After sending away David McGemillan, the chairman of Princeton's chemistry department, Xu Chuan returned his energy to controlling ultra-high temperature plasmas.
The essence of this job is actually to establish a mathematical model of turbulence. Of course, more practically, it can be said to be a study of the phenomenon of plasma turbulence.
In fact, in terms of difficulty, studying the phenomenon of plasma turbulence is not much simpler 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, let alone plasma turbulence in turbulence.
What he wants to study is not only plasma turbulence, but also 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 in the NS equation and has a theoretical foundation, it is still difficult to solve this problem.
Not to mention his 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 application. At present, at the application level of turbulent flow and plasma fluids, most of the results achieved are mixed with experimental experience and some experimental parameters.
For example, Princeton's PPPL Plasma Laboratory has its own set of phenomenological models, which were developed by mathematicians and physicists from the Institute for Advanced Study in Princeton for the PPPL equipment.
This is why Princeton can provide help to other experimental institutions in the United States that study controllable nuclear fusion.
However, it is not that difficult to establish a comprehensive model based on mathematical theory and put aside these experimental experiences and experimental parameters.
At Nanda, Xu Chuan is sitting in his office, making corrections on the manuscript paper with the black ballpoint pen in his hand.
【μi(t)=1/T∫t Tvt0μi～(t)dt】
【μi(t)=LimT→∞1/T∫t Tvt0μi～(t)dt】
For a turbulent flow, the most commonly used method in the mathematics community is to use the statistical average method to start the turbulence discussion.
In the past, when mathematicians studied turbulence, they decomposed the irregular flow field into a mean field and a non-pulsating field, which also led to the century-old problem of blocking the Reynolds equation.
The randomness statistical averaging method of turbulence is the basic method 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, try to explain the two using mathematical language, and make a connection.
Starting from this step, it may be possible to complete a model for plasma turbulence.
After all, no matter how complex turbulence is, from a physical perspective, the problem itself is mainly derived from two aspects: 'external environmental interference' and 'inherent classical complexity'.
External environmental interference is easy to understand. Just like when a car is driving on the highway, its shape, wind resistance and other factors will cause eddy currents at the rear of the car. This includes if there is a large truck or other vehicle passing by while driving.
When, 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 a manifestation of fluid mechanics applied to actual 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 nine-year compulsory education in high school.
When we studied physics at that time, we would tell you that Newton's law starts from the particle point, while Coulomb's law starts from the point charge, Biosafar's law starts from the current element, and the vibration wave starts from the simple harmonic oscillator.
From simple to complex, go deeper layer by layer to achieve the purpose of understanding the material world.
Starting from Newton, people firmly believe that the vast and infinite universe can be calculated. This is the so-called computationalism reductionism.
Computationalists believe that even human nature can be calculated, which even affects the development of artificial intelligence today.
Reductionism subdivides matter into basic units bit by bit, and then establishes the evolution equation of motion based on the interaction rules between basic components.
This sounds simple and easy to understand.
But how easy is it to reconstruct the evolution equation from its basic components?
Just like a car driving on the highway, it is creating and destroying eddies and turbulence all the time.
Especially at the rear of the car, the situation is even more serious. For a car driving on the highway, the air flow caused by its own driving contains at least a micro-flow unit.
And if there happen to be other vehicles passing by, this number will increase by several orders of magnitude, and it can reach the level of tens of trillions at least.
To analyze the structures of so many microfluidic units, we must also consider the disturbances caused by these microfluidic units to each other, 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 so many microfluidic units is definitely beyond the capabilities of any computer you can buy on the market.
Even supercomputers cannot perform 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 establish simulation, commonly known as CFD.
Its basic principle is to numerically solve the differential equation that controls 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 has actually been widely used in all walks of life.
From movable cars, airplanes, rockets, to immovable high-rise buildings, building ventilation, daily air conditioners, refrigerators, etc., everything has its traces.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! However, most of the time, the results obtained by CFD simulation are very different.
Not to mention the simulations created by different CFD methods, even the simulations created using the same method for the same object, such as the movement of an airplane, will produce different results.
Just like domestic and foreign aircraft, the difference is not only in the engine, but also in the application of fluid dynamics. There is also a quite obvious distance.
This gap is mainly reflected in the aircraft's responsiveness and dynamic balance when responding to dangerous situations.
For example, when encountering 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 jet performs those extremely difficult maneuvers. Don't underestimate the fluid and turbulence flowing 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.
By solving it, each stage of results can greatly improve human understanding of fluids in the future.
These things can be converted 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 wholeheartedly to it.
Even the research address was moved back to the villa from the NTU office, and those students in the school who had only enjoyed his classes for a few days stopped paying again.
For the ultra-high temperature plasma in the controllable nuclear fusion reactor chamber, whether it is the current mainstream tokamak device, a stellarator, or a spherical NIF ignition device, the plasma inside
All are in a limited space.
Based on the phased results of the NS equation, he began to sort out the PPPL experimental data he brought back from Princeton bit by bit, and then substituted them into it to prepare for the establishment of a mathematical model.
This was quite a tedious task, but Xu Chuan found that it was not as difficult as he imagined.
He had originally been prepared to be stuck in this job for several months or even a year and a half. But now, he was somewhat surprised to find that so far, his progress seemed to be going quite smoothly.
