Section 231

It was really a bit of a stretch for their laboratory server to calculate such a large amount of data.

So, after taking the data and thanking Tu Ran, they left the supercomputing center directly.

Next, it was the highlight.

I hope these data will not disappoint him.

…

Chapter 207 Explosion Trend Discrimination Model

More than 300T of data is of course a lot, but for the direct numerical simulation data of fluid mechanics, such a large amount of data is normal. After all, Xiao Yi tested too many things at one time, and the amount of data itself would be very large, even in direct numerical simulation, it can be called a large-scale simulation.

Just the more than 100 solid-state drives cost Xiao Yi a lot of money.

More data may even reach the PB level.

The simulation of fluid mechanics is so complicated.

Otherwise, like the scenes involving liquids in the game, manufacturers often take opportunistic ways to show the liquids in the game, and the performance of the liquids has also become a major representative of the manufacturers' muscle show.

Of course, Xiao Yi was quite extravagant. Generally speaking, people would use mechanical hard disks for transportation. However, he took into account that the read and write speed of mechanical hard disks was relatively slow, only about 100-200MB/s. Compared with the 2G/s read and write speed of the hard disks he bought, it was still a bit worse. He didn't have time to waste on waiting for data reading and writing.

Anyway, it was only a few hundred thousand, which was nothing. It happened that the price of solid-state hard disks during this period was relatively low. Maybe when he wanted to calculate other things in the future, these solid-state hard disks could still be used?

In this way, he returned to the laboratory, and the next thing was the top priority.

Data analysis.

Looking at the box of solid-state hard disks in front of him, Xiao Yi shook his head with emotion in his heart.

"Director Zhao, Director Zhao, do you know how many gold coins I exploded for your problem?"

Then he stopped talking nonsense, inserted ten of the solid-state hard disks into the specially prepared NAS next to him, connected to the server, and began to read the data.

If you want to analyze so much data, you must first process it, discard some unnecessary data, and then count other useful data and make corresponding charts.

This is a huge process, and it is impossible for Xiao Yi to do it alone, so he also called some postdoctoral fellows and assistant researchers from the laboratory to help him process the data.

In this way, the data processing process alone took almost half a month.

In the end, Xiao Yi got perfect statistical data.

Looking at the complex charts displayed on the screen, Xiao Yi narrowed his eyes and began to analyze and think about these data.

From time to time, a peak will appear, and each peak represents the occurrence of an explosive solution.

Then, he can try to find the conditions for the formation of the explosive solution based on the appearance pattern of these peaks.

Looking at these charts, if others look at them, they will only feel that these pictures have no rules at all, but Xiao Yi quickly found quite a few points worth careful study.

"Interesting..."

"First, in some cases, for some semilinear heat equations, if some norms of the initial data exceed a certain critical value, such as the L^2 norm of the velocity field, the solution may become infinite in a finite time."

"Second, there is the influence of nonlinear terms. Nonlinear convection terms are also a key factor that causes these solutions to explode, especially in three-dimensional cases. The influence of nonlinear terms is more significant."

"There are also boundary conditions and external drives. Under some periodic boundary conditions or complex boundary geometries, they may also affect the stability of the solution, thereby increasing the possibility of solution explosion."

"Well, there is also the influence of vorticity..."

"Initial conditions, nonlinear terms, spatial dimensions, boundary conditions, and the concentration and growth of externally driven vorticity, that is, the formation of explosive solutions, are basically related to these conditions."

"So what kind of method should be used to achieve the reconciliation of these problems?"

Xiao Yi pondered for a while.

He took out the draft paper and began to deduce on it.

【tu+(u)u=p+νΔu+f……】

As he deduced, the brainstorm in his mind gradually began to condense in the process of deduction, and gradually formed a common goal, and then launched an attack towards this common goal.

Time passed slowly.

…

For several days, Xiao Yi looked through all the data and analyzed a lot of information from it.

"The birth of explosive solutions is always caused by many different reasons."

"But these different reasons, from a mathematical point of view, have a unified reason after all."

"Hmm..."

Sitting in the office, Xiao Yi pondered.

