In the experimental building of Academician Jiang Weixian, Qin Kezheng and Ning Qingyun tried to repeat the "circular tube water flow experiment" done by Renault, a physicist at Yingguo University more than a hundred years ago.

This is just a very simple experiment, so simple that even a child can do it at home by taking a round pipe and connecting it to the faucet. But if you want to clearly observe that as the flow rate increases, the fluid changes from a regular flow to a chaotic and irregular flow.

For turbulence, it is necessary to use modern instruments to accurately record the key points of flow velocity that produce changes, as well as the relationship between turbulence and pipe diameter (d), viscosity of the fluid (μ), and density of the fluid (p).

"vl/μ, where p and μ are the fluid density and dynamic viscosity coefficient, v, l are the characteristic velocity and characteristic length of the flow field..."

"Generally, in a pipeline, 000 will become a complete turbulent state, a transitional state..."

The two of them recorded and calculated while drawing conclusions.

In fact, the answers to this knowledge can be found by searching the literature, but only by conducting experiments yourself and completing the derivation and verification can you greatly deepen your understanding of turbulence and Reynolds number.

This experiment was naturally arranged by Academician Jiang and the two of them.

"Huh?" Ning Qingyun unexpectedly discovered a problem: "Qin Xiaoke, if based on the derivation we made in this experiment, when using the n-s equation for averaging, there will be one more unknown function than the number of equations.

"

Qin Ke knew it well. He had seen similar answers in the first, middle and second parts of the S-level knowledge "Exploration and Detailed Solution of Nonlinear Partial Differential Equations "Navier-Stokes Equation"":

"This is a closed problem, and it will be very difficult to solve the n-s equation. Here you can directly quote the specific form of the n-s equation-Reynold's equation to explain."

The so-called Reynolds equation refers to the averaging method used by Reynolds to average the instantaneous velocity and instantaneous pressure of turbulent flow. Based on the n-s equation, the basic equation derived to describe the average flow field of turbulent flow is an important theoretical basis in turbulence.

Ning Qingyun tried to substitute the Reynolds equation and successfully solved the problem. She exclaimed: "Qin Xiaoke, I find that you really know everything."

"In general, it just so happens that fluid mechanics and n-s equations are the fields I am good at. In fact, the most difficult thing about turbulence is to use nonlinear theory to analyze it. How does it evolve from laminar flow? Currently, the main relevant assumptions are bifurcation theory

, Chaos theory, strange attractor and boundary layer theory..."

Qin Ke happened to take the opportunity to explain to Ning Qingyun the S-level knowledge "Exploration and Detailed Explanation of Nonlinear Partial Differential Equations "Navier-Stokes Equation"" about the theory of turbulence, but just halfway through, his phone suddenly rang.

.

It's an international long distance call.

Qin Ke was startled for a moment, and he had some kind of prediction in his mind. After he answered the phone, sure enough, a man came from the other end and said in English: "Hello, Dr. Qin Ke, I am Dorji Man, a staff member of IMU."

Dele, currently our 'Riemann Hypothesis Review Expert Panel' has basically completed the review of the five expressions of your Riemann Hypothesis. Next, we need to conduct a remote video Q&A with you, which will last from one hour to two hours.

Hours, when do you have time?"

Upon hearing this announcement, Ning Qingyun was both surprised and a little nervous.

Naturally, I was pleasantly surprised to hear that the expert panel had completed the review, which meant that no major problems had been found. Otherwise, there would not have been an in-person "defense" in the second stage. But what was nervous was that there might actually be two "defenses" in the second stage.

It was so long. Thinking that Qin Ke had to face thirty top experts in number theory for two hours, even Ning Qingyun, who had confidence in Qin Ke, could not help but feel a little worried.

After all, no one is a jack-of-all-trades. If there is an expert who is looking at a certain detail and constantly studying it, it will be difficult to deal with it.

She was feeling anxious and worried when she heard Qin Ke say: "Is this question and answer session open to the public in a live broadcast? Or is it just a remote video connection between me and thirty review experts?"

"Both are possible. Our suggestion here is to broadcast the entire process live in the live broadcast area of ​​​​imu's official website. This will undoubtedly allow mathematicians from various countries to understand the situation more intuitively, but if you have any different opinions, you can also raise them.

come out."

