My IQ has been increasing year by year.
Chapter 239 Phenomenological Equations
Let's rewind the story to March for now.
In the dormitory corridor, most of the dormitories had already turned off their lights.
The door to dormitory 215 was pushed open.
Chen Zhuo rolled over in bed, opened his eyes groggily, and glanced at the alarm clock on the bedside table.
1:40 a.m.
Da Yong slammed the door shut behind him.
He walked to his desk and threw his schoolbag on the chair.
"Dayong?"
Chen Zhuo mumbled a call from his sleepy bed.
"Um."
Da Yong responded.
He didn't take off his coat, and even his shoes were kicked off by stepping on each other with his heels.
I lay on my back on the bed.
In less than half a minute, the snoring started.
Chen Zhuo turned over, pulled the blanket over his head, and continued to sleep.
It's 6:30 in the morning.
It was just dawn.
Before the alarm clock on Chen Zhuo's bedside table went off, a soft rustling sound came from below.
Dayong put on his shoes, opened his schoolbag, grabbed two thick books from the table, stuffed them inside, zipped up the bag, and went out the door.
The door closed very quietly.
Chen Zhuo sat up.
He glanced at Dayong's empty bed, the blankets rolled up in a ball.
Chen Zhuo got out of bed, walked to the table, picked up his water glass, and prepared to go outside to get a glass of water.
He paused as he passed Dayong's desk.
Da Yong's desk was messy.
Normally, the screwdrivers, multimeters, and circuit boards that were scattered around were all pushed to the very back.
The space that was cleared out was piled with several large books borrowed from the library.
The two books at the top are "Condensed Matter Physics" and "Statistical Mechanics".
There was a stack of papers next to it.
The paper was covered with various symbols and formulas.
Many formulas were crossed out halfway through writing.
For the next two weeks, Dayong maintained this routine almost every day.
I went back to my dorm after 1 a.m., fell asleep immediately, and left home at 6:30 a.m.
That noon.
Chen Zhuo returned from the cafeteria with his lunchbox.
Pushing open the door, I found Da Yong, who was rarely in his dormitory.
He sat in a chair, holding a steamed bun in his hand, staring blankly at a blueprint on the table.
The drawing on the blueprint is a complex diagram.
Chen Zhuo pulled out a chair, sat down, and opened his lunchbox.
"Didn't you go to the cafeteria?" Chen Zhuo asked.
Da Yong snapped out of his daze and took a bite of the steamed bun in his hand.
"I forgot to go, so I just grabbed a bite."
He chewed on his steamed bun, his brows furrowed.
Chen Zhuo picked up his chopsticks.
"What trouble have you been running into lately?"
Chen Zhuo asked casually.
Dayong swallowed the steamed bun and turned to look at Chen Zhuo.
"Xiao Zhuo."
Da Yong sighed.
"I think I've discovered something new inside the machine."
"What's new?"
"It's hard to say."
Da Yong scratched his head.
"Just before the material broke, I felt a pattern; I think I saw it."
Dayong put down the steamed bun in his hand, picked up the pen on the table, and pointed to the drawing.
"But when I reach out to grab it, it slips through my fingers like water. I'm trying to figure it out, and now I'm almost dying from all the calculations." Chen Zhuo looked at the pile of physics textbooks on Da Yong's desk.
"Can't you figure it out?"
There are too many variables.
Da Yong threw the pen on the table.
"Temperature, deformation, time, atomic displacement... I've crammed them all into a partial differential equation, and if one changes, they all change, making it impossible to solve." Chen Zhuo took a bite of rice and didn't say much more.
"Let's take it slow," Chen Zhuo said.
Da Yong didn't say anything, picked up the steamed bun, and continued to stare blankly at the picture on the paper.
The lab at the end of March.
Zhao Peng and Zheng Nan prepared a data report before the operation.
Dayong squatted next to the vacuum chamber, holding a wrench, and was checking the bolts on the base.
"Dayong, stop being stubborn, this guy is steady enough."
Zheng Nan walked over and handed Dayong a bottle of mineral water.
Dayong stood up, took the water, unscrewed the tap, and took a sip.
"Senior, should we continue with the test data for that batch of titanium-aluminum alloy?" Dayong asked.
Zhao Peng turned around in front of the computer.
"We're not doing it anymore. We've done over a hundred sets, and the average tensile strength has already been determined," Zhao Peng said.
"Professor Liu is urging us to submit the report; it has to be due this Friday."
"But that burr..."
Da Yong frowned.
"Let's put aside the burrs for now."
Zhao Peng walked over and patted Da Yong on the shoulder.
"As long as the general direction is correct, we need to move on and run the fluid simulation."
Dayong held the mineral water bottle, looking at the cold tensile testing machine.
"I'd like some more data," Da Yong said.
Zhao Peng was stunned for a moment.
"What data?"
"The more detailed the numerical values for when burrs appear under different temperature gradients, the better," Da Yong said.
