I was a top student in America.

Chapter 104 Physics Seminar (Please Subscribe)

Li Ao sat in the front row of the tiered conference room, his gaze sweeping over his surroundings, feeling somewhat surprised.

"As expected of a top-tier university."

The academic atmosphere at the University of Chicago is completely different from that awful place like Wyndham High School.

In addition, Professor Rudy's seminar today, which only happens once a semester, focuses on highly practical numerical calculation methods in science and engineering research, and incorporates examples from his own projects. No wonder it attracted so many people.

Besides doctoral students and postdoctoral fellows, you could even see a few young professors in the conference room.

For a high school student like him to come here to attend classes is definitely an exception.

Fortunately, the air conditioning at the Gordon Integrated Science Center was very strong; otherwise, it would have been really uncomfortable to have so many people crammed into a conference room in the middle of summer.

While waiting for the seminar to begin, many people around me were already talking in hushed tones.

"Professor Rudy doesn't seem to be holding many public seminars these days. This is the only one this semester, so it's really not easy to catch up."

""

"I heard he's been really busy lately, and he probably won't be opening any more stores in the second half of the year."

"Is it that project they're working on with the U.S. Department of Energy and Argonne National Laboratory? I heard their group has even temporarily stopped hiring postdocs."

"My friend was hoping to apply for a postdoctoral position there, but now that's out of the question."

"Is this about numerical simulation of three-dimensional crystal lattices?"

""

Li Ao listened quietly to the sounds around him, his gaze fixed on the few pages of notes he had prepared in advance, without participating in the discussion.

There were over a hundred people in the main conference room, but he didn't recognize a single one of them.

A few more minutes passed.

Before the clock on the wall reached the hour, a tall, thin middle-aged man with gray hair walked in with a marker.

The previously noisy conference room instantly fell silent.

Professor Rudy has clearly been in a bad mood these past few days.

Although Jason has sent Amber to help, the project is still far from solving the core problems.

Caltech, in particular, is also pushing forward with similar models.

If the University of Chicago cannot provide more stable simulation methods and calculation results as soon as possible, it is very likely that the other party will beat them to it.

Although the hard work of the past year or so will not be completely wasted, the leading position will certainly not be maintained.

What's more troublesome is that he has a doctoral student under him who is counting on this project to be completed and graduate smoothly.

Standing on the podium, Professor Ludi did not start by telling a research joke to liven things up as he usually does, but instead went straight to the point.

"Today we will mainly discuss several sources of error caused by finite difference discretization, and their application in the energy stability estimation of two-dimensional lattice vibration models."

"Finally, we'll leave some time for questions and discussion."

After a brief opening, Professor Rudy turned around and wrote the model equations on the whiteboard, quickly drawing everyone's attention.

Li Ao had already familiarized himself with the relevant content last night. Now, as he listened to Professor Lu Di talk about continuous models and discrete operators, new ideas kept popping into his mind thanks to the help of "learning by analogy" and "model analysis".

After listening to the rest, he finally understood why Professor Rudy's numerical computing workshops were so popular.

It's definitely all dry goods.

Even if you just listen without typing any code yourself, the prompt will reappear on the panel.

[Under intense study conditions — Intelligence +0.1]

【Intelligence: 121.1】

"This seminar was worthwhile."

Seeing his intelligence attribute increase, Li Ao knew that he had made the right trip today.

Numerical Analysis is a large book suitable for building a foundation, and it is certainly suitable for beginners.

But what he needs now is not just to understand algorithms and examples, but to be able to apply them.

In real-world research scenarios, the reasons for choosing a particular algorithm, where errors might occur, and how boundary conditions affect the results are often more valuable than the standard derivations in textbooks.

In particular, the content of this seminar happens to connect with his previous paper on discrete averaging of convex functions.

"That concludes the lecture. If anyone has any questions, please feel free to ask, and we can discuss them together."

Professor Rudy stopped lecturing, leaned against the podium, picked up a paper cup, and took a sip of coffee to moisten his throat.

As soon as he finished speaking, several doctoral students stood up and asked questions.

Most of the people sitting in this conference room are physics or applied mathematics students, so they are naturally not embarrassed to discuss academic issues.

After all, in the process of scientific research, everyone may encounter bottlenecks in numerical calculation and simulation analysis.

Li Ao, of course, did not intend to remain silent.

He specially rode his bicycle for several miles to get here, so naturally he wanted to make the most of this trip.

Combining his own code testing from last night with what he had just heard, he organized his thoughts and immediately raised his hand and stood up.

"Hello, Professor Rudy."

"When you analyzed the discrete energy drift under non-uniform grids, you mainly attributed the error to the boundary truncation. However, I did a test last night using a simplified two-dimensional lattice model and found that if the spectral radius of the discrete iteration matrix is ​​close to one, the high-frequency modes will be repeatedly amplified near the boundary."

"So I'd like to ask if it's possible to combine the Rayleigh quotient estimate with the boundary weight term to add an adaptive correction to the lower bound of the energy?"

Professor Ludi had been speaking for over an hour and had answered several questions. He looked slightly tired, but his eyes lit up noticeably when he heard Li Ao's words.

"What are the Rayleigh quotient and boundary weight terms for a two-dimensional crystal lattice?"

Just as he was about to ask more questions, a quiet commotion suddenly arose from the audience.

It turned out that someone had recognized Li Ao.

"Isn't he that high school student in Professor Jensen's research group?"

"I heard he was the only one to get a perfect score at this year's IMO, how did he end up in the physics department?"

"Could he be thinking of switching to physics or computer science?"

"Is it too much to expect high school students to attend a seminar on numerical computing?"

"Wait, he just said he did a two-dimensional lattice test last night?"

Li Ao had recently appeared in a local Chicago newspaper, and David had often boasted to his colleagues about the young prodigy in his group, so quite a few people at the school had heard of him.

He had been sitting there quietly listening to the lecture, so naturally no one paid him any special attention.

Now, when he stood up to ask a question, his words immediately attracted everyone's attention.

Hearing the surrounding discussions, Li Ao didn't react much.

Anyway, the seminar didn't stipulate that people from the mathematics department couldn't attend.

However, Professor Rudy on the podium frowned slightly, feeling somewhat disappointed.

Although he had never met Li Ao and did not know what the other party looked like, he had read that newsletter in Jason's office.

This name is not unfamiliar.

He admitted that the child had a great talent for mathematics.

It is truly illogical to say that a high school student has mastered numerical analysis and condensed matter physics to this extent, and can even explain Rayleigh quotients and boundary weight terms in a two-dimensional lattice in such detail.

After all, a person's energy is limited.

It's already outrageous enough that a high school student can get a perfect score on the IMO and write two math papers.

Any one of these things will take a lot of time.

Furthermore, numerical simulation is not just about proving a few theorems; to actually run it, you have to deal with code, data, and boundary conditions repeatedly.

It's like making an NBA player play soccer.

No matter how talented someone is, it's impossible for them to reach a professional level right from the start.

These thoughts flashed through Professor Rudy's mind, and he quickly guessed one possibility.

"Could it be that he heard from Jason that he wasn't selected to help in our group, so he deliberately memorized a few technical terms and came over to ask questions, hoping to get my attention?"

Thinking of this, his tone became slightly more serious.

"You did indeed perform simulation calculations for a two-dimensional lattice model?"

'