After seeing off David McGmillan, the head of Princeton's chemistry department, Xu Chuan returned to controlling ultra-high temperature plasma.

The essence of this work is actually to build a mathematical model of turbulence. Of course, it is more practical to study the phenomenon of plasma turbulence.

In fact, in terms of difficulty, studying the phenomenon of plasma turbulence is not much easier than studying a seven-millennial problem.

First of all, turbulence is a well-known chaotic system, and it is also one of the problems that many physicists and mathematicians are puzzled by, not to mention plasma turbulence in turbulence.

What he wants to study is not only plasma turbulence, but also ultra-high temperature plasma turbulence in the chamber of a controlled nuclear fusion reactor, which is nearly two orders of magnitude higher than the difficult turbulence.

Although he has made great progress on the NS equation and has a theoretical basis, it is still difficult to solve this problem.

In mathematics, not to mention the study of turbulence and the NS equation, he can be ranked in the top three even if he is not the first.

The key lies in the application, and at present, at the application level of turbulence and plasma fluids, most of the results are doped with experimental experience and some experimental parameters.

For example, the PPPL Plasma Laboratory in Princeton has its own image-only model, which was developed by mathematicians and physicists at the Institute for Advanced Study in Princeton.

That's why Princeton can help other U.S. experiments that study controlled fusion.

However, it is not very difficult to start from the mathematical theory and set aside these experimental experiences and experimental parameters to build an overall model.

Nanda, Xu Chuan sat in his office, the black ballpoint pen in his hand scribbled and changed on the manuscript paper.

【μi(t)=1/T∫t+Tˇt0μi～(t)dt】

【μi(t)=LimT→∞1/T∫t+Tˇt0μi～(t)dt】

For a turbulent flow, the most commonly used method in mathematics at present is to start the turbulence discussion by means of statistical averaging.

In the past, when mathematicians studied turbulence, they decomposed the irregular flow field into mean and non-pulsating fields, which also led to the problem of the century that blocked the Reynolds equation.

The randomness statistical average method of turbulence is the fundamental means to deal with turbulent flow, which is determined by the randomness of turbulence.

What he is doing now is to start from the mean field and the non-pulsating field, and try to explain the two in mathematical language respectively, and make a correlation.

From this step, it may be possible to complete a model for plasma turbulence.

After all, no matter how complex turbulence is, the problem itself is only from the perspective of physics: 'external environmental interference' and 'classical complexity itself'.

External environmental disturbances are easy to understand, just like when a car is driving on the highway, its own shape, wind resistance and other factors will bring vortices to the rear of the car. Even if there are large trucks or other vehicles passing by during the driving process, a more complex turbulence system will be formed.

This is also the reason why top sports cars or racing cars will pursue the extreme shape and extreme fluid dynamics of the vehicle, because the presence of turbulence will increase wind resistance, consume more power and reduce speed.

Of course, this is also the manifestation of the application of fluid mechanics in real industry.

As for the classical complexity itself, this comes from classical physics.

In classical physics, there is a method called 'reductionism', which is the content of the high school years in the nine-year compulsory education.

At that time, when we studied physics, we would tell you that Newton's laws start from the point of mass, while Coulomb's law starts from the point charge, Biosafar's law starts from the current element, and the vibrational wave starts from the simple harmonic oscillator.

From simple to complex, layer by layer, to achieve the purpose of understanding the material world.

Beginning with Newton, people believed that the universe, including the vastness and infinity, could be calculated. This is called computationalism + reductionism.

Computationists believe that even human nature can be calculated, which even influences the development of artificial intelligence today.

Reductionism, on the other hand, subdivides matter into basic units little by little, and then establishes the evolution equation of motion based on the interaction law between the basic components.

It sounds simple and easy to understand.

But how easy is it to reconstruct the evolutionary equation from the basic components?

Like a car on a highway, it creates and annihilates eddies and turbulence at every moment.

Especially at the rear of the car, the situation is even more serious, a car driving on the highway, just the air flow brought by its own driving, contains at least 1000000000000 micro-flow units.

And if there happen to be other vehicles passing by, this number will increase by several orders of magnitude, not to mention the number of ten trillion levels.

In order to analyze the structure of so many microfluidic units, it is also necessary to consider the disturbances caused by each other by these microfluidic units, the merging of medium and large microfluidic units, the dissipation of microfluidic units, and the new microfluidic units that are formed every moment.

