With his eyebrows raised slightly, Lu Zhou looked away from his resume and looked at her: "Tell me your point of view."
In fact, she just found this figure very interesting. Although it looked like a regular sphere, the geometric asymmetry made it full of contradictions.
That is, regarding the carbon nanospheres underneath the modified PDMS material.
Although geometry was not his area of expertise, he still had some knowledge in this area.
Sighing, Lu Zhou patted his forehead to calm down.
At first glance, this carbon nanosphere seems to be similar to cage-like carbon atom clusters with hollow spherical structures such as C60, C50, and C240, but if you look closely, this thing is indeed fundamentally different from these fullerene materials. .
This is like multiplying two large prime numbers. Multiplication is very simple. As long as you are bored enough, you can do it with a calculator in the supermarket. But in turn, if the product of two large prime numbers is broken down into two prime factors, if the number of digits in this number exceeds one hundred, even supercomputing may not be able to do it.
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.
However, Lu Zhou had no idea how to prepare it.
Looking back at Vera, he asked casually.
Offices of the Institute for Advanced Study in Princeton.
After learning that she had not disturbed his thinking, Vera showed a comfortable smile on her face.
For example, a junior student from JNU majored in applied chemistry as an undergraduate, and applied for the Fourier inversion transformation problem in his functional analysis direction.
Lu Zhou said happily: "Of course."
The more you write the more calculations you have.
Standing up, Lu Zhou walked to the whiteboard in the office. After thinking for a moment, he drew a cage-like sphere with a composite structure composed of points and lines. He also marked the known parameters next to each point. Build simple mathematical models.
But for Lu Zhou, this idea alone was enough.
After being lifted, dismantled and reorganized in three-dimensional space, the cage-like structure sphere without translational symmetry was disassembled into a circular tube-like structure and a translationally symmetrical sphere!
Sequentially speaking, by establishing a mathematical model, analyzing the mechanical, electrical and other physical properties of the material, and then deducing the materials that may be used to synthesize the carbon nanospheres, and through a large number of experiments, a correct method was found.
At this moment, footsteps were heard outside the office.
Opening the door, Vera walked in holding a stack of A4 paper.
If that were the case, the possibilities he faced would be more uncertain than the chaotic systems of quantum mechanics, and perhaps only Schrödinger's cat could solve the problem.
"This three-dimensional structure is weird."
"It would be great if I could help..."
Lu Zhou, who was sitting at his desk, was meticulously staring at the three-dimensional graphics on the computer screen. The ballpoint pen in his right hand was making drafts on the paper from time to time, and his left hand resting on the keyboard kept pressing the zoom key.
First of all, it is not a "regular sphere".
While Lu Zhou was flipping through these resumes, Vera, who had been staring at the whiteboard for a long time, suddenly frowned slightly.
"Is there a problem?"
Vera: "Can I use a pen?"
Although she was not able to complete this transformation.
Lu Zhou returned to his desk, closed the software on his computer, picked up the list and flipped through it.
The quality of this batch of freshmen is pretty good, but paper scores are not of reference value. He will take time to select a few people for interviews.
"It's okay. My train of thought is not easily interrupted. Just don't suddenly tap me on the shoulder from behind." Lu Zhou said in a joking tone.
Seeing Lu Zhou staring at the whiteboard and thinking, she hesitated for a moment, and finally decided not to disturb his thoughts. She walked quietly to the desk, put the files on his desk, and then went to the coffee next to him. machine and made him a cup of coffee.
To give an example of a particle, take two balls of wool apart and knead them together again.
Although it is not unusual to apply for a master's degree across majors, it is usually from mathematics to chemistry, and it is rare to jump from chemistry to mathematics.
He has considered countless possibilities, including the combination of spheres and surfaces, and the combination of multiple spheres of different sizes, but he has ignored this situation.
Start with math, which he is best at.
[…]
Vera frowned, seeming confused as to how to proceed with this transformation.
Because of this sense of inconsistency, Vera tried to perform a topological transformation on the figure, and finally discovered that the figure was actually a combination of a translationally symmetrical sphere and a cylinder.
"More than just helping! It's been a great help." Thoughts came out like spring water. Lu Zhou did not hesitate to praise him. He took out his mobile phone and took a picture of the whiteboard, then put away his laptop, "I can retreat. I’ll leave it to you to take care of the office duty for a few days.”
The molecular structure of the carbon nanosphere was ready-made, but everything else was unknown to Lu Zhou.
Smelling the aroma of coffee, Lu Zhou realized that there was another person in the office.
Then, a magical scene happened.
But even so, it's enough!
After getting permission, Vera picked up the marker and walked to the whiteboard.
Lu Zhou finally stopped writing, took two steps back, looked at the calculations written on half the whiteboard, and fell into deep thought.
After thinking for a moment, she drew a few strokes on the cage-like sphere composed of dots and lines, marking the pentagons and heptagons, and then drew an irregular curve to divide the figure.
There were many scenarios that he could consider, but he always felt that every possibility was just a little bit off.
Problems still have to be solved one by one.
Vera was stunned for a moment, looked at Lu Zhou, then looked at the equations and topologically transformed graphics on the whiteboard, and smiled shyly.
"The academic administration asked me to give you this freshman interview list." 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."
If he returns to chemistry, he faces even more problems.
"What's this?"
In elementary geometry, this is an unimaginable proposition.
"It's nothing, just something to think about when I'm idle."
Lu Zhou stopped writing in his hand and took a deep breath.
"You are simply a genius..."
The data collected by the scanner gun has been saved in Xiao Ai's server, and what is saved in his laptop is only the part he needs to use.
Looking at the geometric shapes on the whiteboard, Lu Zhou was stunned for a moment, but his eyes became brighter and brighter.
Some people may say that fullerenes are also irregular, and pentagonal and heptagonal carbon atom rings may also appear in a group of six-membered rings.
This small ball seems to be made of two or more carbon nanomaterials. After being disassembled, new chemical bonds are rebuilt between different materials.
[Suppose A ∈
The only thing that surprised Lu Zhou was that the applicants for his master's degree were not only undergraduates majoring in mathematics, but also students from non-mathematics majors.
However, the transformation seemed to have come to an abrupt end at this point.
When he reached the door of the office, Lu Zhou suddenly thought of something. He turned back to look at the little girl and then said, "By the way, if someone comes to see me, just tell him my address and ask him to find me there."
However, the difference of this kind of 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 is just a matter of geometry.
From an abstract point of view, this is a topological problem. He needs to dismantle this "cage-like structure sphere" that does not have translational symmetry.
But in topology, this is a very interesting phenomenon.
Looking at the equations and graphs on the whiteboard curiously, she continued to ask.