From top student in college to scientific research powerhouse

Chapter 4 You've ruled out the only correct answer!

Zhang Minghao was fairly satisfied with the single room he rented.

It's cheap, clean, and comfortable, close to the school, and the two female roommates seem easy to get along with.

He didn't move in immediately; he had to wait for his classmate to send all his luggage, including clothes, bedding, and other miscellaneous items, before he could move in.

Having a place to stay has made me feel more at ease.

The next morning, I took a walk around the university to familiarize myself with the environment.

Jiangzhou University is really too big.

It's no exaggeration to say that a university is essentially a university town.

From the Faculty of Science on the west side to the large stadium on the east side, and then turning a corner to the main gate on the south side, after walking around for a while, my legs felt numb, but the completely unfamiliar environment also brought a sense of novelty.

After having lunch in the cafeteria, I found a study room to start studying in the afternoon.

Pursuing a doctorate mainly involves doing research under the guidance of a supervisor.

The metamaterials project, which applies electromagnetic physics experiments, is at the forefront of electromagnetic materials technology. Its mathematical and physical foundations are very complex, and the materials research involves other disciplines.

Xue Kun didn't provide much material, but the theoretical parts were very complex. Foreign research papers were even more difficult to understand, as many involved purely theoretical issues.

Zhang Minghao patiently studied it for a long time. He was interested in the mathematical content it contained, which was also the part that Xue Kun emphasized.

He is good at mathematics.

Or, to put it another way, among physics doctoral students, his mathematical level is relatively high.

The project's theme is 'Theoretical Design and Property Research of Metamaterials,' which is a basic research project on metamaterials. Basic research is often accompanied by a large amount of mathematical, analytical, and related physical content.

Among the materials at hand, there was a large amount of content related to electromagnetic experimental calculations, mathematical analysis, and mathematical physics, so the first point of attack I found was mathematics.

Mathematics involves complex calculations and analysis.

The most commonly used one is a third-order nonlinear partial differential equation similar to the Kawahara equation, which can be called a 'third-order Kawahara-like equation'.

Solving the 'third-order Kawahara equation' is essential for calculating routine experimental data in the project.

The combination of third-order, Kawahara-like equations, and nonlinearity ensures that the equations cannot be solved exactly.

In experimental data analysis, the conventional approach is to substitute numerical values ​​to solve the problem, but the results are always 'rough approximate solutions'.

"There are problems with the calculation of the preliminary experimental data."

"Professor Chen's group couldn't possibly make such a basic mistake in their calculations; the most likely explanation is that there was a deviation in the solution to the complex equations..."

"This equation is very important!"

Upon closer examination, Zhang Minghao discovered that most partial differential equations do not have exact solutions, let alone the 'third-order nonlinear Kawahara-like equations'.

Obtaining a rough approximate solution by substituting numerical values ​​into a 'prediction' is the most common practice in various scientific research and industrial applications.

Studying this type of equation is extremely difficult.

He wasn't looking for an exact solution, but rather a method to find a 'more approximate solution'.

However, it is still very difficult.

If we were to conduct a conventional study, it would be impossible to obtain results in a short period of time.

"Could we do something with 'correct perception'?" Zhang Minghao thought and started trying.

When dealing with analytical problems involving complex equations, it is necessary to study analytical methods.

'Correct perception' can determine the correctness of the analytical direction.

After some experimentation, he discovered that 'correct perception' could help him determine the direction of analysis and some thought processes.

When the direction of thinking is correct, it means that continuing to study in that direction can solve the problem.

Other problems also arose.

Being able to judge the correctness of the direction of thinking does not mean that you can solve the problem.

Solving a complex equation involves transforming the equation. Thinking in the right direction doesn't guarantee you'll figure it out, because there are many subsequent steps that require further thought.

Step by step...

Not every step can lead to the right approach.

The research quickly stalled at a change in position because it involved an extremely large amount of computation and could not be directly simulated by a computer.

"There must be other ways, or some special method."

"Perhaps I didn't think of it, or perhaps I simply didn't know..."

He pondered for a moment and then shook his head.

'Correct perception' still has its limitations and cannot help solve all problems.

Of course, its auxiliary effect is still very strong. It can help determine the correctness of the research direction, which is itself a very strong ability in scientific research.

Do you have any other abilities?
Zhang Minghao suddenly realized what was happening and opened the system to examine it carefully.

Panel display——

Thinking: 77.

