angles, but either they didn't work, or the final model didn't achieve the effect he wanted, or it showed the same strangeness and instability.

Until finally, he turned his attention back to the problem.

Existence and smoothness of solutions to the NS equations.

"It seems that we really need to solve this obstacle."

Director Zhao, Director Zhao, you have really given me a difficult problem.
Xiao Yi sighed slightly in his heart.

Zhao Zhanyou probably didn't expect that the problem he asked Xiao Yi to help solve would eventually lead to this top-notch problem in mathematics.
But no matter what, since he had promised it in the beginning, he had to give it a try.

Anyway, it's just a millennium problem.

It’s not like he hasn’t solved it before.

"It just so happens that I haven't studied math problems for quite a while."

Although he used mathematical methods to solve various problems in most of the projects he had completed before, he had not studied purely theoretical mathematical problems like this for some time.

"bring it on!"

One of the seven problems of the millennium, the final problem in classical physics!
……

Xiao Yi officially began his research on the existence and smoothness of solutions to the NS equations.

The NS equations, which refer to the Navier-Stokes equations, are named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Stokes. They are a set of partial differential equations that describe the movement of fluids such as liquids and air.

The history of fluid research began more than 20 centuries ago. For example, everyone has heard the story of Archimedes using buoyancy to measure gold. The Archimedes principle that was born from this can be regarded as the earliest scientific theorem of fluid mechanics.

Later, Leonardo da Vinci also observed fluids and made the earliest description of eddies and turbulence. Later, great people such as Newton, Euler, and Bernoulli made more and more contributions to fluid mechanics.

It was not until the 19th century that Navier and Stokes summarized the various studies of their predecessors on fluid mechanics and finally came up with the most important equation, the NS equation.

It can describe the conservation of momentum and mass in the motion of various fluids, and use it to analyze the behavior of fluids during the flow process.
It can be said that this equation is constantly at work in all walks of life.
From airplanes flying in the sky, to pipeline designs under the city, to submarines hundreds of meters under the sea, the NS equations are needed to analyze the fluid problems they bring.

As for why it is said to be the last problem in classical physics, it is because other related problems in classical physics have been able to be well solved. However, when using the NS equations to study fluid mechanics, since every fluid molecule in the fluid is completely free and can be affected by various other molecules around it, there are still things that people cannot analyze.

Especially at high Reynolds numbers, the fluid becomes very complex and forms turbulence, which is also one of the most complex phenomena in fluid mechanics. Because its flow is highly random and irregular, like a chaotic system, its accurate description and understanding remains a huge challenge.

Unlike other classical mechanics problems, which are not as complex as those in fluid mechanics, they can basically be solved quite well, such as in architectural engineering.

Of course, precisely because the NS equation is difficult enough and has a very important position in the industrial field, there are quite a lot of people studying this problem. It can be said to be a pinnacle in the field of mathematical physics.

"However, the complexity of this problem is indeed quite high..."

As Xiao Yi began to study the NS equations, various difficulties followed.

The existence and smoothness of solutions to the NS equations are two different issues.

Existence requires proof: For given initial and boundary conditions, can we always find a solution that satisfies the Navier-Stokes equations?

Smoothness requires proof: Is the solution found smooth over the entire time range? That is, whether all derivatives of this solution exist and are continuous.

Of course, there is an even more abnormal problem above this, which is to solve the NS equations.

As an equation, it can naturally be solved, but the NS equation is too complex, so the possibility of obtaining its analytical solution is too great. The mathematical community generally believes that this is basically impossible to do, so the academic community basically only requires that the existence and smoothness of its solution be proved.

"For the NS equations in two dimensions, their global existence and smoothness have been proven, but for three dimensions, only the existence of local smooth solutions has been proven, that is, the solution exists and is smooth within a finite time interval, but it has not yet been proven for the global case."

“When you’re proving the global picture, you always run into singularities.”

While consulting relevant information about the NS equation, Xiao Yi analyzed the various problems encountered by the current academic community in the process of studying this issue.
Singularity is a problem he encountered in the process of combining the NS equations and the multi-fluid model. It is mainly manifested in that the fluid velocity becomes infinite or its derivative becomes infinite in a finite time, as if it suddenly exploded. Therefore, this problem is also called the explosive solution problem.

