Chapter 285 The Spherical Problem

Office of the Institute for Advanced Study, Princeton.

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

The data collected 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.

Namely, regarding the carbon nanospheres beneath the modified PDMS material.

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

Whether it is mechanical, electrical and other physical properties, or the method of preparing the carbon nanospheres in the laboratory, these things need to be explored by himself.

In terms of sequence, by establishing a mathematical model, analyzing the mechanical, electrical and other physical properties of the material, and then inverting the materials that may be used for the synthesis of the carbon nanospheres, and finding out a correct method through a large number of experiments.

However, Lu Zhou had no idea how to prepare it.

This is like multiplying two large prime numbers together. Multiplication is very simple. As long as you are bored enough, you can buy a calculator in the supermarket to do it. But conversely, if the product of two large prime numbers is decomposed into two prime factors, if the number of digits exceeds one hundred, even supercomputing may not be able to do it.

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

At first glance, this carbon nanosphere seems to be similar to C60, C50, and C240, which are cage-like carbon clusters with hollow spherical structures, but if you look carefully, this stuff is indeed 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 pentagonal and heptagonal carbon atom rings also appear in a group of six-membered rings.

However, the difference of this carbon nanosphere is reflected in the symmetry of the space group. Since there is no translational symmetry, it cannot even be represented by the Bravais lattice in the traditional sense.

This small ball seems to be made of two or more carbon nanomaterials, and new chemical bonds are rebuilt between different materials after disassembly.

To give an image of the particle is to disassemble the two balls of wool and knead them together again.

If that were the case, the possibilities he faced would be far more uncertain than the chaotic systems of quantum mechanics, a problem perhaps only Schrödinger's cat can unravel.

It's just a matter of geometry.

If he returns to chemistry, he faces even more problems.

Sighing, Lu Zhou patted his forehead to calm himself down.

The problems still have to be solved one by one.

Start with math, which he is best at.

Although geometry is not his field of expertise, he still dabbles in the knowledge of this field.

From an abstract point of view, this is a topological problem, and he needs to dismantle this "cage-like structure sphere" that does not have translational symmetry.

Standing up, Lu Zhou walked to the whiteboard in the office. After thinking for a while, he drew a composite cage-shaped sphere made of points and lines on it, and marked the known parameters next to each point. At the same time, Build simple mathematical models.

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

【…】

The more and more calculations are written.

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

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

At this moment, footsteps came from outside the office.

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

Seeing that Lu Zhou was staring at the whiteboard thinking, she hesitated for a while, and finally decided not to disturb his train of thought, walked to the desk lightly, put the document on his desk, and went to the coffee next to him machine and made him 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.

"Is there a problem?"

"The Academic Affairs side asked me to give you this list of freshman interviews." Vera pointed to the list on the table and added in a low voice, "I was afraid of disturbing you, so I didn't knock on the door."

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

After knowing that she didn't disturb his thinking, Vera showed a relieved smile on her face.

Looking at the equations and graphs on the whiteboard curiously, she continued to ask.

"what is this?"

"It's nothing, it's just a matter of idle thinking."

Lu Zhou returned to his desk, closed the open software 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 grades are not of reference value, he will take some time to select a few people for interviews.

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

For example, a junior from Jinda University, majoring in Applied Chemistry, reported his Fourier inversion transformation problem in the direction of functional analysis.

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

While Lu Zhou was flipping through these resumes, Vera, who stared at the whiteboard for a long time, suddenly frowned slightly.

"This three-dimensional structure is very strange."

His eyebrows were raised slightly, Lu Zhou looked away from his resume and looked at her: "Tell me your point of view."

Vera: "Can I use a pen?"

Lu Zhou said happily: "Of course."

After getting permission, Vera took the marker and walked to the whiteboard.

After thinking for a while, she drew a few strokes on the cage-shaped sphere formed by dotted lines, marked the pentagons and heptagons in it, and then drew an irregular curve to divide the figure.

Immediately afterwards, a miraculous scene happened.

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

Looking at the geometric figures on the whiteboard, Lu Zhou froze for a moment, but his eyes became brighter and brighter.

Among the countless possibilities, he considered the combination of spheres and surfaces, and also considered the combination of multiple spheres of different sizes, but he ignored this situation.

However, at this point in the transformation, it seems to have come to an abrupt end.

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

But for Lu Zhou, this idea alone is enough.

"You are simply a genius..."

Vera froze for a moment, looked at Lu Zhou, then at the equations on the whiteboard and the topologically transformed graphics, and smiled shyly.

"If only I could help..."

In fact, she just thinks this figure is very interesting. Although it looks like a regular sphere, the geometric asymmetry makes it full of sense of contradiction.

Because of this sense of incongruity, Vera tried to perform a topological transformation on the figure, 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 topology, this is a very interesting phenomenon.

Although she did not complete the transformation.

But even so, it is enough!

"It's more than helping! It's really a great help." Thoughts gushed out like spring water, Lu Zhou didn't hesitate to praise, took out his mobile phone and took a picture of the whiteboard, then put away the laptop, "I will retreat For a few days, the duty of the office these days is up to you."

Walking to the door of the office, Lu Zhou suddenly thought of something, looked back at the little girl, and then said, "By the way, if someone comes to see me, just tell him my address and let him find me there."