Research starts with PhD students

Chapter 29 Two papers, methods and results!

Partial differential equations is a large category in the field of mathematics, and has the largest number of scholars among all branches of mathematics.

The second-order nonlinear partial differential equation is a giant in the field of partial differential equations, and its application in mathematics, physics and engineering technology is the most extensive.

These equations are also called mathematical physics equations.

Mathematical physics is naturally related to applications, including aircraft and ship design, meteorological monitoring, geology, thermodynamic properties, electromagnetic wave propagation, quantum mechanics, etc. A series of technologies and research involve second-order nonlinear partial differential equations.

Many professional scientific research institutions will set up special computing groups for experimental or technical research. In analytical experiments or technical research, solving partial differential equations is also the most complicated task of the computing group.

The Experimental Physics Center of the Institute of High Energy Physics has a special computing group, which performs a large number of numerical calculations of partial differential equations in order to analyze experimental data.

Another example is aircraft design.

Aircraft design requires the use of dynamics and fluid mechanics, and the design process of each aircraft involves a large number of equation calculations.

If the results of second-order partial differential equations can be directly obtained by computer, the demand for professional computer personnel will definitely be greatly reduced.

Luo Yongjun's sentiment also reflected his own experience. He is a doctoral supervisor and professor in a university, so of course he will not face the problem of unemployment.

However, some jobs have become dispensable.

This is what it’s like to do computational analysis of experimental data at the Institute of High Energy Physics.

If the second-order partial differential equation can be solved directly by computer, there will be no need for so many scholars to participate, and the task can be easily completed by reducing the number of scholars by more than half.

Hearing Luo Yongjun's sigh, Zhang Shuo smiled and shook his head, "Teacher Luo, I haven't reached that level yet. The accuracy of my research cannot catch up with the calculation of the human brain."

"It is not possible to calculate the exact solution, and some boundary values ​​cannot be calculated accurately."

“You can only define the scope of a solution.”

Zhang Shuo gave a brief explanation.

In fact, it is a question of the accuracy of the results.

For example, when solving an equation, professional scholars calculate the solution range to be '3 to 5', while computers can only calculate to '2 to 6', which is slightly larger than the range calculated by scholars.

For some work that does not require high results, computer calculations are sufficient, but for research content that requires very high results, computers can only assist in calculations, and professional scholars are still needed to narrow the scope.

"That's pretty awesome!"

Luo Yongjun still sighs, "In the future, the amount of calculation in the PDE direction will be greatly reduced, and algorithms can replace manpower in fields that do not require high results."

“This is technological progress!”

Sun Xingli doesn't care about the impact of his research results. His research direction is analytic number theory and methodology, and nothing can affect him. "Machines replace manpower, and AI replaces the human brain. This is the direction of social development. Otherwise, how can we make progress?"

"Or you can persuade those companies not to research automation, because automation will reduce jobs."

Gao Xiaohong also laughed and said, "Teacher Luo, you are really worrying about nothing."

"Is it because the results are not yours? If they were yours, you would definitely not think so."

"..."

Luo Yongjun curled his lips and didn't say a word for a long time.

One hit!
He had nothing to say.

Think about it from another perspective. The general algorithm is the result of your own research. Would you still consider researching an issue that might cause other people to lose their jobs?
Totally impossible!
After digesting the information about the completed research, the three people excitedly asked various questions, "How on earth did you accomplish this?"

"This research is so difficult, but it feels like you didn't use it for very long."

“You started thinking about it after you started the project, right?”

"Only a dozen days?"

Zhang Shuo scratched the back of his head and pursed his lips, "I just think about it occasionally."

"I've been thinking about it a lot these past few days, and then I figured it out."

Sun Xingli and Gao Xiaohong stared at Zhang Shuo, while Luo Yongjun scratched his scalp with his hands.

Think about it occasionally?
What have you been thinking about more these days?

Then, solved?

The room fell silent for a moment, and the three people had complicated expressions.

Luo Yongjun shook his head and said, "Let's continue talking about the paper."

