Looking at the turbulence model that had returned to its previous stable state, everyone present knew that Lin Xiao's model still failed.
Of course, at least the failure was not that complete. After all, turbulence still occurred during the process.
Ma Weimin stepped forward and asked: "How is it? What is the specific situation? Why did the turbulence suddenly appear just now?"
Lin Xiao frowned and said: "I just mainly added some new things to it. Your previous turbulence just treated the electromagnetic force as a general Newtonian force and did not perform any special analysis. Then I added the magnetic field of the superconductor
After taking it into consideration, this problem arose."
"Is it equivalent to saying that electromagnetic force caused this situation?"
Ma Weimin frowned and began to think.
From a macro perspective, the magnetic field generated by the superconducting coil in the magnetic fluid thruster and the force exerted on the conductive seawater can be directly regarded as a complete force.
But as we all know, according to quantum mechanics, the world is discontinuous and forces are divided. The electromagnetic force generated by superconducting magnetic fields is obviously different everywhere.
If you think about it this way, it seems that it may indeed lead to this situation.
But then Ma Weimin still had doubts: "But this situation is not very consistent with Newtonian mechanics, right? Even if it is slightly disordered, I can understand it, but such a particularly disordered situation, which leads to a significant decrease in speed, is really a bit
It’s hard to understand.”
"Yes, it's a little hard for me to understand too."
Lin Xiao nodded, then touched his chin and fell into thinking.
This question also made him feel a little puzzled.
Then, he re-wrote a formula on the scratch paper, which was the Navier-Stokes equation.
Looking at this complicated partial differential equation, but full of mathematical beauty, Lin Xiao nodded.
Although the problem is currently considered to be caused by the force of the superconducting magnetic field, it is obviously also closely related to the interaction force between fluids.
After all, the direct cause is the fluid force, and the electromagnetic force only indirectly promotes this change in the conductive seawater.
Of course, such an unexplainable yet miraculous effect still aroused Lin Xiao's other thoughts.
Perhaps, this is a new physical effect that has never been discovered before, rather than simply an accidental mechanical problem.
Just like the Hall effect.
Perhaps, when they unravel the principle of this magical phenomenon and master it, they can use it in other places?
Thinking of this, Lin Xiao also paid a little attention to it, and then focused his attention on the Navier-Stokes equation in front of him again, and he was troubled: "Is it possible that we really need to solve this thing?"
However, he soon made a decision.
Let’s do some research first. If we get any staged results during the research process, maybe we can solve the current problem?
Then he said to Ma Weimin: "Academician Ma, let's do this for now. I'll think about it when I go back. You can also study it experimentally. Since this matter may be related to electromagnetic force, you may be able to change the magnetic field.
Or when the liquid enters the channel, some diverting operations can be performed, or some processing can be done."
"okay, I get it."
Ma Weimin nodded, "We will conduct the test soon and the results will be announced at that time."
"Um."
Lin Xiao nodded and then left the laboratory.
…
In the following time, Lin Xiao entered into the study of Navier-Stokes equation.
Anyway, after solving the problem of artificial nerves and allowing Shi Hao to stand up, he entered a state of rest again. The next time he spent was just in time to study this mathematical problem.
Of course, it's not very simple.
"Professor, are you... studying the Navier-Stokes equations?"
In Lin Xiao's office at Peking University, Chen Mingkai looked at what his professor was studying, which seemed very complicated, and he couldn't help but show curiosity on his face.
Lin Xiao nodded and said, "Yes."
"Then what are you studying? Some kind of application?"
"Uh... no." Lin Xiao said: "Prove the existence and smoothness of its solution."
"Oh, this..." Chen Mingkai suddenly realized, but suddenly he reacted, with a look of shock on his face: "You mean...the Millennium Problem?"
"Ahem, don't be so surprised. Calm down, it's not like I haven't proved the Millennium Problem before." Lin Xiao smiled, and then said: "What's more, it's just proving a Millennium Problem, not solving it.
General explanation."
Chen Mingkai rolled his eyes immediately.
As a teacher, I am good at everything, but I am just too awesome.
Of course, as Lin Xiao said, the difficulty of "proving the existence and smoothness of solutions to the Navier-Stokes equations" in the Millennium Prize problem is compared to the difficulty of being exposed to the Navier-Stokes equations.
The general explanation is still a little simpler.
The Navier-Stokes equation is a partial differential equation. Solving partial differential equations is a direction that mathematicians in this field often study, and this is relatively difficult.
It is even more difficult to solve the Navier-Stokes equations, and is almost considered an impossible problem to solve.
Because it is not as easy to obtain a general solution as the Euler equation. There is an additional second-order derivative term μ△v in the Navier-Stokes equation, which makes it difficult to obtain it except under some specific conditions.
Its general explanation.
Therefore, the Millennium Prize problem only requires proving the existence of its solution, but does not require solving what its general solution is. As for the so-called smoothness, it means that the final general solution can be written as a [smooth function], which has
Infinite differentiability, just like the derivative of e^x is itself.
Once the general solution is solved, it will be amazing. Everything related to fluid mechanics will be greatly simplified. For example, the flow of water can be easily described using this general solution, or the flow of aircraft can be easily described.
Aerodynamic optimization, etc., the process will be greatly simplified.
However, precisely because it is very difficult to find a general solution, few people study this direction.
Chen Mingkai never thought that his teacher could find this general solution, so he asked: "Professor, have you found the proof?"
"No."
Lin Xiao said, then glanced at Chen Mingkai and said angrily: "What are you doing here with nothing to do? Have you chosen the topic of your thesis? You must choose it before July."
"Ah this..."
Chen Mingkai was stunned for a moment, and then said quickly: "The selection will be made soon. Professor, don't worry, I promise I won't procrastinate."
Seeing this guy running away, Lin Xiao shook his head with a smile, then stopped thinking about it and continued to study the Navier-Stokes equation.
"If the current method doesn't work... maybe I should change my mind?"
"Well... let's start with the special solution first."
The special solutions to the NS equation basically belong to the simplest case of parallel flow.
The representative flows in this regard are the Hagen-Poiseuille flow in a circular tube and the Couette flow between two parallel flat plates.
Lin Xiao found these two special solutions.
The first is the Hagen-Poiseuille flow, which is a tube flow, that is, a flow in a circular tube. This flow is obviously relatively simple.
【u=-△p/(4μL)(D^z/4-r^z)】
【Q=-π△pD……】
After writing down a few lines of equations, Lin Xiao directly imagined a tube in his mind, with liquid inside flowing along the tube.
Then he looked at the Couette flow, and then used the same method to first build a model in his mind and then directly simulate it.
"Well...this kind of fluid is relatively simple. What if we change it to a more complicated one?"
For example, Ma Weimin and the others plan to study magnetic fluid propulsion.
It uses conductive water as a magnetic fluid, and then propulsion can be achieved through reaction force.
Lin Xiao began to try to use his brain to simulate it, but this was obviously quite complicated. After simulating it in his mind for a long time, it was almost 100% loaded, and what he could simulate was still very limited.
Of course, if he "loads" it slowly, he can still barely achieve it.
Just like that, his eyes suddenly lit up.
Then he quickly picked up the pen and once again made an improvement on the original turbulence model.
Then, he put the model into the software and started loading it and running it.
Still the same, it was very stable at first, but as time passed, suddenly, these liquids began to move randomly and became very unstable.
This turbulence lasted for more than ten minutes.
But more than ten minutes later, it once again returned to its original stable flow state.
Lin Xiao was not surprised to see this.
However, a smile appeared on his face.
He gradually understood everything (crossed out) - he gradually understood the nature of these fluids.