shadow of britain

Chapter 436 The issue of whether or not to exceed the syllabus in the college entrance examination
In the morning at the Paris Academy of Sciences, the spring sunshine passes through the classical-style window lattice, casting mottled light and shadow on the polished marble floor, like an oil painting with a golden frame.

Outside the window, the ancient plane trees swayed gently in the breeze, and the new green leaves complemented the blue sky, adding a bit of vitality and tranquility to this temple of knowledge.

On the tree-lined path under the plane trees, two French gentlemen were walking together.

They were not moving very fast, and their steps were neither fast nor slow. Accompanied by the rustle of leaves being blown by the breeze, you could occasionally hear their chatter and laughter.

The slightly younger gentleman looks to be in his early forties. He has thin and strong cheeks, a high nose, and a pair of deep blue eyes in his eye sockets. Wearing a black silk top hat, with meticulously combed silver-gray hair exposed under the brim, he is wearing a dark blue double-breasted swallowtail coat, which is thick in texture and well-tailored. A dark silk tie is tied around his neck, making it even more... Highlight his scholarly demeanor. Wear a white high-collar shirt underneath, and the delicate lace trim at the cuffs reveals his attention to detail.

As for the older gentleman, he simply wore a black woolen robe. The wide cuffs and loose hem swayed gently in the wind, showing his calm and calm academic temperament.

Occasionally, there are teaching assistants passing by them. When almost every teaching assistant passes by them, they will politely take off their hats and say: "Good morning, Mr. Navier. Good morning, Mr. Coriolis."

For most people at the Paris Academy of Sciences, just two simple surnames are enough to understand the outstanding academic abilities and professional experience of these two gentlemen.

Claude-Louis Navit, a disciple who inherited the legacy of his mentor Jean-Baptiste Joseph Fourier, is an academician of the French Academy of Sciences, a former member of the High Commission for Bridge Construction of the Paris High Court, and is currently a calculus and mechanics professor at the Ecole Polytechnique in Paris. Professor and Professor of Mechanics at the National Institute of Roads and Bridges in France.

Gustave Coriolis, a backbone scholar in the French scientific community who studied under Augustin-Louis Cauchy, a member of the Department of Mechanics of the French Academy of Sciences, a former professor of geometric analysis and general physics at the Ecole Centrale Supérieure des Beaux-Arts, and currently a professor at the Ecole Nationale des Beaux-Arts in France. Professor of Applied Physics.

"Is he still doing research?"

Navigation was also helpless, but out of concern for his old friend, he still asked Coriolis about Corsi's current situation: "Is Corsi still in Prague now? He is still the Duke of Bordeaux, Crown Prince of the Bourbon Dynasty. 'The tutor?"

Judging from real experience, pressure does not significantly affect the resistance generated by the molecular interaction between various parts of the moving fluid, and these resistances are more derived from the speed or direction differences of adjacent molecules. Therefore, based on this premise, I further derived a classified expression of the force exerted on molecules by the motion of adjacent molecules based on the Euler equation.

Navigation leaned on his cane and shook his head slightly: "It's not that I don't consider going back, but the bridge construction committee will probably not re-accept me. When I was in charge of the design of the Invalides Bridge, I didn't leave a certain safety margin in the calculations. As a result, the bridge cracked and had to be demolished and rebuilt. Since then, the government committee has been doubting my design ability. They felt that my design relied too much on mathematical calculations, and they also ridiculed me for sometimes even engineering construction. It is not as realistic as an ordinary mason. Although the committee was reorganized after the July Revolution, most of the people from that year were re-elected. With them there, the bridge construction committee would probably not consider letting me go back to preside over the construction of the project. "

When Coriolis heard this, he couldn't help but smile: "I can't hide anything from you. Do you still remember the discovery I mentioned to you before? When an object moves in a straight line in a rotating reference frame, Due to the effect of inertia, the object will tend to maintain its original direction of movement. However, due to the rotation of the reference frame itself, the actual movement trajectory of the object will shift. You said that my discovery was very interesting and suggested that I keep moving. Keep studying. This time, I have thought about this problem carefully. In order to explain this phenomenon, I think it is advisable to introduce an additional force to describe the deflection of the object in the rotating reference system. "

At this point, Navier felt happy but also felt his head hurt. He said: "The greatest luck of the French Academy of Sciences is that we have two mathematical monsters, Cauchy and Poisson. Therefore, in the process of researching many problems, Intentionally or unintentionally, they have saved us a lot of trouble. If it were not for them, I believe that many of the current research of the Academy of Sciences would still be in the stage of hypothesis and derivation. The biggest misfortune of the French Academy of Sciences is that there are two mathematical monsters. One left last year. Rather than asking me to return to the Bridge Construction Committee, I still think the government should find a way to bring Kexi back."

I thought that the study of Euler's equations would end here, but what I didn't expect was that one day a few months later, Cauchy suddenly walked into my office holding a stack of paper. He said that he introduced the concept of stress tensor of fluid particles into the Euler equation under the prerequisites I gave, and then he found a set of formulas in a daze, and he could accurately reflect the fluid motion through this set of formulas. Differences from solid motion.