Body: 59.

Academic reputation: -177.

Wealth: 4980.

On the personal data assessment page, the only change is the 'wealth value'.

It was obvious, because the money had been spent. "Less than five thousand yuan—even among doctoral students, I'm one of the poorest..."

The stipends for physics doctoral students are not low, including various basic subsidies, scholarships, research salaries, supervisor allowances, etc. He received about 60,000 yuan in his first year of doctoral studies.

But things have been different in the past six months.

Xue Kun is gone.

The new supervisor, Deng Hongjun, doesn't have any major projects. He's a temporary student, so he doesn't receive any research grants or salary, and his supervisor stipend is pitifully small.

In six months, I only received basic subsidies and basic scholarships.

The cost of living in Donggang is relatively high. With such meager income, it's already quite good if you don't have any debt, let alone savings.

Body, 59, data normal.

I usually spend my days doing research, often staying up late, and I hardly ever exercise.

Thinking ability, 77. I don't know how it was judged. Could it be related to the amount of knowledge?

Academic reputation...

The score of -177 is clearly related to his paper being posted online. In most people's eyes, he's an academic fraudster, right?
I chuckled to myself and continued watching.

The second part of the system is the capability interface, which contains only one capability—

"Correct Perception"

The introduction to "Correct Perception" is just one sentence: You can judge the correctness of the conclusions you understand.

Below that...

The second part of the ability has a small question mark next to it, which turns out to be 'upgrade requirement'.

Upgrade requirements —

[Mindset: 80; Physical Fitness: 70; Academic Reputation: 1000; Wealth: One Million.]

"Wealth, one million?"

"So, to upgrade, you have to make money at the same time? A million is no small sum. Are you going to buy a lottery ticket and wait to win?"

Take a deep breath and calm down.

Both mind and body can be improved through accumulating knowledge and exercise.

Academic prestige, naturally, comes from publishing papers or doing other things that demonstrate academic achievement.

wealth……

Making money is indeed the most difficult condition.

An average person can't save a million in their lifetime. Even after graduating with a doctorate and starting work, earning a monthly salary of over 20,000, it would still take more than ten years to save a million after deducting living expenses.

Just as I was pondering this, a female voice suddenly came from beside me, tinged with surprise, "You physics department also studies equations?"

Zhang Minghao was startled.

Turning my head, I saw my future roommate, Yu Minxia. I had just met her yesterday, and we weren't familiar with each other today.

He explained, "Third-order nonlinear equations similar to Kawahara are used in experimental calculations, usually by substituting them into numerical simulations."

Are you trying to figure out a solution?

Yu Minxia asked curiously, then explained, "I study this too!"

He took a few pages of documents out of his bag and placed them on the table. “Take a look! The format is different, but it should be about the same after the transformation.”

Zhang Minghao looked at it carefully and confirmed that the data contained partial differential equations of the same type.

For the same type, the solution methods may differ, but they are generally applicable.

Yu Minxia sat down to the side and sighed, "My advisor suggested a few directions, but they might not be right. I still want to use this research to write a paper, but it feels like it's a long way off!"

"What directions are there?" Zhang Minghao asked, continuing the conversation.

Yu Minxia pulled up a stool, sat down closer, and began to explain simply, “One method is transformation, continuous transformation, continuous substitution or direct discretization, until the amount of computation is greatly reduced, and the computer can be used to approximate the value.”

"It's impossible to even think about it; the discreteness and variation involved are too complex."

"Furthermore, conventional difference-based discretization is still complex, and the discretization deviation is too large..."

"Furthermore, using the finite element method involves building a model and performing unlimited decomposition, which I think..."

She pointed out several directions.

After she finished speaking, she looked up and noticed that Zhang Minghao's eyes were looking a little strange.

What do you mean?
Yu Minxia touched her cheek, frowning in confusion, "What's wrong?"

Zhang Minghao pursed his lips and said, "You've ruled out the only correct answer."

"what?"

"The right direction is to use brute force of substitution and direct discretization."

"impossible."

Yu Minxia's tone was flat, even indifferent. She was just having a casual chat with the other party, but she didn't really intend to solve any problems.

It's impossible for a physics department doctoral student about to enroll to offer meaningful advice on analytical problems involving complex equations.

Zhang Minghao couldn't wait to pick up his pen. "Let's try to analyze it."

His eyes lit up as he spoke.

(End of this chapter)