Judging from the mathematics papers that Xu Chuan has published in the past, he has covered quite a lot in various fields of mathematics, so much that he can be compared to Terence Tao.
In addition to mathematics, he is also deeply involved in physics, astronomy, materials and other fields.
Although he mainly relied on mathematical methods to win the Nobel Prize in Physics, it is impossible to master the calculation methods without in-depth understanding of the corresponding astrophysical knowledge that he is not familiar with.
But if he remembered correctly, the man in front of him was only twenty-two years old this year.
Even if prenatal education begins in the womb, it is difficult to imagine how it is learned.
To be honest, Qiu Chengtong also considers himself to be a genius in mathematics. When he was 22 years old, he studied under Chen Shengshen from the University of California, Berkeley, and received his PhD. He is already very good in mathematics.
But compared to this one, it's nothing.
This freak had already won the Fields Medal and the Nobel Prize at the age of twenty-two, and stood at the pinnacle of the entire mathematical world and even the scientific world.
.......
In the office, Wei Yong boiled a pot of hot water and quickly brought it over.
Qiu Chengtong personally took out the treasured tea leaves from the cabinet, picked up the hot water kettle and brewed a pot of hot tea.
The hot mist swirled up on the purple clay pot, and Xu Chuan stared at the mist and fell into deep thought.
Theoretically speaking, the mist on this teapot floats upward, and the shaped water mist gradually disperses and disappears in the air. Is it not a fluid with a very low viscosity coefficient?
Staring at the fog dissipating on the teapot, an idea flashed through his mind.
Sometimes, the study of fluids or turbulence is like the fog on this purple clay teapot. Starting from the root of the teapot, it rises in an orderly and stable manner, then begins to spread and become chaotic due to external interference in the middle, and finally loses completely.
Control completely disappears into thin air.
Although from a physical level, the dissipated fluid still exists, it can no longer be described mathematically.
From being initially predictable to eventually being completely out of control, from being able to derive motion using mathematical formulas to being unable to even be recorded with data, this is turbulence.
However, turbulence is not boundless.
Just like the water mist in front of you, human breathing, the breeze outside the window, and the alternating influence of hot and cold on the air can all interfere with the mist.
Staring at the hazy mist in front of him, Xu Chuan's thoughts became active.
Perhaps, we can construct multiple linear operators in three-dimensional space, satisfy the standard orthogonal basis matrix for any vector, and use the Hilbert method to find soliton solutions to nonlinear equations...
A pattern of ideas gradually became clear in his mind, but no one was sure what was at the end.
........
Opposite the desk, Qiu Chengtong was just about to pick up the purple clay pot and share the tea when he noticed Xu Chuan, who was staring at the purple clay pot, lost in thought.
He was very familiar with this state, and he knew very well that the other party might have had inspiration or an idea. After looking at it with interest, he did not continue to disturb him, and waited silently.
On the side, Wei Yong was about to step forward when he was stopped by his instructor Qiu Chengtong. The silence movement of his fingers in front of his lips made him understand instantly, and he cautiously shrank into the corner, looking at Xu Chuan who was deep in thought without even daring to say anything.
Panting, trying his best to reduce his sense of presence, for fear that his presence will disturb the other person's thinking.
The atmosphere in the office fell into an eerie silence for a while.
Xu Chuan pondered deeply and did not come back to his senses until the water mist rising from the birds disappeared as the temperature in the teapot dropped.
Looking at Qiu Chengtong who was waiting quietly on the side, he smiled sheepishly and said, "Sorry, I just got distracted."
Qiu Chengtong smiled nonchalantly, stood up, took away the purple clay pot, drained the tea and brewed another pot, then asked, "Do you have an idea?"
Xu Chuan nodded and said: "Well, I had a little inspiration, so I thought about it."
Qiu Chengtong asked curiously: "Can we chat?"
Xu Chuan: "Of course, it's mainly about some control calculations for external interference and prediction..."
He briefly talked about the inspiration he had just received, saying that sometimes going out for a walk can really benefit people a lot.
If he were in his own villa in Jinling, it would be impossible to get inspiration from the steaming mist of tea given his character who rarely drinks tea. But here with Qiu Chengtong, he has not yet started to communicate with the other party.
, you have already gained something.
After listening to Xu Chuan's narration, Qiu Chengtong pondered for a moment and then said: "This is indeed a good idea. From a computational point of view, this path should be feasible. However, I recommend replacing the bilinear operator with
Compared with linear transformation, which is the latter, the former still has limitations, especially when facing some special spaces, the ability of bilinear operators may not be enough."
