1900: A physics genius wandering around Europe

Chapter 577 Random Phenomena in the Macroscopic World! Chaos Theory! Shocking! Shocking the Audience!

Plant's question is not easy to answer.

In later generations, some special branches did emerge in the field of mechanics, such as computational mechanics and nanomechanics.

Computational mechanics refers to the use of the enormous computing power of computers to find exact solutions to complex mechanical situations.

Its core thinking is "finite element".

For example, for a very irregular object, the force conditions inside it are extremely complex.

If you want to solve it by manually writing equations, it is almost impossible to do it.

But computers can break down irregular objects into very small units.

These units can be processed using standard mechanical formulas, and finally by adding up the parameters of all units, the overall force analysis can be obtained.

This is the idea of ​​finite element analysis.

In the future, any graduate student in science or engineering will definitely use this method.

Nanomechanics, as the name suggests, is the study of the mechanics of nanoscale materials.

Nanopowders, nanotubes, nanofilms, etc.

In later generations, anything with the word "nano" in it instantly becomes a high-tech product in the eyes of ordinary people.

There are nano hand cream, nano magnetic therapy, and even nano underwear.

Of course, all of these are, without exception, just a waste of money.

Although nanomaterials have many unique properties that are completely different from macroscopic materials, they are still in the research stage.

Those excellent properties are only significant at the nanoscale, but the situation is different once they are transplanted to the macroscopic field.

However, Li Qiwei had no interest in discussing these so-called new branches of mechanics.

As for the reason, he smiled and said:

"If I just want to predict a few research directions, I do have some ideas."

“However, I think those directions don’t have much practical significance for everyone here.”

“Whatever new mechanics are, they are not truly innovative compared to fluid mechanics.”

Wow!
Everyone was shocked!
Professor Bruce's remarks made them both happy and sad.

The good news is that their strength has been recognized by Professor Bruce, and the new direction is not a problem for these big guys.

The sad thing is, doesn't that mean that mechanics has no future?
Before people could think about why it was not considered innovation.

Li Qiwei suddenly continued:

"I want to ask you a question."

"What do you think are the most significant commonalities among the various branches of mechanics, such as fluid mechanics?"

Everyone frowned when they heard this.

If someone else asked this question, it would seem like they were being mysterious.

But if Professor Bruce spoke, the situation would be completely different.

There must be a deep meaning!

Everyone present is a big shot in the field of mechanics, and their understanding of mechanics far exceeds that of ordinary people.

However, faced with this problem, few people are confident.

Obviously, this issue needs to be considered from a high perspective.

Li Qiwei's eyes swept over everyone one by one with a smile on his face. He hoped someone could answer.

After a while, Plant spoke.

There was still a hint of uncertainty in his tone.

"Based on my personal experience, I think it's precision."

"Take the fluid mechanics that I study as an example, whether it is a formula derived from theory or a semi-empirical formula summarized from experimental results."

"They have one purpose: to make the predictions more accurate."

"We want to be able to include complex fluids in the formula and predict their state at any time."

“It’s like calculating the trajectory of celestial bodies.”

Snapped!
Li Qiwei couldn't help but applaud!

Prandtl is indeed worthy of being called a master of mechanics, and his insight is extremely profound.

When everyone heard this, they were all touched.

Li Qiwei said:
"Yes, it is precise!"

“Precision and correctness are not the same thing.”

"Mechanics, electromagnetism, relativity, quantum mechanics, these are all correct theories that have been verified by experiments."

“But mechanics is a very technical subject. I call it [technical science].”

“For example, structural mechanics is used to design building structures, and fluid mechanics is used to design the shape of aircraft.”

“When various branches of mechanics are applied to engineering, what they pursue is no longer correctness, but precision.”

“Take fluid mechanics, for example.”

"The motion of a single water molecule certainly conforms to quantum mechanics, and the motion of a stream of water also conforms to Newtonian mechanics."