Coriolis shook his head and said: "No, he went to Graz with the Bourbon royal family a while ago. Metternich of the Austrian Empire ordered all the orthodox dynasty exiles in the country to be moved there."

I had just finished this work, and the next day I excitedly showed my latest research results to Cauchy. He happened to be very interested in this aspect, and he could see the shortcomings of the formula at a glance. ——This is just a set of equations describing the dynamic equilibrium and motion of incompressible fluids. It is obviously not enough to describe the laws of fluid motion at the macroscopic level. I am also aware of this flaw, but with my ability, deriving it to this point is already the limit.

Hearing this, Coriolis said helplessly: "Mr. Navier, you also know that that is impossible. You and Mr. Cauchy are old friends, and Mr. Cauchy is my mentor. We both understand his temper and stance." , he is an out-and-out orthodox dynasty who has devoted his life to supporting the Bourbon dynasty. Although Napoleon can also make him willing to serve, our current King is Louis Philippe, and he is obviously interested in Mr. Cauchy. Without the same appeal as Napoleon, Mr. Cauchy would never be able to swear allegiance to the July Monarchy."

When Coriolis heard this, he suddenly thought of something: "Ah! So, the civil engineering structure design method you proposed - the allowable stress method, was summarized after the construction of this bridge failed?"

"He should have done less recently, at least not as crazy as when he was in Paris. He now devotes most of his attention to educating the Duke of Bordeaux."

Navi frowned and thought for a while after hearing this: "Introducing a brand new force? This idea is indeed bold, but until it is completely falsified, I can't say that this idea is wrong. Well...you found this Do you know the mathematical expression of force?”

Later, Cauchy told Mr. Poisson of my new discovery in the chat. As a result, Poisson also spent only a few months to establish the Euler equation under the same conditions. An equation of motion describing a compressible fluid. "

Navier was quite helpless about this: "You are right. If Mr. Cauchy was still in Paris, as long as your hypothesis is correct, he would be able to find the laws of mathematical expressions in a few months. At the time, I When studying the Euler equation, I believe that the reason why the Euler equation does not match the actual fluid motion is because the Euler equation treats the fluid as a collection of molecules. This assumption only applies to completely uniform flows, while in reality Fluid motion is often non-uniform.

Coriolis felt the cool breeze in the morning and asked, "Mr. Navi, are you really not considering returning to serve on the Bridge Construction Committee?"

Navi nodded slightly and said: "For the same mistake, making it once is a mistake, but making it twice is stupid. Although I can't be called a smart person, I don't want to be regarded as a fool by others, so of course I have to learn a lesson. After all, I I still have a teaching position at the National Road and Bridge School. Although I may not have the opportunity to lead bridge design again, at least I can’t let the students make the same mistake I did.”

Having said this, Navi suddenly stopped and asked: "Speaking of which, why are you suddenly free to come to the Academy of Sciences today? Today is neither Wednesday nor Saturday. There should be no meetings to be held in the Mechanics Department? Could it be that you are What’s new?”

"This can be considered a good thing. After all, if he uses his brain so much to write papers, his body can't sustain it for too long. You don't know that when he was young, writing papers was like a printing press, because The papers he wrote were so numerous and thick that he almost took up all the pages of the journal, so the Academy of Sciences passed a special resolution stipulating that the length of each published paper should not exceed 4 pages. He could take a break. Rest, it’s a good thing for those young scholars who are eager to show themselves on the stage.”

Almost every highly educated guy will be in awe in front of these two gentlemen, but unlike the collision of ideas that everyone imagines between academic masters, the two of them are not always happy when they are together. Discuss some academic issues.

Coriolis said: "I haven't reached that step yet. I have been doing related experiments on rotating systems such as waterwheels. Judging from the experimental results, this hypothesis is very likely to be correct. If you If you don't mind, I would like to invite you to study with me the relationship between energy transformation and conservation in similar rotating systems. After all, as you know, not everyone is Euler, Fourier, Poisson and Cauchy, mathematical expressions. For most researchers, it may take several years to get to the bottom of things like this.”

When Coriolis heard this, he couldn't help laughing and said: "You are right. Mr. Cauchy's temporary departure is a misfortune for the entire French scientific community, but it is a blessing for all French scientists. When he was at the Academy of Sciences, he was simply Like the Alps, the only one who can be indifferent to him is a genius of the same level as Mr. Poisson."

Navi said as he walked: "Speaking of Mr. Poisson, I heard that the Royal Society of Britain seems to be planning to award him this year's Copley Medal. Yesterday, the person they sent to award the award even sent someone to contact the Academy of Sciences to inquire about Poisson. When will Mr. Song have time to accept that medal?”

Coriolis was quite envious and said: "For an honor of this level, I guess the Academy of Sciences will hold an award ceremony specifically for Mr. Poisson, right?"