This problem can be said to be the key difficulty in proving the NS equation.

Xiao Yi began to deduce the process of explosive solution on the draft paper.

[{[u/t+(u)u=p+νΔu], [u=0]……]

【lim(t→T)∥u(，t)∥Hk=∞】

At some point in time, the speed becomes infinite.

In physical terms, this means that at some point the velocity or energy density of the fluid becomes infinite.

It is as if the originally calm water in the pond suddenly exploded violently. You can even use your imagination to turn the hand grenade into a water grenade. Shake it vigorously before throwing the water grenade to make the fluid inside turbulent enough, then throw it out. Finally, throw it next to the enemy and it will explode directly. The power caused may even be stronger than that of a hand grenade.

It can even be used to explain the principles of the abilities of those who have mastered water-related superpowers, that is, they can control the fluid force in the water and accurately control it to reach the conditions for "explosion" at a certain moment.

But obviously, this is a completely impossible thing.

This problem has been discussed in academia for many years, but people have never had a good way to explain the conditions for the formation of blast solutions.

"So far, we have discovered some related mechanisms, um... one is called energy cascade and turbulence, which means that in turbulence, energy is transferred from large scales to small scales, which may cause the speed or velocity gradient on the small scale to become very large, eventually leading to an explosion."

This is easy to understand, because of the law of conservation of energy, the original one cubic meter of fluid energy is condensed into one cubic millimeter, which naturally causes the fluid energy within this cubic millimeter to increase sharply, and then an explosion occurs.

"Also, the impact of initial conditions, such as some highly concentrated initial flow fields with strong rotational characteristics, may produce explosive solutions."

"Therefore, finding a good initial condition is the key to proving the NS equations."

"Initial conditions... initial conditions..."

Xiao Yi fell into deep thought.

Until finally, he stood up suddenly.

“Need data!”

Since we want to find appropriate initial conditions, there is a simple method, which is to set various initial conditions, and then use numerical simulation methods to determine the subsequent impact of different initial conditions on the fluid, such as when the explosive solution will appear, and how the data changes in the period before the explosive solution occurs.

This requires the help of computers.

He went to the computer room, set up the model, and started running it on the laboratory server.

But at this time, problems arose.

The computing power of the laboratory server is not enough!
Looking at the slowly moving progress bar, his expression darkened.

Wang Hao, who was standing next to him, was also stunned when he saw this scene. He said, "Our server is worth 1000 million. Professor, what do you think this is?"

Xiao Yi pulled the corner of his mouth and said, "Some direct numerical simulation models of the NS equations."

"Oh, that's not surprising."

Wang Hao nodded. The direct numerical simulation of the NS equation is one of the models with the highest computing power requirements. Moreover, Xiao Yi has to calculate not only one model, but hundreds of models, covering various situations of fluid operation, such as pipe flow, boundary layer flow, open channel flow, etc., which requires even higher computing power.

"Make a note. Next time we expand the lab, we need to expand the computer room as well. By the way, ask how much it would cost to build a supercomputing center. What is the scale of 100 million?"

Xiao Yi waved his hand and prepared to build a supercomputing center for their laboratory.

There’s nothing I can do, I have a lot of money and I can be willful!
Wang Hao next to him swallowed.

Wow, one hundred million. It seems their lab is really rich.

"Yes, Professor!"

……

It is not convenient to do it in the laboratory. After all, the laboratory server is not only used by him, but also by others sometimes. He is not that dictatorial.

The amount of data this time requires the use of a supercomputer.

It just so happens that their Fei City has a supercomputing center that was established in recent years, and the name is also very nice, called Chaohu Mingyue.

Looks like it's time to go and take a look.

……

The Chaohu Mingyue Supercomputing Center is located in the Feishi High-tech Zone. Its name naturally comes from a famous lake in Anhui Province - Chaohu Lake.

"Professor Xiao, I have heard of you for a long time!"

Director Tu Ran of Chaohu Mingyue Supercomputing Center was standing at the door. When he saw a group of people coming, he greeted them with a smile and said hello to the leader.