Looking at the manuscript paper on the desk, Xu Chuan said with a smile: "It doesn't seem that difficult. Maybe this problem can be solved soon!"
Full of motivation, he devoted himself to research again.
The days passed like this, and I don’t know how long it took.
In the study, Xu Chuan looked up at the previously compiled data on the computer screen, while waving the ballpoint pen in his hand and continuing to write some mathematical formulas on the manuscript paper.
“(t)/Vi(t)=1/▽i(ξ,η,ζ,t)dξdηdζ,ft
ξ·xf =1kQ(f, f),.,"
Staring at the data written on the manuscript paper, he frowned and fell into deep thought.
By deducing to this point, he had already described the plasma flow in the reactor chamber through mathematical equations, but new problems also emerged.
At present, he can only describe the turbulent flow field with a nearly uniform volume mean value, while the relatively chaotic non-pulsating field is still a mystery.
After pondering for a while, Xu Chuan threw aside the ballpoint pen in his hand, leaned back on the chair, and stared at the ceiling silently.
After a while, he breathed 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 went too smoothly, which made him think that he would get the results soon with sufficient theoretical support, which made him confidently set the flag.
But now it seems that he is still not sure how far away from the exit of this maze.
In fact, he now began to have some doubts that there might be something wrong with the path he was taking.
As we all know, at the macroscopic scale, gases and fluids are viewed as a continuum.
Their motion is described by macroscopic quantities such as material density, macroscopic velocity, absolute temperature, pressure, tension, heat flow and other macroscopic quantities.
But on the contrary, at the microscopic scale, gases, fluids and even any matter are regarded as a multi-body system composed of microscopic particles (atoms/molecules).
The most famous among the equations proposed in fluid mechanics are undoubtedly the (compressible or non-compressible) Euler equations and the Navier-Stokes equations.
However, in the study of fluid dynamics, there is another famous equation, and that is the Boltzmann equation.
The Boltzmann equation is a partial differential equation that describes the statistical behavior of a thermodynamic system in a non-thermodynamic equilibrium state. It was 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 during transport.
In addition, we can also derive other fluid characteristic properties from it, such as viscosity, thermal conductivity, and electrical conductivity (treating the carriers in the material as a gas).
But like the NS equation, the problem of the existence and uniqueness of the solution is still not completely solved.
However, when modeling plasma turbulence, Xu Chuan used part of Boltzmann's equation.
Although strictly speaking, the application range of the traditional Boltzmann equation is only for neutral gas molecular systems, when it is applied to common non-equilibrium plasmas including non-equilibrium plasmas flowing under atmospheric pressure conditions, certain corrections must be made to the results.
is still correct.
After all, theoretically speaking, plasma can be regarded as a mixed gas composed of positively and negatively charged particles.
Of course, this theory is not completely correct, and mathematically using the Boltzmann equation to study plasma requires certain corrections, but it is not impossible to use it.
However, here, a new problem arises.
This chapter is not over, please click on the next page to continue reading! When using the Boltzmann equation to describe the turbulent flow field, a ravine blocks between the mean field and the non-pulsating field.
He couldn't find a suitable room to connect the two.
After 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 will not give up.
Even if this is a road that no one has touched, and no one can provide him with experience and knowledge. He will conquer all the thorns and difficulties along the way, but he will not give up.
Moreover, it is precisely because of difficulties that people can have the desire to conquer, and the contentment that comes after solving the problem.
If there is no bridge between the mean field and the non-pulsating field, then he built a bridge across the abyss.
His purpose in focusing on mathematics in this life is not to take a step forward on his original peak. Now the road is at his feet, he just needs to keep moving forward.
In front of the desk, Xu Chuan held the pen and stared at the calculations on the manuscript paper and began to think.
"Theoretically speaking, plasma contains a variety of particles, at least ions and electrons, so it can be regarded as the Boltzmann equation under 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 assumed to be fa(r,u,t)drdu, then the kinetic equation evolving in phase space is: fa/t V·fa/r Fa/ma·fa/v=(
fa/t)."
"If the distribution function of hydrogen ion ions is assumed to be."
Little by little, 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 and materials to draw from.
After all, no one has ever gone so far in the theory of plasma turbulence models.
The days passed like this day by day for who knows how long. Xu Chuan stayed in his study and didn’t go out for who knows how long. In order to build this microscopic bridge between the mean 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 startled.
"Professor, how did you do this?"
When Xu Chuan opened the door, Zheng Hai was shocked. Who was this man with messy hair, a beard that looked half-month old, bloodshot eyes, and even dark circles?
If he hadn't confirmed that this was Xu Chuan's study, he would have thought that Xu Chuan had been replaced by someone.
"What's the matter?" Xu Chuan raised his head and asked. Although the fatigue on his face was obvious, his eyes were extremely bright.
These days of busyness are not fruitless. Between the average 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 there has passed the acceptance inspection. A celebration banquet and commendation meeting have been arranged. 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 thinking that the research on plasma turbulence has now entered a critical node, and he did not want to interrupt his thoughts at this time and go to the capital to receive the award.
"Forehead"
Zheng Hai was stunned for a moment, and said with a mixture of laughter and tears: "This is not good, after all, you are the person in charge."
Although he is not a scientific researcher, he has followed Xu Chuan 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 held specifically for him.
If he doesn't go, the remaining researchers and engineers will probably be too scared to accept the commendation~