"However, we cannot directly use quantum mechanics and Newtonian mechanics to study the motion of water flow."

"Instead, the sub-discipline of fluid mechanics had to be created."

“Because quantum mechanics and Newtonian mechanics are more fundamentally correct.”

"Fluid mechanics is about pursuing an accurate fit between the calculation results and the real world."

"That's why I say that even if there are new directions in mechanics in the future, such as solid mechanics, its essence will not change."

“It’s just a shift from studying the precise state of a fluid to studying the precise state of a solid.”

"Whether it is a fluid or a solid, its nature is known."

"It's just that because of the complexity of a macroscopic system composed of a large number of molecules, it is impossible to directly calculate it. We need to create theories to study the entire system."

“All theories and methods are aimed at making the calculation results closer to the experiments.”

“The results are inaccurate only because the theory is not good enough or the computing power is not strong enough.”

Everyone nodded.

They easily understood what Professor Bruce meant.

From this perspective, predicting the so-called new direction of mechanics is indeed meaningless.

It's like a football player switching careers to become a basketball player.

From the more essential basis of sports, football and basketball are just forms of sports.

For the big guys present, it’s just a matter of learning more things.

For a moment, everyone was a little disappointed.

The kind of earth-shaking shock that relativity and quantum mechanics brought to physics seems impossible to happen in the field of mechanics.

However, Li Qiwei's next words immediately made everyone exclaim.

"Although predicting new branches of mechanics doesn't make much sense."

“But I found a very interesting problem.”

“Maybe it will change the mechanics a little bit.”

Wow!
Everyone was shocked.

What would it be?
Li Qiwei smiled and said:

"When I was at the University of Paris, I gave a lecture to the contestants of the Physics Olympiad."

"In my speech, I mentioned Laplacemon."

Everyone nodded, of course they knew about this.

The concepts of the three mythical beasts and information entropy are deeply rooted in people's minds.

For the big guys present, Laplacemon is very familiar.

"Although the uncertainty principle denies the existence of Laplacemon."

"But that means that at the microscopic level, the determinism of mechanics no longer applies."

"However, it is undeniable that in the field of macroscopic mechanics, determinism is still absolutely correct at present."

"In other words, within the scope of classical mechanics, random phenomena like those in quantum mechanics have not yet appeared."

“We can use mechanics to predict the orbits of celestial bodies, and fluid mechanics to predict the motion of water currents.”

"Maybe because of the complexity, we don't know what the water will look like in the next second."

"But mechanics must firmly believe that the movement of the system is regular."

"This rule is the certainty of mechanics itself." "I think this should be the consensus of all mechanics scientists."

Everyone looked strange when they heard this.

Is there any doubt about this?

This is the greatness of Newtonian mechanics.

Given the basic initial parameters, the evolution process of the entire mechanical system is determined.

Could it be possible that Newtonian mechanics could produce uncertainty?
This is a bit far-fetched.

For a time, everyone was talking about it.

Plant frowned slightly, thinking seriously about the meaning of this sentence.

It must not be simple!
At this time, von Karman could not help but ask:
"Professor Bruce, is there a problem with this?"

“The various branches of mechanics we study are based on this core.”

"Although the emergence of quantum mechanics and relativity has overturned many conclusions of classical mechanics."

"But at low speeds and macroscopic conditions, Newtonian mechanics can still be described as perfect."

Li Qiwei smiled slightly and said mysteriously:
"has a problem."

"Because I discovered a very strange phenomenon."

"Some time ago, Master Qian Wu asked me a question."

"For viscous fluids, when the temperature is uneven, for example, the temperature of the upper layer of the fluid is low and the temperature of the lower layer is high, how will it move?"

Wow!
Everyone exclaimed!

Master Qian Wu nodded to everyone and confirmed the matter.

Everyone was impressed that Mr. Qian was really interested in studying mechanics, and this problem was definitely one of the difficult and obscure ones in fluid mechanics.

