Research starts with PhD students

Chapter 3 The first paper has been finalized!

Gao Xiaohong sat for a while and then left.

Luo Yongjun continued his verification work, mainly focusing on difficult differential equations and systems of equations.

Verification means substituting the result into the equation or group of equations to see how big the deviation is.

For difficult equation calculations, as long as the accuracy of the results is within an acceptable range, it can be considered that there is no problem.

Luo Yongjun checked all the difficult ones and found no problems in the end.

He pursed his lips and stared at the results on the table, his expression full of complexity and disbelief. He was very clear about the work content of the two students.

Even if it were him, it would still take a long time to complete. For the more difficult equations, he could only get a rough estimate for now and had no time to do more detailed calculations.

His main research direction is computational mathematics and numerical solution of PDE. Based on this, he completed a general project in the direction of PDE and was successfully promoted to full professor at Soochow University.

Now, are there students who have completed all the calculations in just over an hour?

Is the level of the master's degree from Donggang University so high?
"Or is it that Zhang Shuo is very special..."

“However, a graduate student of this level plagiarized his master's thesis?” Luo Yongjun found it a little funny.

He stood up and walked behind Liu Chengjie pretending nothing had happened. He found that Liu Chengjie had only completed a small part and was very nervous, with sweat even on his forehead.

'That's normal.'

Luo Yongjun felt a little relieved, and patted Liu Chengjie on the shoulder to comfort him, "Don't compare yourself with Zhang Shuo, these calculations are difficult."

"Ah."

Liu Chengjie quickly agreed.

Luo Yongjun glanced at Zhang Shuo again, thought for a moment, turned around and took a few pages from the table, then walked to Zhang Shuo's side and said admiringly, "Zhang Shuo, the result is fine, well done!"

"We still have some tasks to do. Take a look and complete these as well."

Zhang Shuo took it and glanced at it, then nodded and asked, "You don't want it to be completed in the afternoon, right?"

"We have three days, and we have to submit the report by the afternoon of the day after tomorrow at the latest." Luo Yongjun said with a smile, "After submitting the report, you can go around the capital for the next few days."

Zhang Shuo took a few pages and read them carefully.

Luo Yongjun gave him more content than before, and it would be a bit too much to finish it in a hurry.

The high efficiency just now was due to the effect of "Scientific Research Coins", but it was only assisted by the task system, and the speed was at least half as slow.

He looked at the time and started working at a leisurely pace.

……

In the end, Zhang Shuo managed to complete the calculations given by Luo Yongjun before dinner.

This time it took a little longer.

With the help of the 'Task Progress Guide', difficult calculations can be solved faster, but it still cannot catch up with the effect of scientific research coins.

He handed the results to Luo Yongjun and went to the restaurant with Liu Chengjie.

Luo Yongjun continued to stay in the office, staring at the pages on the table in a daze.

He didn't expect Zhang Shuo to be able to complete it.

The subsequent calculations were his own work. A few pages might not seem like much, but there were several difficult calculations that were not something an ordinary doctoral student could solve.

He just wanted to test Zhang Shuo's level.

If there is anything that Zhang Shuo cannot solve, just go and ask him. By then, you will have a rough idea of ​​the problem.

“You’ve finished it?”

Luo Yongjun was not in the mood to eat and just wanted to quickly check the result.

By the time the verification was completed, half an hour had passed, and the problem was still not found.

He went to the restaurant with mixed feelings and happened to meet Gao Xiaohong who had just arrived.

He picked up his plate and sat opposite Gao Xiaohong, and couldn't help but sigh, "Xiaohong, I found that Zhang Shuo's calculation level... is really catching up with me!"

"Maybe it's clever."

Gao Xiaohong thought about it carefully and said, "Some people are born smart, their brains work quickly, and they are very sensitive to numbers and calculations."

"I know that, but..."

Luo Yongjun pursed his lips tightly and said, "The calculation level of the students I just taught is better than mine... ahem, almost catching up with me. I study PDEs, and the main direction of calculation, it seems that there is nothing to teach?"

“Isn’t it a good thing that students have high levels?”

Gao Xiaohong laughed and said, "Teacher Luo, are you showing off? How great it is to have a genius student. Looking at this experiment, your three days of work may be completed tomorrow."

"Yup!"

Luo Yongjun reacted immediately. He slapped his thigh hard, his eyes lit up, "You really reminded me!"

He scooped a few bites of the food into his mouth, swallowed it whole, and quickly walked back to the office.

Zhang Shuo and Liu Chengjie are already here.

Luo Yongjun walked in and shouted at the two of them, "Work overtime!"

"We'll try to finish it today and hand in the report tomorrow morning!" He added, "Then we can spend one more day in the capital."

In fact, playing one more day is not important.

The important thing is to let others see that his team can complete the work quickly and with high quality.

The scale of the experiments at the Institute of High Energy Physics is not large, but there are also hundreds of people involved in the experimental data and analysis work.