Xu Chuan thought for a while, nodded, and said: "Indeed, but bilinear operators also have unique advantages. For example, the displacement of bilinear operators in vector space has symmetrical properties. In special spaces, such as squares,
, quite suitable in spaces such as ellipses and circles.”
"Maybe they can be mixed together?"
Qiu Chengtong shook his head and said: "Mathematically speaking, this should be feasible, but if you want to use this to build a control model for turbulence, it may not work."
"Especially for ultra-high-temperature plasma turbulence, the amount of change is too great. Today's computer performance and intelligence may not be able to achieve it, and even the use of supercomputers may not be feasible."
"You should know that when a mathematical model operates with too many variables, it will be a computing task that even a supercomputer cannot complete."
He already knew Xu Chuan's purpose, so after thinking about it for a while, he reminded this issue from an engineering perspective.
This chapter is not over yet, please click on the next page to continue reading! Xu Chuan thought for a moment and said: "What you said makes sense. If the model operation is too complex, the requirements for computing power are also too high, especially for controllable
As far as the plasma turbulence in the nuclear fusion reactor chamber is concerned, if there is a little bit of chaos, it is easy to cause a substantial increase in the amount of calculations."
It has to be said that Qiu Chengtong's ability is indeed terrifying, and he pointed out the problems in his ideas in a straight-forward manner.
His scientific research ability is not only in mathematics, but also in physics and engineering.
He was a tenured professor of physics at Harvard University and the only person in the history of Harvard University to hold concurrent posts in the Department of Mathematics and the Department of Physics.
When he was the director of the "Center for Mathematical Sciences and Applications" at Harvard University, Qiu's contributions involved various aspects such as cybernetics, graph theory, data analysis, artificial intelligence and three-dimensional image processing. It can be said that he is a dual-line theoretical and application
Top notch.
It is a blessing for the country that such a talented person is now returning to the country to contribute to the country.
........
In the office, Xu Chuan and Qiu Chengtong continued to exchange their views and ideas in the field of partial differential equations, which did not stop until the sunset fell on the two of them through the glass window.
After bidding farewell to Qiu Chengtong, Xu Chuan returned to Jinling.
This exchange was of great benefit to both him and Qiu.
Two truly top mathematicians opened their hearts and exchanged their respective opinions in the field of partial differential equations. This was a collision of sparks of wisdom, which may merge into a larger firework to illuminate the seemingly chaotic fog.
Returning to Jinling, Xu Chuan temporarily put aside other work and locked himself in the villa.
Establishing a mathematical model for ultra-high temperature plasma turbulence in a controllable nuclear fusion reactor chamber is an ambitious goal that is almost impossible to achieve in one step.
But now, he has enough qualifications and abilities to open up this road further.
In the study, Xu Chuan took a stack of manuscript paper and pen, sat at the desk and meditated.
Next to it, web pages and papers were opened on the laptop and desktop monitors.
These are preparations before starting official work.
Whether you are writing a paper or proving a certain problem, you often need to cite or look up various materials.
In front of the desk, after Xu Chuan thought for a long time, he finally raised his right hand and wrote a line of titles on the blank A4 page with the black ballpoint pen in his hand.
"Study on the nonlinear exponential stability and global existence solution of compressible navier-s in three-dimensional space!"
After writing a title line, he began to write an introduction to the entire proof.
[Introduction: The equation of motion of viscous fluid was first proposed by Navier in 1827, which only considered the flow of incompressible fluid. Poisson proposed the equation of motion of compressible fluid in 1831. Sai in 1845, Stokes in 1845....]
[The Navier-Stokes equation (okes equation) is an equation of motion that describes the conservation of momentum of a viscous incompressible fluid, referred to as the n-s equation. The n-s equation summarizes the universal laws of viscous incompressible fluid flow, so it has special characteristics in fluid mechanics
significance.....】
【......】
[The compressible viscosity n-s equation consists of three conservation equations: mass conservation equation, momentum conservation equation, and energy conservation equation. It also includes three unknown functions: ( v ( x, t ), u ( x, t ), θ ( x
, t )), respectively represent the specific volume (reciprocal of density), velocity, and absolute temperature of the fluid. Next, we will discuss the existence and uniqueness of the solution to the initial boundary value problem of the system of equations.】
[Currently, all discussions are in the bounded domain. 】
[Therefore, given the conditions of a finite domain and a dirichlet boundary, can the Okes equation have a real solution in a three-dimensional space and the solution is smooth? 】
.......
ps: There will be another chapter tonight, please vote for me.
