Princeton Institute for Advanced Study office.
Lu Zhou was sitting at his desk. He meticulously stared at the 3D graphics on his computer screen. The pen in his right hand would occasionally scribble on a piece of paper, and his left hand would constantly press the zoom button on the keyboard.
The data collected by the scanner gun was stored in Xiao Ai's server. What was stored on his laptop was only what he needed to use.
Which was, the carbon nanosphere under the modified PDMS material.
The molecular structure of the carbon nanosphere was ready-made, but other than that, everything else was unknown to Lu Zhou.
Whether it was the mechanical, electrical, or other physical properties, or the method of preparing the carbon nanosphere in the laboratory, he had to figure it out himself.
In terms of sequence, he had to establish a mathematical model, analyze the mechanical, electrical, and other physical properties of the material, then synthesize the materials that might be used in the carbon nanosphere. Through a lot of experiments, he had to figure out the correct method.
However, as for how to prepare it, Lu Zhou had no idea at all.
It was like multiplying two large prime numbers. Multiplication was easy, as long as you were bored enough, you could buy a calculator from the supermarket. However, if the product of two large prime numbers was decomposed into two prime factors, even a supercomputer might not be able to do it if the number of digits exceeded one hundred.
Lu Zhou put down the pen in his hand and took a deep breath.
At first glance, this carbon nanosphere seemed to be similar to C60, C50, and C240, which had a hollow spherical structure. However, if one looked closely, this thing was actually different from these fullerenes.
First of all, it wasn't a "regular sphere".
Some people might say that fullerenes were irregular as well, and there would be pentagonal and heptagonal carbon rings in a group of six-membered rings.
However, this carbon nanosphere's difference was reflected in the symmetry of the space group. Because it didn't have translation symmetry, it couldn't even be represented by the traditional Bravais lattice.
This sphere was like two or more types of carbon nanomaterials that were disassembled and reconstructed new chemical bonds between the different materials.
For example, take two balls of wool and knead them together.
If that was the case, the possibilities he faced would be more uncertain than the chaotic system in quantum mechanics. Perhaps only Schrödinger's cat could solve this problem.
This was just a problem of geometry.
If he returned to chemistry, he would face even more problems.
With a sigh, Lu Zhou patted his forehead to calm himself down.
The problems had to be solved one by one.
Let's start with his best subject, mathematics.
Although geometry wasn't his forte, he still had some knowledge in this field.
Abstractly, this was a topology problem. He needed to dismantle this "cage-like sphere" that did not have translational symmetry.
Lu Zhou stood up and walked to the whiteboard in his office. After thinking for a bit, he drew a composite cage-like sphere composed of points and lines. He then marked each point with known parameters and built a simple mathematical model.
[Let A ∈ X; f, g ∈ C (X, Y), if there is a homotopy from f to g, such that when a ∈ A, H (a, t) = f (a) …]
[…]
More and more equations were written.
Finally, Lu Zhou stopped writing and took two steps back. He looked at the equations on the whiteboard and began to think.
There were many scenarios that he could consider, but he felt like all of them were missing something.
Suddenly, he heard footsteps coming from outside the office.
Vera pushed open the door and walked in with a stack of A4 papers.
She saw that Lu Zhou was staring at the whiteboard and thinking. She hesitated for a bit and decided not to disturb his train of thought. She quietly walked to his desk and placed the documents on his desk. She then went to the coffee machine and made him a cup of coffee.
When Lu Zhou smelled the aroma of the coffee, he realized that there was someone else in the office.
He looked back at Vera and asked casually.
"What's up?"
"The academic affairs department asked me to give you this list of freshmen interview." Vera pointed at the list on the table and said quietly, "I didn't want to disturb you, so I didn't knock."
"It's fine, my train of thought isn't that easy to interrupt, as long as you don't suddenly pat me on the shoulder," said Lu Zhou in a joking tone.
After knowing that she didn't disturb his train of thought, Vera had a comfortable smile on her face.
She curiously looked at the equations and graphs on the whiteboard and continued to ask.
"What is this?"
"Nothing, I was bored and thought about it."
Lu Zhou went back to his desk and closed the software on his computer. He picked up the list and roughly flipped through it.
The quality of this batch of new students was quite good, but the results on paper did not have any reference value. He would find some time to interview a few people.
The only thing that surprised Lu Zhou was that his master's students were not only mathematics students, but there were also non-mathematics students.
For example, a student from the University of Jin Ling, who was an applied chemistry major, applied for the Fourier inversion transformation problem in the field of functional analysis.
Although it was not uncommon for a master's student to apply for a master's degree, they usually jumped from mathematics to chemistry. It was rare to jump from chemistry to mathematics.
While Lu Zhou was flipping through the resumes, Vera stared at the whiteboard for a while and suddenly frowned.
"This 3D structure is strange."
Lu Zhou raised his eyebrows and looked at her as he said, "Tell me your opinion."
Vera: "Can I use a pen?"
Lu Zhou happily said, "Of course."
After receiving permission, Vera picked up the marker and walked in front of the whiteboard.
She thought for a bit and drew a few strokes on the cage-shaped sphere composed of dots and lines. She marked the pentagon and heptagon and then drew an irregular curve to divide the graph.
Then, a magical scene happened.
After being pulled up, disassembled, and reassembled in the three-dimensional space, the cage-like sphere without translational symmetry was disassembled into a tubular structure and a translational symmetrical sphere!
Lu Zhou looked at the geometric figures on the whiteboard and paused for a second. His eyes became brighter and brighter.
He considered countless possibilities. He considered the combination of spheres and surfaces, and he also considered the combination of multiple spheres of different sizes. However, this was the only situation he ignored.
However, the transformation seemed to have come to an abrupt end.
Vera frowned. She seemed to be confused about how to proceed with this transformation.
However, for Lu Zhou, this idea alone was enough.
"You're a genius …"
Vera paused for a second and looked at Lu Zhou. She then looked at the equations on the whiteboard and the graph after the topology transformation. She then smiled shyly.
"It would be great if I could be of help …"
In fact, she just felt that the figure was very interesting. Although it looked like a regular sphere, the geometric asymmetry made it feel very strange.
Because of this, Vera tried to topologically transform the graph. In the end, she found that the graph turned out to be a combination of a translational symmetric sphere and a cylinder.
In elementary geometry, this was an unimaginable proposition.
However, in topology, this was a very interesting phenomenon.
Even though she couldn't complete the transformation …
Even so, this was enough!
"It's more than just helping! You've helped a lot. " Lu Zhou's thoughts gushed out like a fountain. He took out his phone and took a picture of the whiteboard. He then put away his laptop and said, "I'm going on a retreat for a few days, so I'll leave the office to you."
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