Four professors and eleven doctoral students from Soochow University, together with researchers from Tongzhi University, Capital University of Science and Technology, and six researchers from the Institute of High Energy Physics, formed the Area B data group. Within the Area B data group, universities and professors are in a cooperative relationship, but there is also competition among them, and everyone hopes that their group will perform better than other groups.

Luo Yongjun only supervised two doctoral students, but because their majors were related, the workload they were assigned was no less than that of other professors.

He took his time at the beginning and just managed to finish it in three days.

If you can finish it quickly, doesn't that show your level?
……

If you want to submit the report tomorrow morning, you must maximize your efficiency.

Luo Yongjun rearranged his work.

Liu Chengjie had the worst calculation ability, so he asked Liu Chengjie to be responsible for analyzing and entering the results.

He and Zhang Shuo were responsible for the calculations.

In this way, efficiency has been significantly improved.

The three of them worked together until 11 o'clock in the evening and completed the calculation, analysis and entry of all the data.

Luo Yongjun was worried that the calculations might be wrong, so he repeated the calculations for all the results.

When checking the approximate solution interval of a partial differential equation system, he suddenly frowned and said, "Isn't this value too narrow?"

"The deviation range of gamma should be larger."

He simply did some research on his own and found that the calculated values ​​were much wider than the range of results given by Zhang Shuo.

The approximate solution interval obtained by numerical method will be inaccurate if the range is large, but may "miss the solution" if the range is small.

Missing a solution is an error.

Luo Yongjun was actually a little happy. He called Zhang Shuo over, pointed at the corresponding equations, and asked, "Look at this equation. Is the result you gave too narrow?"

"Have it?"

Zhang Shuo lowered his head and looked carefully.

Luo Yongjun pointed to the computer screen and said, "Look at this. Using the program to assist in calculations, we found that even if γ (gamma) takes a larger value outside the region, it is still within the solvable threshold range."

Zhang Shuo stared at the equations and analysis on the screen, then looked carefully at Luo Yongjun's results, pursed his lips and thought, "Teacher Luo, did you directly substitute the proposed values ​​and then use the program to verify your conclusion?"

"What is the problem?"

Luo Yongjun said, "For systems of equations with partial differential equations, numerical methods combined with computer verification are the fastest and most accurate."

“But there could be mistakes.”

Zhang Shuo reminded.

Luo Yongjun didn't take it seriously at all. Instead, he laughed and said, "Zhang Shuo, you still don't have enough experience in solving PDE systems."

He pointed to the original equation on the paper and said, "This type of PDE system generally cannot be transformed to solve it."

"If you study it carefully, of course, it is possible to make certain changes, but it is too complicated."

Zhang Shuo looked down at the original set of equations and asked in confusion, "But this set only has one partial differential equation, and the other three are orbital equations and numerical equations."

"There is only one, and it is very difficult!" Luo Yongjun shook his head and said, "I'm not talking about the difficulty of the transformation, but your result is wrong."

"That's because you didn't make any changes."

Zhang Shuo's voice was very confident. He took a blank piece of manuscript paper, copied the original equation, and began to write. Lines of symbols quickly appeared on the paper.

After filling up a piece of manuscript paper, he took out a new one and quickly filled it up as well.

Luo Yongjun sat next to him without saying a word, just looking at the contents on the manuscript paper, following the train of thought to try to understand it, and also trying to find the problems.

In his opinion, there must be something wrong.

Generally speaking, it is difficult to transform such a complex set of equations.

Zhang Shuo completed the last part and gave a brand new set of equations. He explained, "This is the changed set of equations. It is easy to solve it numerically. When a single value is substituted, it will not affect other unknowns."

"If no transformation is done and the proposed values ​​are substituted into the original equations, when the calculation is performed again, the results may be wrong due to the influence of the proposed values."

Luo Yongjun pursed his lips tightly.

He took what Zhang Shuo had written and read it carefully from beginning to end. He scratched his scalp with his hand and asked with a frown, "Zhang Shuo, who taught you this transformation method?"

"Forehead……"

Zhang Shuo was stunned for a moment.

The transformation method he used was seen in a mathematics paper and was used several times when doing calculations.

When I saw a similar system of equations, I naturally thought of this method.

He realized that something was wrong, and asked tentatively in a low voice, "Teacher Luo, isn't there a way to do this?"

Luo Yongjun immediately shook his head and said, "I've never heard of it." Then he suddenly realized what was going on and asked with wide eyes, "Did you research it yourself?"

"Uh, yes."

Zhang Shuo nodded reluctantly.

“That’s really amazing!”

Luo Yongjun slapped the table excitedly, "The analysis of PDE equations has always been one of the most difficult problems in mathematics."

"Your method is applicable to a system of equations with one PDE, and can also be expanded to two. The transformation will just become more complicated. But even if it only applies to one, it will have high application value!"

“This is a very good result!”

"Your first paper has been found. Based on my experience, it should be no problem to submit it to zone three!"

(End of this chapter)