Scholar’s Advanced Technological System

The office of the Princeton Institute of Advanced Studies.

Lu Zhou, sitting at the desk, stared at the three-dimensional graphics on the computer screen meticulously. The right hand ballpoint pen was drafted on paper from time to time, and the left hand resting on the keyboard kept pressing the zoom button.

The data collected by the scanner has been saved by him on the Xiao AI server, and what he needs to use in his notebook is only the part he needs.

That is, regarding the carbon nanospheres under the modified PDMS material.

The molecular structure of the carbon nanosphere is readily available, but everything else is unknown to Lu Zhou.

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

In order to solve the mechanics, electrical and other physical properties of the material by the establishment of the mathematics model, and then the materials that may be used in the carbon nanospheres are synthesized, and a correct method is explored through a large number of experiments.

But on how to prepare, Lu Zhou is a nodded thread.

This is like two large prime numbers. Multiplication is very simple. As long as you are bored, you can do a calculator in the supermarket. But in turn, the product of the two large prime numbers is broken down into two prime factors. If the number of digits exceeds one hundred, even the super-calculation may not be possible.

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

At first glance, this carbon nanosphere seems to be similar to caged carbon clusters with hollow spherical structures such as C60, C50, and C240, but if you look closely, this thing does have fundamental differences with these fullerene materials. .

First of all, it is not a “rule of rules.”

Some people may say that fullerenes are irregular, and a group of six-membered rings also have pentagon and heptagonal carbon atom rings.

However, this carbon nanosphere, its difference is reflected in the symmetry of the space group, because it has no translational symmetry, it can not even be represented by the traditional Bravais lattice.

This ball is like a two- or more-carbon nanomaterial that has been reassembled to recreate a new chemistry bond between different materials.

The image of an image is that the two wool balls are taken apart and then re-twisted together.

If this is the case, the possibilities he faces will be more uncertain than the chaotic system in quantum mechanics. Perhaps only Schrödinger’s cat can solve this problem.

This is just a geometric problem.

If he returns to chemistry, he will face more problems.

Sighed, Lu Zhou patted his forehead and calmed himself down.

The problem still has to be solved one by one.

Start with the mathematics that he is best at.

Although geometry is not an area he is good at, he still has some knowledge of this field.

Abstractly, this is a topological problem, and he needs to disassemble this “cage structure sphere” that does not have translational symmetry.

Standing up, Lu Zhou walked over to the whiteboard in the office. After thinking for a while, he drew a composite cage cage made up of dots and lines, and marked the known parameters next to each point. Create a simple mathematics model.

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

[…]

The more the formula is written.

Finally stopped the pen, Lu Zhou stepped back two steps, looked at the formula filled with half of the whiteboard, and fell into meditation.

There are many situations that he can consider, but he always feels that every possibility is a little worse.

Just then, footsteps came from outside the office.

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

Seeing that Lu Zhou was staring at the whiteboard, she hesitated and finally decided not to disturb his thoughts. She walked to the desk with a light hand, placed the documents on his desk, and went to the coffee next to him. Machine, help him make a cup of coffee.

After smelling the smell of coffee, Lu Zhou realized that there was another person in the office.

Looking back towards Vera, he asked casually.

“Is there a problem?”

“Teaching the other side will let me send you this freshman interview list.” Vera pointed to the list on the table and whispered, “I am afraid that I will disturb you, and I will not knock.”

“Nothing, my thoughts are not so easy to interrupt, as long as you don’t suddenly shoot my shoulders from behind.” Lu Zhou said in a joking tone.

After learning that she did not disturb his thinking, Vera’s face showed a comfortable smile.

Curiously looked at the equations and graphics on the whiteboard, she continued to ask.

“what is this?”

“Nothing, idle and boring.”

Back to the desk, Lu Zhou, turned off the software that was opened in the computer, and picked up the list and roughly turned it over.

The quality of this batch of freshman is not bad, but the paper grade does not have reference value, he will take a time to select a few interviews.

The only thing that surprised Lu Zhou was that his master’s degree was not only related to undergraduate mathematics majors, but also to non-mathematics professional students.

For example, a Junior Brother of National Quemoy University, the undergraduate major in chemical science, reported the Fourier inversion transformation problem in his functional analysis direction.

Although the master’s interdisciplinary application is not a rare thing, it is generally a jump from mathematics to chemistry, and it is rare to jump from chemistry to mathematics.

Just as Lu Zhou flipped through these resumes, she stared at the whiteboard and looked at Vera for a long time, suddenly frowned slightly.

“This three-dimensional structure is very strange.”

The eyebrows picked up slightly, and Lu Zhou’s gaze removed from the resume and looked at her: “Talk about your point of view.”

Vera: “Can I use a pen?”

Lu Zhou said with pleasure: “Of course.”

After getting permission, Vera picked up the marker and walked over to the whiteboard.

After thinking for a moment, she drew a few strokes on the cage sphere formed by this dotted line, marking the pentagon and the heptagon, and then drawing an irregular curve to divide the figure.

Then, a magical scene happened.

After three-dimensional lifting and disassembly and recombination changes, the cage structure sphere without translational symmetry is disassembled into a circular tubular structure and a translationally symmetric sphere!

Looking at the geometry on the whiteboard, Lu Zhou squinted slightly and his eyes were brighter and brighter.

He considered a myriad of possibilities, considering the combination of spheres and faces, and considering the combination of multiple spheres of different sizes, but it was ignored.

However, the change to this step seems to have come to an abrupt end.

Vera frowns, seems to be confused about how to transform this.

But for Lu Zhou, this idea is enough.

“You are a genius…”

Vera squatted slightly, looked at Lu Zhou, and looked at the equations on the whiteboard and the topologically transformed graphs, somewhat laughed.

“If you can help, just fine…”

In fact, she just thought that the graphic was very interesting. Although it looked like a regular sphere, the geometric asymmetry made it full of violating feelings.

Because of this sense of violation, Vera tried to make a topological transformation of the graph, and finally found that the graph turned out to be a combination of a translationally symmetric sphere and a cylinder.

In elementary geometry, this is an unimaginable proposition.

But in the slogan, this is a very interesting phenomenon.

Although she did not complete this transformation.

But even so, it is enough!

“It’s just a help! It’s a big help.” The idea was like a spring, and Lu Zhou did not praise the words. He took out his mobile phone and took a photo of the whiteboard, then put away the laptop. “I will close. In a few days, the office is on duty for you these days.”

When I got to the door of the office, Lu Zhou suddenly thought of something. She looked forward to the little girl and then groaned. “Right, if someone comes to me, you can tell him directly about my address and let him go there to find me.”