"I have no objection, the whole process will be broadcast live. As for the time..." Qin Ke looked at his watch: "The day after tomorrow is Sunday, our time here is from 9 am to 9 pm."

"The day after tomorrow? Let me look at the calendar and the time difference... The time is Sunday the day after tomorrow. The local time in Xia Country is four o'clock in the afternoon. How about? The time difference between us in Berlin and Xia Country is seven hours, which happens to be nine o'clock in the morning on the same day."

"No problem. Then set this time."

"Okay, in ten minutes we will announce the live broadcast time of this defense on imu's official website and various social platform accounts. Please prepare in advance. Please prepare your own venue and required props.

If expenses are incurred, you can scan the voucher and send it to my email address. My email address is... We will reimburse you based on the facts..."

After explaining all the details, the imu staff politely ended the call.

Ning Qingyun was a little nervous and said: "Qin Xiaoke, would it be too much to hurry if you directly decide the day after tomorrow? Do you have time to prepare?"

Qin Ke smiled: "Last weekend, didn't Uncle Chen arrange for five mathematics academicians, including Teacher Tian, ​​to come and rehearse with me? That's enough. If I didn't think about the rare holiday tomorrow and wanted to go out on a date with you, I

We’ve already made plans for tomorrow.”

"Aren't you going to prepare well tomorrow?" Ning Qingyun was still a little worried.

"Don't worry, your husband and I have never seen anything like that, so it's nothing to face thirty old men. It's a pity that you haven't seen the majesty when I punched Nanshan Nursing Home and kicked Beishan Kindergarten, otherwise you wouldn't be so worried.

."

Seeing Qin Ke joking as usual and looking at ease, Ning Qingyun finally felt relieved.

Qin Ke was indeed full of confidence in the "defense" of the Riemann Hypothesis proof this time, but according to the procedure, he still notified the school.

As a result, the school immediately became nervous. Wei Yuanfu called Qin Ke almost as soon as he received the news and asked what Qin Ke needed. Qin Ke said: "Please ask the school to prepare a venue with a large whiteboard and erasable pens, oh,

You can also watch videos remotely.”

Wei Yuanfu asked cautiously: "Qin Ke, can you just prepare these? Do you need more professors from the school to conduct a second drill with you? The ones who came last time were all academicians, so I didn't dare to waste them too much.

The rehearsal time is only one hour. This time we have used the mathematics professors in the school to cooperate with you for the whole day to rehearse."

Wei Yuanfu is not nervous until now. Now the whole world knows that the expert jury sent by IMU this time directly determines whether the "Riemann Hypothesis" will become the "Riemann Theorem", and it is also related to whether Qin Ke can obtain the "Riemann Theorem".

For Qingmu University, the reputation and international academic status of "Riemann Hypothesis Proofer" are also related to whether the school can become famous around the world and rank among the top 100 famous universities in the world.

"Thank you, Director Wei, for your concern, but I think it is more effective to relax your mind than to tense up before the final defense."

Wei Yuanfu immediately thought so, and when he saw that Qin Ke had made up his mind, he did not dare to persuade him. After hanging up the phone, he hurriedly reported to Vice Principal Gu Bojun.

Gu Bojun was also a little worried, but he was used to big winds and waves after all, so he immediately said: "Just do what Qin Ke wants. Qin Ke knows better than us how to prepare. He has created so many miracles. This time,

I still choose to believe him. However, the classroom for the live broadcast must be carefully prepared and cannot be careless, especially the network equipment. Qin Ke’s normal defense cannot be interfered with by the network condition. Please contact the School of Computer Science and let them know about this

Send someone to follow up the whole process..."

Qingmu University is responding with all its strength here, but Qin Ke is already preparing to take Ning Qingyun out for fun tomorrow.

The two of them have been busy since they returned from Yuanzhou, busy visiting their elders, busy studying, busy doing experiments, busy preparing lessons, but they have no time to enjoy the fun of life itself.

Qin Ke felt that being so busy that he had no time for a good date should not continue, so he originally had to do experiments on Saturday, so Qin Ke decisively asked Teacher Jiang for leave.