The so-called "using the same method to study the general algorithms of various partial differential equations and publish more papers in the four major journals" is just a fantasy. In fact, it is impossible to do.

Generally, only one paper of the same type will be accepted. Of course, you can submit general algorithms for different partial differential equations to different academic journals, but the impact after publication is not good, and it is obvious that the number of papers is increased.

Doing so would have no practical significance and would also have a negative impact on the authors of the paper.

“It is not very meaningful to repeat the research using the same method,” Sun Xingli concluded, “but the content can be split.”

He said seriously, "In mathematics, the method is more important than the result."

"Your results are very valuable for application, but the value of the method is higher. You can submit two manuscripts, one for the method and one for the application results. In this way, the possibility of both being accepted is very high."

Sun Xingli hit the nail on the head.

In the field of mathematics, methods are more important than results. Using the same method to solve multiple similar problems becomes a small research.

Once the paper is actually published, others will use the methods in the paper to study general solutions to other types of partial differential equations.

That is only an achievement in computer algorithms, not a mathematical achievement, because there is no urgent mathematical research, and there is not even any breakthrough in algorithms.

……

Zhang Shuo accepted Sun Xingli's suggestion.

After returning to the dormitory, the first thing he did was to open the system interface and create a task.
【Task 1】

[Project name: General solution of second-order parabolic partial differential equations (Difficulty rating: D). ]

【Progress: 0.011%.】

"Using the same research method, even the system does not recognize it..."

Zhang Shuo chose to give up.

The D-level task settlement only rewards two scientific research coins, probably just because of the innovative research, otherwise the difficulty coefficient may be reduced to E.

He thought about it carefully and decided to split the research into two parts: one is the method, and the other is the application of the method, that is, the results.

The methodological paper in the first part mainly consists of three parts, including the substitution transformation method, parameter analysis simulating human brain thinking, and proving the substitution of numerical asymptotic solutions based on the above methods.

The substitution transformation method is the knowledge in memory, which can transform the system of equations containing partial differential equations.

If the system of equations is transformed, it will be much simpler and the analysis will be clearer.

Transforming the equations makes things more complicated, but computer calculations can simplify them.

It's like the difference between addition and division.

In the human brain's understanding, the representation of division is easy to understand, but for a computer, the division operation will be much more complicated, and addition is also simple with a few more steps.

Simulating human brain thinking to perform parameter analysis is an algorithm based on mathematical thinking.

Based on the substitution transformation method and parameter analysis, analyzing and calculating the numerical values ​​and proving the approximate solution interval is a purely mathematical type of research.

The second part is the application of methods, which is the result of the general algorithm.

The titles of the two papers are "Transformation Method of Second-Order PDE and Proof of Asymptotic Solution by Parameter Analysis" and "General Algorithm for Second-Order Elliptic PDE Equations".

……

In the next few days, Zhang Shuo continued to be bombarded with messages of concern from Luo Yongjun, Sun Xingli and Gao Xiaohong.

He receives several messages every day, "How is the paper going?"

"What? Going to class? How can going to class be as important as writing a paper?"

"Hurry up and finish writing. I calculated the time and I can submit it in time for the next issue. Otherwise, I may have to wait another two months!"

"Pay attention to the format. I found you an official website link with submission instructions."

"Do you want me to help you find someone to guide you? Professor Qi Zhixiang from the High School has submitted a paper to New Advances in Mathematics. He has experience!"

"..."

With so much concern and urging, Zhang Shuo had no choice but to patiently finish writing the paper.

It is relatively easy to write a mathematical paper. As long as you have the core content, you can make some annotations in English, study the requirements of the journal you are submitting to, and modify the format, image type, and text description.

That's pretty much it.

After writing two papers, he checked the submission requirements on the official website of Advances in Mathematics and suddenly thought of a question, "Will there be research subsidies if I submit to the four major journals?"

He is a doctoral student at Soochow University, not a faculty member. The research he conducts is not a project and does not involve funding, management and other issues.

So, it seems that there is no subsidy for papers?
(End of this chapter)