Xiao Yi, who had not studied such a difficult mathematical problem for a long time, gradually regained the feeling at the beginning.

For this problem that has been studied thoroughly by the academic community and has a history of hundreds of years, it is impossible to solve it simply.

As for the method that can perfectly prove the existence and smoothness of the solution to the NS equation in one fell swoop, it does not exist at all.

But at this moment, so much information has been summarized, and the storm in Xiao Yi's mind is like a centrifuge, stirring and centrifuging this information. And now, everything is connected like a thread. Separation and precipitation are also completed in this centrifuge in the mind.

"Professor, your water."

As a conscientious assistant, Wang Hao refilled his empty water glass and placed it next to him.

The jasmine tea inside is constantly rotating along with the vortex in the cup, and the effect of fluid mechanics is constantly playing out between the collision and adhesion of microscopic water molecules.

Xiao Yi's eyes were fixed on the glass of water, but in his mind, there was another scene:

The water in the cup rotated slower and slower until it finally stopped completely, including the tea leaves inside, which basically stopped, except for the tea leaves on the surface, which were still swirling.

Until finally everything came to a standstill.

However, at that moment of stillness, a certain volume of tea in the center suddenly exploded. The air pressure in the entire cup increased a lot, and then with a "bang", the glass teacup exploded.

Liquid splashed across a desk, and fragments of glass exploded.

And one of the fragments was about to rush towards Xiao Yi's eyes at a glance.

But as soon as he blinked, the scene of the water glass exploding disappeared.

All that was left was the boiling water and tea leaves that were still rotating slightly, and the white steam coming out of the cup.

"professor?"

Probably seeing Xiao Yi suddenly unresponsive when looking at the water glass he brought over, Wang Hao couldn't help but ask.

Xiao Yi came back to his senses, then smiled and nodded to him: "Thank you."

Wang Hao also smiled and was about to leave, but at this moment, Xiao Yi suddenly looked at the water in the cup and said, "Did you see it explode?"

Wang Hao was startled: "What? Explosion? How could this cup explode? "

He didn't understand.

Xiao Yi smiled and nodded: "Yes, the cup will not explode inexplicably, and the same goes for water."

In the world of mathematics, it explodes, but in the real world that abides by various physical laws, it does not explode, and it still has the soft feeling that comes with water.

Then, he picked up the cup, shook it, and then took a sip to feel the temperature of the tea.

Then he put down the water glass and looked at the computer again.

"It's time to take this crucial step."

Open LaTeX and enter a title.

"The formation mechanism of PDEs and power system explosive decomposition"

Explosive solutions are not only found in fluid mechanics, but also in nonlinear partial differential equations (PDEs) and dynamical systems in many other fields.

In many studies such as the nonlinear wave equation, the nonlinear heat equation, the Keller-Segel model, etc., there will be problems with explosive solutions.

It can be said that this problem is basically a chronic disease in many fields of academia, and it has always been a key issue that has plagued people's research.

If this problem can be solved, it will be of extremely important significance both in academia and in practical applications.

But now, Xiao Yi already has such confidence.

…

Half a month passed quietly.

"nailed it."

"The most important thing about the formation of explosive cracks lies in a [trend] in the equation."

"Under the setting of different initial conditions, a [trend] will inevitably appear, and all fluid mechanics of the fluid model will move towards this common goal."

"So, the most important thing is to set the initial conditions to avoid such a trend."

Now, Xiao Yi has summarized all the rules in his paper, and at the end provides a model that can simply judge whether there is a [trend] in the initial condition setting.

"Well, let's just name this trend the explosion trend, and this model is also called the explosion trend identification model."

It is conceivable that his explosive trend identification model will play a huge role in related practical applications.

In any industrial technology research related to fluid mechanics, in the process of direct numerical simulation, problems caused by blasting will be faced. Now if we can use his blasting trend identification model to carry out the initial conditions they set. By doing calculations, one can easily determine whether their model is likely to be cracked.

This model is of great significance. After all, every time direct numerical simulation is used, companies or research teams need to spend part of the cost of computing resources, and renting a supercomputer costs a lot of money.

And if their model runs around and explodes in the end, it will not only be a waste of time, but also a waste of cost.