Great Country Academician

After sending away David McGmillan, the head of Princeton's chemistry department, Xu Chuan returned to the control of ultra-high temperature plasma.

The essence of this job is actually to build a mathematical model of turbulent flow. Of course, more practically, it can be said 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 one of the seven millennium problems.

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

And what he wants to study is not only plasma turbulence, but also the ultra-high temperature plasma turbulence in the controllable nuclear fusion reactor chamber, 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 foundation, it is still difficult to solve this problem.

Not to mention the research on turbulence and NS equations in mathematics, even if he is not the first person, he can still be ranked in the top three.

The key lies in the application. At the application level of turbulent flow and plasma fluid, most of the achievements made are mixed with experimental experience and some experimental parameters.

For example, the PPPL Plasma Laboratory in Princeton has its own set of phenomenological models, which were developed by mathematicians and physicists at the Institute for Advanced Study in Princeton for PPPL equipment.

This is why Princeton can help other experimental institutions in the United States studying controlled nuclear fusion.

However, it is not so difficult to build an overall planning model based on mathematical theory and put aside these experimental experience and experimental parameters.

At Nanjing University, Xu Chuan sat in his office, scribbling and altering the manuscript paper with a black ballpoint pen in his hand.

【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 use the statistical average method to start the turbulence discussion.

When mathematicians studied turbulence in the past, they decomposed the irregular flow field into the mean field and the non-pulsating field, which also led to the century-old problem of blocking the Reynolds equation.

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

What he is doing now is to start with the mean field and the non-pulsating field, try to explain the two with mathematical language, and make a connection.

Starting from this step, it may be possible to complete the model for plasma turbulence.

After all, no matter how complicated the turbulent flow is, the problem itself, from a physical point of view, is nothing more than two major aspects of "external environmental interference" and "classical complexity itself".

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

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

Of course, this is also the performance of fluid mechanics applied to actual industry.

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

In classical physics, there is an approach called 'reductionism', which is part of the nine-year compulsory education in high school.

When we learned physics at that time, we would tell you that Newton's law starts from the particle, Coulomb's law starts from the point charge, Biosafal's law starts from the current element, and vibration wave starts from the simple harmonic oscillator.

From simple to complex, layers of in-depth, to achieve the purpose of understanding the material world.

Since Newton, people have firmly believed that the universe, including the vast and infinite, can be calculated. This is the so-called computationalism + reductionism.

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

Reductionism is to subdivide matter into basic units bit by bit, and then establish the evolution equation of motion based on the interaction rules between the basic components.

This sounds simple and easy to understand.

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

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

Especially at the rear of the car, the situation is even more serious. A car driving on the highway contains at least 1,000,000,000,000 microflow units in the air flow brought by its own driving.

And if there are other vehicles passing by, this number will increase by several orders of magnitude, and at least it can reach the number of ten trillion.

To analyze the structure of so many microfluidic units, we must also consider the disturbance caused by these microfluidic units, the merged medium and large microfluidic units, and the dissipated microfluidic units, as well as the in the newly formed microfluidic unit.

Believe me, analyzing this many microfluidic units is definitely not something that any computer you can buy on the market can handle.

Even a supercomputer cannot do real-time analysis because the amount of data is too large.

And if you want to analyze and process these things, the only way is to build a simulation, commonly known as CFD.

Its basic principle is to numerically solve the differential equations that control fluid flow, and obtain the discrete distribution of the flow field of fluid flow in a continuous area, thereby approximately simulating the fluid flow situation.

This technology is now widely used in various industries.

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

However, most of the time, the results obtained by CFD simulation are very different.

Not to mention the simulations established by different CFD methods, that is, the simulations established by using the same method for the same object, such as aircraft driving, have different results.

Just like domestic and foreign aircraft, the difference is not only in the engine, there is also a considerable distance in the application of fluid dynamics.

This gap is mainly reflected in the reaction force and dynamic balance of the aircraft when dealing with dangerous situations.

For example, when encountering thunderstorms and storms, the aircraft can quickly complete the adjustment of the balance of the fuselage through the computer.

It may also be reflected in the pilot's control over the aircraft when the fighter jet is doing those ultra-difficult maneuvers. Don't underestimate the fluid and turbulent flow across the surface of the fuselage, they still have a considerable impact on the balance of the aircraft.

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

Through solving it, each phased result can greatly improve human understanding of fluids in the future.

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

As the research deepened, Xu Chuan began to devote himself to it.

Even the research site was moved back to the villa from the NTU office, and the students in the school who had only enjoyed his class for a few days stopped offering again.

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

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

This is a rather tedious job, but Xu Chuan found that this job is not as difficult as imagined.

He had already prepared to be stuck in this job for several months or even a year or so. But now, he was a little surprised to find that so far, his advancement seemed to be going smoothly.

