Chapter 284: Spherical problem

Office of the Princeton Institute for Advanced Studies.
Sitting at the desk, Lu Zhou was meticulously staring at the three-dimensional graphics in the computer screen. The right-hand ball-point pen was occasionally drawing drafts on the paper, and the left hand resting on the keyboard kept pressing the zoom key.
The data collected by the scanning gun has been stored in Xiao Ai's server, and what is stored on his laptop is only the part he needs.
That is, the carbon nanospheres under the modified PDMS material.
The molecular structure of the carbon nanospheres is readily available, but everything else is unknown to Lu Zhou.
Whether it is the physical properties of mechanics, electricity, etc., or the method of preparing this carbon nanosphere in the laboratory, he needs to explore it by himself.
Sequentially, by establishing a mathematical model, analyzing the mechanical properties of the material, such as physical properties, and then inferring the materials that may be used to synthesize the carbon nanospheres, and through a large number of experiments, worked out a correct method.
However, Lu Zhou had no clue about how to prepare it.
It's like two large primes multiplying. Multiplication is easy. As long as you are bored, you can do it in the supermarket with a calculator. But in turn, the product of two large prime numbers is decomposed into two prime factors. If the number of digits exceeds one hundred, even super calculations may not be possible.
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, C240, which have hollow spherical structures of cage-like carbon atom clusters, but if you look closely, this stuff does have fundamental differences from these fullerene materials. .
First of all it is not a "regular sphere".
One might say that fullerenes are irregular, and pentagonal and heptagonal carbon atom rings will also appear in a group of six-membered rings.
However, the difference of this carbon nanosphere is reflected in the symmetry of the molecular point group. Since there is no translational symmetry, it cannot even be expressed in the traditional Bravais lattice.
This small ball seems to be composed of two or more carbon nanomaterials. After dismantling, new chemical bonds are reconstructed between different materials.
One example of particles is to take apart the two yarn clusters and knead them together again.
If this is the case, the possibility he faces will be more uncertain than the chaotic system in quantum mechanics, and perhaps only Schrödinger's cat can solve this problem.
It's just a matter of geometry.
If he returns to chemistry, he will face more problems.
Sighing, Lu Zhou patted his forehead, calming himself down.
The problems still have to be solved one by one.
Start with the math that he is best at.
Although geometry is not his field of expertise, he still has some knowledge of this field.
Abstractly, this is a topology problem, and he needs to disassemble this "cage structure sphere" which does not have translational symmetry.
Standing up, Lu Zhou walked to the whiteboard in the office. After thinking for a moment, he drew a composite structure cage sphere composed of points and lines on it, and marked the known parameters next to each point. Build simple mathematical models.
[Let A ∈ X; f, ​​g ∈ C (X, Y), if there are homotopes from f to g, such that when a ∈ A, H (a, t) = f (a) ...]
[……]
The more the formula is written, the more it is written.
Finally stopped the pen, Lu Zhou stepped back two steps, looked at the formulas written on half a whiteboard, and fell into meditation.
There are many situations he can consider, but he always feels that every possibility is a little worse.
Just then, footsteps came from outside the office.
Pushing the door open, holding a stack of A4 paper, Vera came in.
Seeing Lu Zhou staring at the whiteboard and thinking, she hesitated, and finally decided not to disturb his thinking, walked lightly to the desk, put the documents on his desk, and went to the coffee next to him Machine and helped him make a cup of coffee.
Smelling the scent 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 freshmen interviews." Willa pointed to the list and added a soft whisper, "I was afraid I would disturb you, so I didn't knock."
"It's okay, my mind is not so easy to interrupt, as long as you don't pat my shoulder suddenly from behind." Lu Zhou said in a joking tone.
After learning that he hadn't disturbed his thinking, Vera's face showed a pleasant smile.
Looking curiously at the equations and graphics on the whiteboard, she continued to ask.
"what is this?"
"Nothing, nothing to think about."
Back to Lu Zhou at his desk, he turned off the software that was open in the computer and picked up the list roughly.
The quality of this batch of freshmen is pretty good, but the paper results are not of reference value. He will take time to select a few people for interviews.
The only thing that surprised Lu Zhou was that his master's degree was not only for undergraduate mathematics majors, but also for non-mathematics students.
For example, one of Jin's masters, an undergraduate major in application science, reported the problem of Fourier inversion transformation in his functional analysis direction.
Although it is not uncommon to apply for a master's degree across majors, it is generally a jump from mathematics to chemistry, and it is rare to jump from chemistry to mathematics.
As Lu Zhou flipped through these resumes, staring at Willa for a long time while staring at the whiteboard, he suddenly frowned slightly.
"This three-dimensional structure is strange."
She raised her eyebrows slightly, and Lu Zhou's gaze moved away from her resume to look at her: "Talk about your point."
Vera: "Can I use a pen?"
Lu Zhou said happily, "Of course."
After getting permission, Vera picked up the marker and walked to the whiteboard.
After thinking for a while, she drew a few strokes on this cage-shaped sphere composed of dotted lines, marked out the pentagon and heptagon, and then drew an irregular curve to divide the figure.
Immediately afterwards, a magical scene happened.
After being lifted and disassembled in three-dimensional space, and reorganized and changed, the cage-shaped structure sphere without translational symmetry was disassembled into a circular tubular structure and a translationally symmetrical sphere!
Looking at the geometry on the white board, Lu Zhou froze slightly, but his eyes were getting brighter.
He considered countless possibilities, considered the combination of spheres and faces, and considered combining multiple spheres of different sizes, but he ignored this situation.
But at this point, the transformation seems to have come to an abrupt end.
Vera frowned, as if confused as to how to carry on the transformation.
But for Lu Zhou, this idea alone is enough.
"You are a genius ..."
Willa stunned slightly, looked at Lu Zhou, and looked at the equations on the whiteboard and the graph after the topological transformation, and smiled a little slyly.
"If only I could help ..."
In fact ~ EbookFREE.me ~ she just thinks this figure is very interesting. Although it looks like a regular sphere, the geometric asymmetry makes it full of contradiction.
Because of this sense of contradiction, Willa 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.
This is an unimaginable proposition in elementary geometry.
However, this is an interesting phenomenon in Putuo science.
Although she failed to complete the transformation.
But even that is enough!
"It's more than just helping! It's a big help." The idea was pouring out like spring water. Lu Zhou did not hesitate to praise. He took out his mobile phone and took a picture of the whiteboard. Then he put away the laptop. A few days, I'll take care of you on duty in these days. "
When he came to the door of the office, Lu Zhou suddenly thought of something. He looked back at the little girl, and then ordered, "Yes, if anyone comes to me, you tell him my address directly and let him find me there."