When Jiang Weixian heard that Qin Ke's reason for asking for leave was "to go on a date," he was startled for a moment, then smiled and said, "Okay." He approved Qin Ke's leave form with a wave of his hand, and added: "On weekends from now on,

You and Ning Qingyun don’t need to come to the laboratory. I know you have other projects to be busy with, and no matter how busy you are, you can’t ignore life itself. I appreciate this choice of yours."

Academician Jiang, who has always been serious, rarely praised Qin Ke in person like this, which made Qin Ke not used to it.

However, since he doesn't go to the laboratory on weekends, Qin Ke feels more relaxed. Physics is also a long road, and it will not be easier than mathematics. Qin Ke still feels like before, he should be busy when he should be busy, and relax when he should be relaxed.

It is the most correct scientific research attitude.

So he took Ning Qingyun back to Xingguang Mingyuan's new home that night and cooked a big meal himself.

Qin Ke's calmness and relaxation also allowed Ning Qingyun to step away from the busy study and scientific research and enjoy the sweet world of two people with him.

The two of them were cuddling together and watching TV, and the sound of pattering autumn rain could be heard outside the window.

"Oops, it's raining." Ning Qingyun hurriedly stood up and ran to close the window. Qin Ke smiled and said, "Did you forget that there is a new function of the low light?" He snapped his fingers: "Low light, turn on automatic

Manage window mode."

The hidden speaker in the living room immediately heard the mechanical voice of Shimmer: "Understood, Master Qin Ke. The automatic window management mode has been activated. It has detected that it is raining, and the windows in the whole house have started to close automatically..."

Ning Qingyun then remembered that her family had asked her assistant Fang Yongtang to automate the windows some time ago, and she couldn't help but exclaim: "Technology is really convenient."

"Technology is changing the world. But I have to mention that the accuracy of the weather forecast is still low. At noon, I checked that it was only cloudy for the past two days, but it rained at night."

"Yes, I hope our turbulence project can improve the accuracy of weather forecasts in the future." The girl stood by the window, watching the rain outside the window disappearing and appearing under the orange light of the street lamp, with longing in her eyes.

Qin Ke looked at Ning Qingyun's delicate and beautiful face reflected in the window, and said with a smile: "This is inevitable. As long as we can completely crack the mystery of the n-s equation, the accuracy of the weather forecast within three days will not be reached.

100%, but more than 90% is not a problem. Forget it, let’s not talk about academic research during the holidays, let’s just think about where to go tomorrow.”

"Look at the rain, it may continue to rain tomorrow."

Qin Ke smiled and said: "You are just too serious about doing things, always thinking that everything will be prepared perfectly. In fact, it is not necessary. More surprises are not a bad thing. Let's drive out tomorrow. If it rains, we will have a date indoors. If it doesn't rain, we will go there.

Outdoor date.”

Ning Qingyun winked playfully: "What if we are outside and it suddenly starts raining?"

Qin Ke looked at her and smiled: "When it rains, we just run away. Are we going to stay where we are in the rain?"

Ning Qingyun was amused and laughed, and she began to feel excited. As expected, being with Qin Ke was a joy. No matter what happened, everything seemed to be easy and fun in his eyes.

…

The next morning, before the two were about to go out, it really started to rain, and it was a heavy rain. Dense lines of rain fell from the sky, as if the sky and the earth were covered with bead curtains. The big raindrops hit the glass of the window and splashed.

There were large raindrops.

The most troublesome thing is that the wind is still very strong, and the green plants in the community are shaking violently.

"Yeah, the weather forecast this time is completely inaccurate."

It's not safe to drive out in such weather. Qin Ke thought about it and came up with a good idea. He dug out two sets of raincoats, boots and a water gun, and handed them to Ning Qingyun: "It's raining heavily now, so we can't go out for the time being.

How about going to the balcony and playing with water guns."

Ning Qingyun's eyes widened, and she turned to look at the balcony. Because of the strong wind, the balcony was also wet by the rain: "Go there to play with water guns?"

Qin Ke was very interested: "Yes, that girl Qin Xiaoke played with me before, and it was quite interesting. There are two rules. The water gun can only catch the falling rainwater, and the water gun can only shoot on the raincoat, not in the face.
To be continued...