Trust me, analyzing so many microfluidic units is definitely not something you can do with any computer you can buy on the market.

Even supercomputers can't do real-time analysis because the amount of data is so large.

And if you want to analyze these things, the only way is to create simulations, commonly known as CFD.

The basic principle is to numerically solve the differential equations that control the fluid flow, and obtain the discrete distribution of the flow field of the fluid flow over a continuous area, so as to approximate the fluid flow situation.

This technology is now being used in a wide range of industries.

From movable cars, airplanes, and rockets, to immovable high-rise buildings, building ventilation, daily air conditioners, refrigerators, etc., there are all traces of it.

Most of the time, however, the results of CFD simulations vary widely.

Not to mention the simulation established by different CFD methods, that is, the simulation established by the same method on the same object, such as airplane driving, has different results.

Just like domestic and foreign aircraft, there is not only a gap in the engine, but also a fairly obvious distance for the application of fluid dynamics.

This gap is mainly reflected in the aircraft's reaction power and dynamic balance when dealing with dangerous situations.

For example, in the event of thunderstorms and storms, the aircraft can quickly adjust the balance of the fuselage through the computer.

Or it may be reflected in the pilot's control of the aircraft when the fighter is doing those ultra-difficult maneuvers, etc. Don't underestimate the fluids and turbulence that cut across the fuselage surface, they still have a considerable impact on the balance of the aircraft.

This is the reason why the NS equation has been pursued by countless mathematicians and physicists.

By solving it, each phase of the results can greatly improve the human understanding of fluids in the future.

These things can be transformed into mathematical models or other things that help improve people's control and application of fluids.

With the deepening of his research, Xu Chuan began to devote himself wholeheartedly.

Even the research address was moved back to the villa from the NTU office, and the students at the school who had only enjoyed his classes for a few days were cut off again.

For the ultra-high temperature plasma in the chamber of a controllable nuclear fusion reactor, whether it is the current mainstream tokamak device, or the stellar, or the spherical NIF ignition equipment, the plasma inside is in a limited space.

On the basis of the phased results of the NS equation, he began to sort out the experimental data of PPPL that he brought back from Princeton little by little, and then substituted it into it to prepare for the establishment of the mathematical model.

This is quite a tedious job, but Xu Chuan found that the work does not seem to be as difficult as he imagined.

He was ready to work in this job for months or even a year and a half. But now, he was somewhat surprised to find that so far, his progress seems to be going well.

Looking at the manuscript paper on the desk, Xu Chuan had a smile on his lips: "It doesn't seem to be so difficult, maybe you can solve this problem soon!" ”

Motivated, he threw himself back into research.

The days went by like this, and I don't know how long it was.

In the study, Xu Chuan looked up at the data that had been sorted out on the computer screen, and at the same time waved the ballpoint pen in his hand and continued to write some mathematical formulas on the manuscript paper.

“（τ）/Vi（t）=1/▽i（ξ，η，ζ，t）dξdηdζ，ft +ξ·xf =1κQ(f， f)，.，”

Staring at the data written on the paper, he frowned and fell into deep thought.

By deduction to this point, he had managed to describe the plasma flow in the reactor chamber by means of mathematical equations, but new problems arose.

At present, he can only describe the turbulent flow field with a nearly uniform body mean, and the relatively disordered non-pulsating field is still a fog.

After pondering for a while, Xu Chuan threw the ballpoint pen in his hand aside, leaned back into the chair, and stared at the ceiling silently.

After half a sound, he breathed a long sigh of relief and shook his head helplessly, and said to himself: "It seems that it is really not a good thing to set up a flag before researching. ”

At the beginning, it was too smooth when he went deep into the core research, which made him think that he would get the results soon on the basis of sufficient theoretical support, which made him confidently set the flag.

But now it seems that he is not far from the exit of this labyrinth.

Even, he was now beginning to suspect that the path he was taking might be problematic.

It is well known that at the macroscopic scale, gases and fluids are seen as a continuum.

Their motion is described by macroscopic quantities such as density of matter, macroscopic velocity, absolute temperature, pressure, tension, heat flux, etc.

Conversely, at the microscopic scale, gases, fluids, and even any matter are seen as a many-body system of microscopic particles (atoms/molecules).

The most famous of the equations proposed in fluid mechanics are the Euler equations (compressible or non-compressible) and the Navier-Stokes equations.

However, in the study of fluid dynamics, there is another well-known equation, that is, the Boltzmann equation.

