Scholar’s Advanced Technological System

Chapter 284: Spherical Problems

The office of the Princeton Institute for Advanced Study.

Lu Zhou sat in his office desk and meticulously stared at the three-dimensional graphics image on his computer screen. His right hand would write on the draft paper from time to time while his left hand was tapping on the keyboard.

The data collected by the scanner gun was in Xiao Ai’s server. He stored what he needed on his laptop.

Which was the carbon nanospheres under the PDMS material.

The molecular structure of the carbon nanospheres was available, but everything else was unknown.

Whether it was the mechanical or electric properties or the method of creating carbon nanospheres, Lu Zhou had to find these things out himself.

He first had to establish a mathematical model and analyze the physical properties of the model. Only then, could he inversely synthesize the carbon nanospheres material. After that, through a large number of experiments, he could find a way of producing carbon nanospheres.

However, Lu Zhou had no idea where to start.

This was like two large prime numbers, multiplying them was simple, any calculator could do it. However, finding two products of the multiplication of the two numbers, was almost impossible.

Lu Zhou stopped writing and took a deep breath.

At first glance, the carbon nanospheres were similar to C60, C50, and C240. They all had a hollow spherical structure. However, upon further inspection, there was something fundamentally different about the carbon nanospheres compared to fullerenes.

First of all, it was not strictly a “sphere”.

Some people may argue that neither was fullerenes since a group of six-membered rings also had pentagon and heptagonal carbon atom rings.

However, the difference in carbon nanospheres was the reflection symmetry. It had no translational symmetry, so it could not even be represented by the traditional Bravais lattice.

This small ball was like two carbon nanomaterials that have been reassembled to create a new chemical bond.

The image of the ball was like two wool balls taken apart and re-twisted together.

If this was really the case, Lu Zhou could be facing a quantum mechanics problem involving chaotic system. Perhaps only Schrodinger’s cat could solve this problem.

This was only the geometric issue.

He had a lot more problems in terms of chemistry.

Lu Zhou sighed and patted his forehead as he tried to calm himself down.

The problems had to be solved one by one.

He should start with his best area, mathematics.

Although geometry was not an area he was good at, he still knew a little about it.

Abstractly, this was a topology problem. He needed to disassemble this asymmetrical “cage structure sphere”.

Lu Zhou stood up and walked to his office whiteboard. He thought for a while before he drew a composite structure cage ball composed of points and lines. He then marked down the known parameters next to each point and created a simple mathematical 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)…]

[…]

More and more formulas were being written.

Lu Zhou finally stopped writing and took a step back. He looked at the whiteboard filled with equations and started to think deeply.

He thought about many possibilities, but he always felt like all of the possibilities were missing something.

Suddenly, footsteps sound came from outside his office.

Vera pushed open the door while holding a stack of A4 papers.

When she saw Lu Zhou staring at the whiteboard, she hesitated. She decided not to disturb his thoughts, so she placed the documents on his desk and went to make a cup of coffee for him.

When Lu Zhou smelled the coffee, that was when he finally realized that someone was in his office.

He looked at Vera and asked casually, “Is there a problem?”

“The education office asked me to give you this list of interviewees,” said Vera as she pointed at the documents on the table. She then added, “I was afraid to disturb you so I didn’t knock.”

“It’s fine, my thought process isn’t that easily disturbed. Just don’t suddenly touch me from behind,” said Lu Zhou in a joking manner.

Vera smiled when she realized that she did not disturb Lu Zhou’s thinking.

She took a curious look at the shapes and equations on the whiteboard and asked, “What is this?”

“Nothing, some random question.”

Lu Zhou returned to his desk and turned on his computer. He then picked up the interview list and glanced at it.

This cohort of students was not bad, but just academic grades were not enough. He would have to spend time interviewing them.

The only thing that surprised Lu Zhou was that there were non-mathematics students applying to him.

Like an applied chemistry major from the University of Jin Ling, who wanted to research Fourier inversion transformation problems.

Even though it was not unusual for someone to jump disciplines, most people jumped from mathematics to chemistry, instead of the other way around.

While Lu Zhou was flipping through these resumes, Vera, who was staring at the whiteboard, frowned and said, “This 3D structure is very strange.”

Lu Zhou looked up from the resumes and asked, “What do you think about it?”

Vera, “Can I use a pen?”

Lu Zhou said with pleasure, “Of course.”

Vera picked up a marker and walked to the whiteboard.

She drew a few lines on the caged sphere and marked the pentagons and heptagons. She then drew an irregular curve to divide the figures.

Then, a miracle happened.

After a three-dimensional disassembly and recombination, the asymmetrical cage structure sphere was disassembled into a circular tubular structure and a symmetrical sphere!

Lu Zhou looked at the 3D drawings on the whiteboard and was stunned. His eyes began to light up.

He had considered a myriad of possibilities, the combination of spheres and surfaces, sphere of different sizes, but he had not thought of this combination.

However, the disassembly came to an end.

Vera was confused. She did not know how to continue the transformation.

However, for Lu Zhou, this train of thought was enough.

“You’re an absolute genius…”

Vera was stunned as she looked at Lu Zhou. She then looked at the whiteboard filled with topology drawings. A smile emerged on her face.

“I’m glad to help…”

She only thought that this shape was very interesting. Although it looked like a regular sphere, it was asymmetrical, which made it full of mystery.

Due to this mystery, Vera tried to make a topological transformation of the structure and finally found out that the structure was a combination of a symmetrical sphere and a cylinder.

This was an unimaginably difficult elementary geometry problem.

However, this was only an interesting topology phenomenon.

Even though she did not complete the transformation, she had already done enough!

“Of course you helped! You helped a lot!”

Ideas were flowing from Lu Zhou’s brain. He took a photo of the whiteboard and closed his laptop before he said to Vera, “I’ll have to go away for a few days, so take care of the office for me.”

Lu Zhou walked to this office door and suddenly remembered something. He then looked back at the girl and said, “Oh yeah, if anyone comes to find me, just give them my address and tell them to find me there.”