Office of the Institute for Advanced Study in Princeton.

Lu Zhou, sitting at his desk, was meticulously staring at the three-dimensional graphics on the computer screen, the ballpoint pen in his right hand was sketching on the paper from time to time, and his left hand resting on the keyboard kept pressing the zoom key.

The data recorded by the scanner has been saved by him in Xiao Ai's server, and what is saved in his notebook is only the part he needs to use.

i.e., with regard to the carbon nanospheres underneath the modified PDMS material.

The molecular structure of that carbon nanosphere is ready-made, but everything else is unknown to Lu Zhou.

Whether it is mechanics, electricity and other physical properties, or the method of preparing this carbon nanosphere in the laboratory, these things need to be explored by himself.

Sequentially speaking, through the establishment of a mathematical model, the mechanical, electrical and other physical properties of the material were analyzed, and then the possible materials used in the synthesis of the carbon nanospheres were reversed, and a correct method was explored through a large number of experiments.

However, Lu Zhou had no clue about how to prepare it.

It's like two large prime numbers multiplied together, multiplication is very simple, as long as you are bored enough, you can buy a calculator in the supermarket. But on the other hand, the product of two large prime numbers is disassembled into two prime factors, and if the number of digits exceeds one hundred, even supercomputing may not be able to do it.

Stopping the pen in his hand, Lu Zhou took a deep breath.

At first glance, this carbon nanosphere appears to be similar to C60, C50, and C240 cage-like clusters of carbon atoms with hollow spherical structures, but if you look closely, they are fundamentally different from these fullerene materials.

First of all, it is not a "regular sphere".

Some people may say that fullerenes are also irregular, and rings of pentagonal and heptagonal carbon atoms will also appear in a group of six-membered rings.

However, the difference of this carbon nanosphere is reflected in the symmetry of the molecular point group, because there is no translational symmetry, it cannot even be represented by the Bravi lattice in the traditional sense.

The ball is like two or more carbon nanomaterials that have been disassembled to reconstruct new chemical bonds between different materials.

For example, two yarn balls are disassembled and kneaded together.

If that were the case, he would face a possibility that would be more uncertain than chaotic systems in quantum mechanics, and perhaps only Schrödinger's cat would be able to solve the problem.

And that's just a matter of geometry.

If he goes back to chemistry, he faces even more problems.

With a sigh, Lu Zhou patted his forehead to calm himself down.

Problems still have to be solved one by one.

Start with math, which he is best at.

Although geometry is not his specialty, he has a knowledge of it.

In the abstract, this is a topological problem, and he needs to disassemble this "cage-like sphere" that does not have translational symmetry.

Standing up, Lu Zhou walked to the whiteboard in the office, thought for a while, and drew a composite structure cage-like sphere composed of points and lines, and marked the known parameters next to each point, and established a simple mathematical model.

[Set A∈X; f,g∈C(X,Y), if there is homotopy from f to g, such that when a∈A,H(a,t)=f(a)......]

【……】

The more you write the equation, the more you write.

Finally stopped writing, Lu Zhou took two steps back, looked at the equation that filled half of the whiteboard, and fell into deep thought.

There were many scenarios he could consider, but it always felt like every possibility was a little bit worse.

Just then, footsteps could be heard outside the office.

Pushing open the door and holding a stack of A4 papers, Vera walked in.

Seeing that Lu Zhou was staring at the whiteboard and thinking, she hesitated, and finally decided not to disturb his train of thought, walked to the desk lightly, put the documents on his desk, and then went to the coffee machine next to him and helped him make a cup of coffee.

Smelling the aroma of coffee, Lu Zhou realized that there was another person in the office.

Looking back at Vera, he asked casually.

"What's the matter?"

"The academic department asked me to send you this freshman interview list." Vera pointed to the list on the table and added in a low voice, "I didn't knock on the door for fear of disturbing you." ”

"It's okay, my train of thought isn't so easy to interrupt, just don't suddenly tap me on the shoulder from behind." Lu Zhou said in a joking tone.

Knowing that she hadn't disturbed his thoughts, Vera's face spread a reassuring smile.

Curiously glancing at the equations and graphs on the whiteboard, she continued.

"What is this?"

"Nothing, idle and boring questions."

Lu Zhou, who returned to his desk, turned off the software opened on the computer, picked up the list and flipped through it roughly.

The quality of this batch of freshmen is not bad, but the paper results are not of reference value, and he will take time to select a few people for interviews.

The only thing that surprised Lu Zhou was that it was not only undergraduate mathematics majors that applied for his master's degree, but also non-mathematics majors.

For example, a junior student of a certain Jin University, majoring in applied chemistry in the undergraduate science, reported the Fourier inverse evolution problem in his functional analysis direction.

Although it is not uncommon for master's students to apply for cross-majors, it is generally rare to jump from mathematics to chemistry, and from chemistry to mathematics.

Just as Lu Zhou was flipping through these resumes, Vera, who had been staring at the whiteboard for a long time, suddenly frowned slightly

"It's a strange three-dimensional structure."

Eyebrows raised slightly, Lu Zhou's eyes moved away from his resume and looked at her: "Tell me your opinion." ”

Vera: "Can I use a pen?" ”

Lu Zhou said happily: "Of course." ”

With permission, Vera picked up her marker and walked over to the whiteboard.

After thinking for a moment, she drew a few strokes on the cage-like sphere of dots and lines, marking the pentagons and heptagons in it, and then drew an irregular curve to divide the figure.

Then, a magical scene happened.

After pulling, dismantling and reorganizing changes in three-dimensional space, the cage-like structure sphere without translational symmetry is disassembled into a circular tubular structure and a translational symmetrical sphere!

Looking at the geometric figures on the whiteboard, Lu Zhou was slightly stunned, but his eyes were getting brighter and brighter.

He had considered countless possibilities, including the combination of spheres and surfaces, and the combination of multiple spheres of different sizes, but he ignored this situation.

But the transformation seems to have come to an abrupt halt at this point.

Vera frowned, as if confused as to how to proceed with the transformation.

But for Lu Zhou, this idea alone is enough.

"You're a genius......"

Vera was slightly stunned, looked at Lu Zhou, and then at the equations and topological transformations on the whiteboard, and smiled a little shyly.

"It would be nice if I could help......"

In fact, she just found the figure interesting, although it looked like a regular sphere, but the geometric asymmetry made it full of contradictions.

Because of this sense of dissonance, Vera tried to transform the graph topologically, and finally found that the figure turned out to be a combination of a translationally symmetrical sphere and a cylinder.

In elementary geometry, this is an unimaginable proposition.

But in topography, this is a very interesting phenomenon.

She didn't make the transition, though.

But even then, it's enough!

"It's more than help! It simply helped a lot. Thinking like a spring of water, Lu Zhou did not hesitate to praise, took out his mobile phone and took a photo of the whiteboard, and then put away his laptop, "I will retreat for a few days, and I will entrust you with the duty in the office these days." ”

Walking to the door of the office, Lu Zhou suddenly thought of something, looked back at the little girl, and then instructed, "By the way, if someone comes to me, you can directly tell him my address and let him go there to find me." ”

Genius one second to remember the address of this site:. Mobile version reading URL: m.