Navi curled his lips slightly and said: "Whatever, I don't like to get involved in this kind of thing anyway. I just hope that the ceremony can end quickly and not delay us from doing business. And, compared to the award ceremony, I obviously like the London guy. The award presenters are more interested.”

Coriolis asked: "Who is the guest of honor?" "Sir Arthur Hastings, a young British electromagnetic researcher. I heard that he has a very good relationship with Mr. Faraday and often participates in For his work in Faraday's laboratory, he should be regarded as a leader among the current young electromagnetic researchers in Britain. Unfortunately, I don't do much research on electromagnetism, otherwise I would definitely ask him to tell me about the current British electromagnetics. Recent developments and breakthroughs in research.”

Coriolis also smiled and said: "Me too, I think mechanics is more interesting than electromagnetism. Electromagnetic induction is certainly magical, but I am obviously more interested in the equation of fluid motion you just mentioned."

"Really?" Navi seemed to be in a good mood: "Then I will take you to see it. Most people in the Mechanics Department think this is an unpopular direction. It would be strange if you are interested. I study fluid motion. The manuscript of the system of equations is over there in the library. If you are interested, let’s go over there now. By the way, let’s talk about the issue of introducing a new force into the rotation system that you just mentioned.”

Coriolis asked: "You mean the easternmost library?"

"Well, that library is too remote, so few people go there. But like me, Amp, and Kesi, we all like quiet places, so we all want to get together there. What do you think?"

"Being respectful is worse than obeying orders."

The two chatted and laughed along the way, and soon followed the tree-lined path to the door of the library.

Navier just wanted to open the library door, but found that the door opened by itself from the inside.

Liouville led a gentleman they didn't know out of the library and happened to bump into them.

When Willie Liu saw the two academic leaders, he was startled for a moment, then took off his hat and saluted: "Ah! Good morning, gentlemen!"

Seeing this, Arthur also said good morning: "Good morning, gentlemen."

"morning."

Coriolis knew Liouville, but this was the first time he met the tall young man in front of him, but he had no interest in asking about his identity.

After all, at the French Academy, teaching assistants come in and out every day, and there is nothing unusual about new people coming and going.

He turned sideways to get out of the way and watched Liouville take Arthur away. Just as he was about to enter, he heard Navi say: "Is that young man the new assistant coach?"

Coriolis shrugged and said, "Probably. Are there any outsiders in the Academy of Sciences? Even if there are, they are some officials, but as we all know, officials will not come to the library."

Navi said in surprise: "If he is a teaching assistant, how could I not know him? I have taught at Ecole Polytechnique for so many years, and I know every student in the Department of Mathematics and Natural Philosophy in every session, but just now I actually have no impression of this person at all.”

Coriolis joked: "Do you mean to say that the Academy of Sciences has recruited a teaching assistant who did not graduate from Ecole Polytechnique? Stop joking, Mr. Navi. Even if it is just the most ordinary teaching assistant at the Academy of Sciences in Paris, They must be the most outstanding researchers of their age, and the most outstanding scholars of each age group are almost all graduates of Ecole Polytechnique. This is true for Mr. Cauchy, this is true for Mr. Poisson, and this is true for you and me. , even Liu Weier, who just left school. Are you trying to say that among our group of École Polytechnique students, there is a graduate from a no-name school? I think the Academy of Sciences is not that stupid and incompetent? degree."

After hearing this, Navi did not go into details, but stepped into the door and said: "Well, why do you care about this? Let's talk about interesting things. You sit down first, I will look for the manuscript that I found Where was it lost?"

As soon as Navig entered the door, he went straight to the bookshelf at the back. He remembered which book he seemed to have stuffed the calculation paper into.

Coriolis walked towards the chair that was still cold. As soon as he got closer, he discovered the calculation paper on the oak table filled with calculations and derivation processes.

Coriolis picked up the calculation paper and glanced up and down, and quickly exclaimed: "Mr. Navier, you must be looking for this. This derivation is indeed exquisite. However, you seemed to have missed something with me just now. "Hey, you recently put forward three hypotheses based on the original derivation?"

"Three hypotheses?"

After hearing this, Navi put down the book in his hand and walked towards Coriolis. He took the calculation paper from the other party's hand.

On the calculation paper that should have contained only his personal derivation process, there were surprisingly three more derivation equations, and at the top of each equation, their scope of application was thoughtfully noted.

The first one is Navier recognition, because it is the system of equations derived by Cauchy.

Navier also recognizes the second one, because it is a system of equations derived by Poisson.

But the third kind...

Assumptions:

1. Fluids are isotropic.

2. When the fluid is at rest, the normal stress is equal to the static pressure.

3. There is a linear relationship between stress and deformation rate.

Based on the above assumptions, the constitutive relationship of fluid stress can be deduced, and substituted into the above differential equation of fluid motion, and the following derivation can be performed to obtain a system of motion equations suitable for viscous fluids that can compress and change viscosity...

(End of this chapter)