That person was naturally Xiao Yi. After confirming that he needed to use a supercomputer, he directly contacted the Chaohu Mingyue Supercomputing Center and prepared to come and observe.

"Hello, Director Tu."

Xiao Yi walked up to Director Tu and shook hands with him, then looked at a glass cube in front of him.

The Chaohu Mingyue supercomputer is placed in this cube, and it looks pretty nice.

After exchanging a few pleasantries, Xiao Yi pointed at the glass cube in front of him and asked, "Is this Chaohu Mingyue?"

Tu Ran laughed, then nodded and said, "Yes, our Chaohu Moon is inside. We can also see it from the outside."

"Let me introduce Professor Xiao to the 'strongest brain' in Fei City."

Xiao Yi nodded, "I'm all ears."

Then, Tu Ran began to introduce: "This glass cube is 16.8 meters long and wide, and 13.5 meters high..."

While listening to Tu Ran's introduction, Xiao Yi followed him in.

Tu Ran knew them all, but Xiao Yi only remembered the most critical data.

Double-precision computing peak 12PFlops.

“How does this peak computing power rank in the world?”

Xiao Yi asked.

Tu Ran was stunned for a moment, then replied: "As for rankings, China is not participating in the ranking comparison now, but according to the data released now, it can probably be ranked around 100th in the world."

Xiao Yi nodded.

This amount of computing power should be enough to calculate his model.

Then he said, "Well, Director Tu, as I said before I came here, I plan to use the Chaohu Moon to calculate a model. Can I go up and try it now?"

"Haha, of course no problem."

Tu Ran smiled and nodded, then led the way: "Come with me, the computer room is over here."

Arriving at the computer room, Xiao Yi took out the laptop he was carrying.

Connect the laptop to the supercomputer host, upload the model, and soon the calculation will begin.

This time, the progress was faster.

Tu Ran was a little surprised. "Professor Xiao, what is the model you used to calculate this? The occupancy is so high."

It’s not enough to connect to one server, you have to connect to four servers.

"Fluid mechanics stuff."

"I see." Tu Ran expressed his understanding.

At this time, Xiao Yi waved to Wang Hao behind him. Wang Hao understood and put the box in his hand on the table next to him. When he opened the box, he could see that it was full of hard drives.

Then Xiao Yi said, "I'd also like to trouble Director Tu to help copy some of the calculated data to these hard drives."

For him, the calculation results of these models are not important, because these results are destined to suddenly "explode" at some point in time.

The most important thing is the changes that occur during the process from the beginning of calculation to the explosion.

The data generated in this process is the most important.

Seeing this, Tu Ran didn't know whether to laugh or cry, and said, "Okay, now I understand why you, Professor Xiao, came here specifically to calculate a model. It turns out it was for the data."

Xiao Yi also smiled knowingly.

If he just wants to calculate the model results, he can of course do the calculation directly in the laboratory by connecting his computer to a supercomputer via the Internet.

But the problem this brings is that the speed at which the data calculated by the supercomputer is transmitted to his side is limited by bandwidth and will be very slow.

Therefore, the fastest way is to transport the hard drive physically.

It only takes him half an hour to drive back to the laboratory from here, and he can also visit the supercomputing center while he is here. If he waits for the data to be uploaded here and then downloads it there, the transmission speed will probably be about the same, or even lower.
This is what is called physical transport speed being faster than network transmission speed.

For example, in the case of the original black hole photo, the amount of data that several observatory observation centers ultimately obtained was about 5PB in size, and in the end several vehicles were sent directly to pull the hard drives to the research center.

Just like that, while waiting for the calculation to be completed, Tu Ran continued to take Xiao Yi to visit their supercomputing center.

Xiao Yi also asked for opinions on building a supercomputer for the Science Island Laboratory.

And just like that, time passed quickly.

until night.

The data calculation was completed, and during the calculation process, the data was also stored in the hard drives brought by Xiao Yi.

The total amount of data is more than 300T.

With so much data, it is really like a small horse pulling a big cart for their laboratory server to calculate it.

Just like that, they took the data and expressed their gratitude to Tu Ran, then left the supercomputing center directly.

Next, comes the main event.

I hope these data will not disappoint him.

……

(End of this chapter)