Looking at the manuscript paper on the desk, Xu Chuan had a smile on his lips: "It doesn't look that difficult, maybe we can solve this problem soon!"

Full of motivation, he devoted himself to the research again.

The days passed like this day by day, and I don't know how long it has passed.

In the study, Xu Chuan looked up at the data sorted out on the computer screen, while waving 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 manuscript paper, he frowned and fell into deep thought.

By extension, he had managed to describe the plasma flow in the reactor chamber through mathematical equations, but new problems arose.

At present, he can only describe the turbulent flow field with a volume average value that is nearly uniform, while the relatively turbulent non-pulsating field is still a cloud of fog.

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

After a while, he let out a long sigh of relief, shook his head helplessly and said to himself, "It seems that setting a flag before doing research is really not a good thing."

At the beginning, the in-depth core research was too smooth, which made him think that the results would be obtained soon with sufficient theoretical support, which made him confidently set the flag.

But now it seems that he is still far away from the exit of this maze.

Even now, he began to suspect that the path he took might be problematic.

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

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

But on the contrary, at the microscopic scale, gas, fluid and even any substance are regarded as a many-body system composed of microscopic particles (atoms/molecules).

Among the equations proposed in fluid mechanics, the most famous (compressible or incompressible) Euler equations and Navier-Stokes equations are the most famous.

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

The Boltzmann equation is a partial differential equation describing the statistical behavior of a thermodynamic system in a non-thermodynamic equilibrium state, proposed by Ludwig Boltzmann in 1872.

It can be used to determine how physical quantities change, such as the thermal energy and momentum of a fluid as it is transported.

In addition, we can also derive other characteristic properties of the fluid from it, such as viscosity, thermal conductivity, and electrical conductivity (considering the charge carriers in the material as a gas).

But it is the same as the NS equation, the existence and uniqueness of the solution are still not completely resolved.

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

Although strictly speaking, the traditional Boltzmann equation is only applied to neutral gas molecular systems, when it is applied to common non-equilibrium plasmas, including non-equilibrium plasmas flowing under atmospheric pressure conditions, certain corrections are made to the results is still correct.

After all, in theory, a plasma can be thought of as a mixture of positively and negatively charged particles.

Of course, this theory is not entirely correct, and mathematically using the Boltzmann equation to study plasma requires certain corrections, but it is not impossible.

Here, however, a new problem arises.

When using the Boltzmann equation to describe the turbulent flow field, a gully is blocked between the average field and the non-pulsating field.

He couldn't find the right room to connect the two.

Staring at the ceiling in a daze 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 this is a road that no one has touched, no one can provide him with experience and knowledge. The thorns and difficulties along the way conquered him alone, and he will not give up.

Moreover, it is precisely because of difficulties that people are born with the desire to conquer and the fullness of the heart after solving the problem.

If there is no bridge connecting the mean field and the apulsating field, then he built a bridge over this abyss.

The purpose of putting his focus on mathematics in this life is not to want to go further on the original peak, now the road is under his feet, just go forward.

In front of the desk, Xu Chuan stared at the formula on the manuscript paper with a pen in his hand and began to think.

"Theoretically speaking, plasma contains many kinds of particles, at least ions and electrons, so it can be regarded as the Boltzmann equation under the multi-particle system.

"In controlled 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 of evolution in phase space is: fα/t+V·fα/r+Fα/mα·fα/v = (fα/t).”

"If the distribution function of hydrogen ions is set to be."

Bit by bit, Xu Chuan sorted out what he needed from the source, and occasionally turned on the computer to search for some needed information.

This is a very arduous task, and there are not many papers that can be used for reference.

After all, no one has ever gone this far in theoretically modeling plasma turbulence.

The days passed day by day like this for an unknown amount of time, and Xu Chuan nestled in his study for an unknown amount of time without going out. In order to build this microscopic bridge between the average field and the non-pulsating field, he almost did nothing but eat and sleep. Time is spent exploring possible solutions.

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

"Professor, how did you do this?"

When Xu Chuan opened the door, Zheng Hai was taken aback. Who was this man with messy hair, a beard that hadn't been worn for half a month, bloodshot eyes, and even dark circles?

If it hadn't been confirmed that this was Xu Chuan's study, he would have even thought 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 be concealed, his eyes were extremely bright.

The busyness of these days is not fruitless. Between the average field and the non-pulsating field, he has found a way to the other shore.

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

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

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

"Forehead"

Zheng Hai was stunned for a while, and said dumbfoundedly: "This is not very good, after all, you are the general manager."

Although he is not a scientific researcher, he has followed Xu Chuan's relationship throughout the whole process, and he is very aware of the contribution of this person in front of him in the project.

It could even be said that this celebration banquet and commendation conference was specially held for him.

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