Because nonlinear conditions are involved, generally speaking, the process and results are very complicated.

At the same time, everyone envied Master Qian Wu, because he had a great god like Professor Bruce standing behind him, and they could get answers to any questions they had.

At this time, Li Qiwei took out a pen and paper and started to calculate directly.

"Everyone, please take a look."

“I simplified this a little bit.”

"I expanded the velocity and temperature functions in the equation into a series and only took the first three terms."

“So, we can get a set of equations.”

“As shown in the picture.”

"The constant R of this system of equations is a variable. Different values ​​of R represent different stable solutions."

"When R=30, the fluid happens to undergo unstable convection."

"At this point, I need to solve this system of equations."

All the big guys came over to listen to Professor Bruce's explanation, and some even stood up.

The more everyone watched, the more shocked they were.

If Professor Bruce also studied mechanics, everyone here could go home and build rockets instead of doing academic research.

Bruce is enough for mechanics!

As an authority on fluid mechanics, Prandtl smiled and said:

"Professor Bruce, your idea is so brilliant."

However, he was curious.

Although this question is difficult, it is not so difficult that it makes people feel strange or subversive.

Plant was confident that if he was given some time, he would be able to do it.

"Is there any mystery?"

Li Qiwei smiled and said:

"Next, it's time to witness the miracle!"

"Everyone, take a look."

"When R is 30, the solution to this system of equations is a dynamic solution."

“Although I don’t understand mechanics, I know that there is a very important concept in this field: [periodic solution].”

“For a dynamic system, its solutions in the evolution process show regular periodicity.”

“For example, after the system has been running for a month, it may be back to the starting point.”

"Or the system keeps running, but there is some kind of pattern to it."

“This is the periodic solution.”

“I wonder if there will also be periodic solutions for viscous fluids with internal inhomogeneities.”

"However, calculating the solution to such an equation may require thousands of steps, which is very time-consuming."

"So I left the job to the guys in the institute."

"They counted all the way up to 3500 steps."

“Now, I write the results directly.”

Swish swish!
Everyone was suppressing their smiles.

"So that's how my subordinates use it."

"He has learned another trick to exploit students."

Soon, Li Qiwei finished writing the solution to the equation.

He exhaled lightly and said:
"Now, I can tell you what strange phenomenon I discovered."

"When the calculation reaches 1500 steps, it can be clearly seen that the solution of the equations shows periodic changes."

"This means that the movement of viscous fluids is regular."

"That may not be surprising."

"After all, many phenomena show cyclical changes."

"According to the normal development process, the system of equations will maintain periodic solutions and continue to cycle."

"However."

"After 1500 steps, things suddenly changed."

"The solutions to the system of equations have become completely random!"

"The periodic solution disappeared!"

“This is a bit unbelievable.”

"If it was a periodic solution before, how could it become a non-periodic solution without the influence of external forces?"

"That's impossible."

"At first, I thought the students were careless in their calculations and got the results wrong."

"So I asked Dirac to recalculate it."

"After his approval, the result was fine."

"So, it is true that the periodic solution of the system has become a non-periodic solution for some reason."

"To describe it in academic language, it is a deterministic dynamic system whose solution will transform into random irregular behavior under certain conditions."

"Its behavior is not repeatable, predictable, or deterministic."

"I gave this irregular phenomenon a name: chaos."

“I believe that chaos is a property unique to nonlinear mechanical systems and does not occur in linear systems.”

“Chaos theory overturns the consensus that classical mechanics remains deterministic in the macroscopic realm.”

"In other words, random phenomena can also occur in classical mechanics!"

"I think this conjecture should give you a little inspiration."

“These are my new discoveries in the field of mechanics.”

hiss!
quiet!
Deathly silence!

Everyone was shocked!

Their hearts were like a huge wave!
Chaos theory!

Random phenomena in macroscopic world mechanics!

These contents are simply subverting everyone's three views!
"Professor Bruce is horrible!"

(End of this chapter)