The Boltzmann equation is a partial differential equation that describes the statistical behavior of thermodynamic systems in a non-thermodynamic equilibrium state, and was proposed by Ludwig Boltzmann in 1872.

It can be used to determine how physical quantities change, such as the heat energy and momentum of a fluid during transport.

In addition, it can be used to derive other characteristic properties of the fluid, such as viscosity, thermal conductivity, and electrical conductivity (think of the carriers in the material as gases).

But like the NS equation, the problem of the existence and uniqueness of the solution is still not fully solved.

However, when modeling plasma turbulence, Xu used part of the Boltzmann equation.

Although the traditional Boltzmann equation is strictly only applied to neutral gas molecular systems, it is still correct with some correction when applied to common non-equilibrium plasma, including non-equilibrium plasma flowing at atmospheric pressure.

After all, plasma can theoretically be seen as a mixture of positive and negative charged particles.

Of course, this theory is not entirely correct, and the mathematical use of the Boltzmann equation to study plasma requires some correction, but it is not impossible.

And here, however, new problems arise.

When describing the turbulent flow field using the Boltzmann equation, a gully is blocked between the mean field and the non-pulsating field.

He couldn't find a suitable room to connect the two.

Staring at the ceiling for a while, Xu Chuan sat up straight again and picked up the ballpoint pen on the table.

No matter what, he won't give up.

Even if it's a path that no one has touched, no one can give him experience and knowledge. The thorns and difficulties along the way will be conquered by him alone, and he will not give up.

Moreover, it is precisely because of difficulties that people can give birth to the desire to conquer, and the sufficiency of the heart after solving the problem.

If there is no bridge between the mean field and the non-pulsating field, then he has built a bridge over this abyss.

The purpose of his life to focus on mathematics is to go further on the original peak, and now the road is under his feet, just go forward.

In front of the desk, Xu Chuan pinched the pen and stared at the manuscript paper and thought about it.

"Theoretically, plasma contains a variety of particles, at least ions and electrons, so it can be regarded as the Boltzmann equation in a multi-particle system.

"In controlled nuclear fusion, the plasma in the reactor is usually composed of 5% hydrogen ions and 95% deuterium ions."

"If the distribution function of deuterium ion particles is fα(r,υ,t)drdυ, then the kinetic equation for evolution in phase space is: fα/t+V·fα/r+Fα/mα·fα/v=(fα/t)."

"If the distribution function of hydrogen ions is .

Little by little, Xu Chuan sorted out the things he needed from the source, occasionally turning on the computer to search for some information he needed.

It's a very difficult job, and there is not much material to draw on.

After all, no one has so far gone so far in the theory of plasma turbulence modeling.

I don't know how long the days have passed, and Xu Chuanwo has not gone out for a long time in the study, in order to build this microscopic bridge in the mean field and the non-pulsating field, he almost has to eat and sleep, and the rest of the time is exploring feasible solutions.

So much so that when Zheng Hai knocked on his door, he was startled.

"Professor, how did you get to this?"

When Xu Chuan opened the door, Zheng Hai was taken aback, who was the person in front of him with messy hair, beard that looked like he hadn't hung up for half a month, bloodshot eyes, and even dark circles?

If it weren't for the confirmation that this was Xu Chuan's study, he would even think that Xu Chuan had been dropped.

"What's the matter?" Xu Chuan raised his head and asked, although the fatigue on his face could not hide the obviousness, his eyes were unusually bright.

The busyness of these days has not been fruitless, and between the mean field and the non-pulsating field, he has found a way to the other side.

"It's about the nuclear waste power generation project, the nuclear energy industrial park over there has passed the acceptance, and a celebration banquet and commendation meeting have been arranged, let me inform you." Zheng Hai said quickly.

"Let them go, I won't go, I don't have time lately."

Xu Chuan replied without thinking that the research on plasma turbulence has now entered a critical node, and he does not want to interrupt his train of thought at this time and go to the capital to receive the award.

"Amount"

Zheng Hai was stunned for a moment, and said with a smile: "This is not good, after all, you are the person in charge." ”

Although he is not a scientific researcher, he follows Xu Chuan's relationship throughout the whole process, and he clearly knows the contribution of the person in front of him in the project.

It can even be said that this celebration banquet and commendation meeting were specially held for him.

If he doesn't go, the rest of the researchers and engineers will probably be too scared to accept the commendation~

(End of chapter)