Scholar’s Advanced Technological System

Princeton Institute of Advanced Studies.

Sitting in front of the desk, the ark is staring meticulously at the three-dimensional graphics in the computer screen, the right-hand ballpoint pen is drafted on paper from time to time, and the left hand resting on the keyboard is constantly pressing the zoom key.

The scanner captured data that he had saved on Em's server, and on his notebook, just part of what he needed to use.

That is, about carbon nanospheres beneath the modified PDMS material.

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

Whether it's the physical properties of mechanics, electronics, or the way the laboratory makes this carbon nanosphere, it takes him to find out for himself.

Sequentially, by building a mathematical model, analyzing the mechanical, electrical and other physical properties of the material, and then inversely synthesizing the material that the carbon nanosphere may use, a large number of experiments have been carried out to figure out the correct method.

But the ark has no idea how to prepare it.

It's like two multiplied primes, and the multiplication is simple, so long as you're bored enough, you can buy a calculator in the supermarket. But in turn, the product of the two primes is broken down into two prime factors, and if the number of digits exceeds a hundred, it is not necessarily even possible to do the calculation.

The pen stopped in his hand and the ark took a deep breath.

At first glance, this carbon nanosphere appears to be similar to these caged carbon atom clusters with hollow spherical structures, C60, C50, C240, but if you look closely, there is a real difference between this thing and these fullerene materials.

First of all, it's not a "sphere of rules."

It may be argued that fullerenes are also irregular, and pentagonal and heptagonal carbon atomic rings appear in a group of six-membered rings.

However, this carbon nanosphere, whose differences are reflected in the symmetry of the space population, cannot even be represented by the Bravi dot array in the traditional sense because there is no translational symmetry.

This sphere appears to be made of two or more carbon nanomaterials that have been dismantled and reconstructed between different materials.

One image of the particles is that the two wool clumps are removed and rubbed together again.

If that were the case, he would face more uncertainty than the chaotic system in quantum mechanics, and perhaps only Schrödinger's cat could solve the problem.

It's just a matter of geometry.

If he returns to chemistry, he faces more problems.

Sighing, the ark patted itself on the forehead and calmed itself down.

Problems still have to be solved one by one.

Let's start with his best math.

Though geometry is not his area of expertise, he has some knowledge of the field.

In the abstract, this is a topological problem, and he needs to dismantle this “cage-shaped structural sphere” that has no translational symmetry.

Standing up, the ark went to the whiteboard of the office, and after a moment of reflection, a composite structural cage-shaped sphere composed of dots and lines was drawn on it, with known parameters labeled next to each dot, while creating simple mathematical models.

Set A ● X; f, g ● C (X, Y), if there are f to g congeners, so that when a ● A, H (a, t) = f (a) …

……

The more formulas you write, the more you write.

Finally, the pen stopped, the ark retreated two steps, and the formula was detailed with half a whiteboard, caught in contemplation.

There were many things he could take into account, but he always felt that every possibility was a little worse.

At this point, footsteps were heard outside the office.

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

Seeing the ark staring at the whiteboard, she hesitated and eventually decided not to disturb his thinking, walking lightly to the desk, placing the documents on his desk, then going to the coffee machine next to him and making him a cup of coffee.

Smells like coffee, the ark realizes there's someone else in the office.

Looking back at Vera, he asked casually.

“Can I help you? ”

“Let me give you this freshman interview list from the faculty.” Vera pointed to the list on the finger table and added, "I didn't knock on the door for fear of disturbing you. ”

“Nothing, my thoughts are not so easy to interrupt, just don't suddenly slap me in the shoulder from behind.” The ark said in a joke.

Vera's face revealed a comfortable smile after learning that she had not disturbed his thinking.

Looking curiously at the equations and graphics on the whiteboard, she continued.

“What is this? ”

“Nothing, boring questions. ”

Returning to the ark in front of the desk, he switched off the software opened in his computer and picked up the list and roughly flipped it.

This batch of newcomers is of fairly good quality, but the paper scores are not informative and he will take the time to pick a few people to interview.

The only thing that surprised the Ark was that his master's degree was not only related to undergraduate mathematics, but also non-mathematics students.

For example, one of Kim Dae's brothers, an undergraduate science adaptation major, reported on the inverse evolution of Fourier in the direction of his general correspondence analysis.

Although it is not uncommon to apply for a master's degree, it is generally rare to jump from mathematics to chemistry, from chemistry to mathematics.

Just as the ark looked through these resumes, stared at the whiteboard for half a day and suddenly frowned slightly.

“This three-dimensional structure is strange. ”

The eyebrows picked slightly, and the ark's gaze shifted away from her resume, looking at her: "Tell me your point of view. ”

Vera: “May I use a pen? ”

"Of course," said the Ark. ”

After obtaining permission, Vera picked up the marker pen and walked to the whiteboard.

After a moment of reflection, she drew several pieces on the cage-shaped sphere of this dotted line, marking the pentagons and heptagons, and then drew an irregular curve to divide the graph.

And then, a magical scene happened.

After lifting and dismantling in three-dimensional space and restructuring changes, cage-shaped structural spheres without translational symmetry were dismantled into a circular tubular structure and a translational symmetrical sphere!

Looking at the geometry on the white board, the ark was slightly stunned, but the eyes were getting brighter and brighter.

Among the myriad possibilities, he considered combining spheres with faces and combining multiple spheres of varying sizes, but only ignored this situation.

But the transformation came to this point, and it seemed to have stopped.

Vera frowned and seemed confused about how to proceed with the conversion.

But for an ark, this idea alone is enough.

“You are a genius...”

Vera glanced slightly, looked at the ark, looked at the equations on the whiteboard and the topologically transformed graphics, and smiled a little.

“I wish I could help...”

In fact, she just found the graph interesting, and although it looked like a regular sphere, the geometric asymmetry made it feel uncomfortable.

Because of this discord, Vera tried to topographically transform the graph and finally found it to be a combination of a translationally symmetrical sphere and a cylinder.

In primary geometry, this is an unimaginable proposition.

But in topology, it's an interesting phenomenon.

Although she was not able to complete this transformation.

But even so, it's enough!

“More than help! That was a big help.” Thoughts poured out like spring water, and the ark was not stingy with compliments, took a picture of the phone against the whiteboard, and put away the laptop, "I'll shut it down for a few days, and the office duty will be on you for the next few days. ”

When he walked to the door of the office, the ark suddenly thought of something and looked back at the little girl and said, "By the way, if anyone comes to me, you tell him my address and let him go there to find me. ”