Zheng Nan and Zhao Peng exchanged a glance.
"Dayong, that tiny fluctuation in the data doesn't mean anything. Don't get hung up on it," Zheng Nan advised him.
"I know," Dayong nodded.
"I just want to take another look."
Zhao Peng looked at the bloodshot in Da Yong's eyes.
"Okay, you can copy the original data packet as you like. As long as we don't use the tensile testing machine, you can turn it on and do the tests yourself anytime," Zhao Peng said. "Thank you, senior."
Dayong turned around and walked to the spare computer, then plugged in the USB drive.
Mid-April.
USTC Library.
Dayong sat at a table by the window.
There were more than a dozen books on solid-state physics and thermodynamics piled up in front of him.
He's been soaking here for almost a month or two.
The attempt to explain the macroscopic stress drop using microscopic atomic displacements has completely failed.
He couldn't figure it out.
He was just an ordinary student, lacking the ability of theoretical physicists to handle multidimensional nonlinear coupled equations.
He held a pen in his hand and was drawing circles aimlessly on a piece of draft paper.
My gaze fell on an open old book beside me.
It is a Chinese translation of "Statistical Physics" by Soviet physicist Landau.
The book turned to the chapter on phase transition theory.
Dayong's gaze swept across the pages of the book.
Suddenly, he stopped writing.
His eyes were fixed on one of the passages.
When dealing with the extremely complex phase transition problem, Landau did not calculate the microscopic motion of every single atom.
He invented a macroscopic term.
Order parameter.
Then, this parameter was directly plugged into a very simple Taylor series expansion.
Da Yong was stunned.
He read that derivation over and over again.
A sensation of electric current shooting through the body exploded from the scalp.
He sat up abruptly.
Since the microscopic details are impossible to calculate, then we won't bother calculating them.
When designing high-frequency circuits, if the influence of a bypass capacitor is so small as to be negligible, he will not hesitate to treat it as an open circuit and cross it off the drawing.
Aren't physical equations the same?
Dayong grabbed the draft paper in front of him, which was covered with complex partial differential equations.
These equations are packed with temperature, stretching rate, microscopic lattice constant, slip plane angle...
He looked at these variables.
"0.1 second..."
Da Yong muttered something under his breath.
The process of the material unloading force before the critical point lasted less than 0.1 seconds.
In such a short time, the heat simply doesn't have time to conduct.
Da Yong drew a heavy horizontal line on the variable representing the temperature gradient.
I crossed it out.
"Set it as a constant," Dayong said in a low voice.
Let's look at the next variable.
Weak disturbances in the secondary slip system.
The impact of this on the overall situation is like the high-frequency background noise in a circuit.
There's no need to calculate exactly how it works; you just need to add a filter.
Da Yong's pen fell to the ground once more.
Cross it out.
The number of variables on paper is decreasing.
Da Yong's wrist moved faster and faster.
He eliminated all those microscopic dimensions that attempted to precisely describe how each atom transitioned.
He created a dimensionless parameter himself.
A phenomenological parameter representing the degree of lattice unloading.
The original nonlinear equation, which was half a page long and involved a variety of interrelated variables, was cut down to just the bare trunk.
Da Yong stopped writing.
Looking at the last line of calculations on the paper.
A simple polynomial containing only three terms.
Dayong looked at it, his eyes shining with an alarming intensity.
He knew that it was sufficient for the tensile testing of this batch of titanium-aluminum alloys.
Early May.
Professor Liu's laboratory.
Zhao Peng and Zheng Nan are preparing for a new phase of destructive retesting.
This is the 120th test.
The vacuum chamber opened, and a new titanium-aluminum alloy sample was clamped into the fixture.
Zheng Nan took the torque wrench and tightened the bolt.
Dayong pushed open the laboratory door and walked in.
"Dayong? What brings you here today?"
Zhao Peng looked up at him from in front of the computer.
"Come and take a look."
Da Yong walked over to the control panel.
He looked at the software interface on the screen, which hadn't started running yet.
"Senior, what are the parameters for this test?" Dayong asked.
Zhao Peng pointed to the parameter box in the upper right corner of the screen.
"Constant room temperature of 25 degrees Celsius, tensile rate of 0.05 mm per second, routine destructive testing."
Da Yong nodded.
He took his notebook out of his pocket and opened it.
Tucked inside was the draft paper on which he had written the phenomenological equation in the old library.
Dayong took out a pen, leaned it against the edge of the workbench, and began to calculate on the blank page of his notebook.
Zhao Peng and Zheng Nan looked at him with some surprise.
Dayong calculated very quickly, taking less than a minute.
He stopped writing and closed his notebook.
He raised his head.
"Senior brother, we can begin," Dayong said.
Zhao Peng placed his hand on the mouse, ready to click the start button.
"etc."
Da Yong's voice was very steady.
"If we run it with these parameters, when the absolute tensile force reaches 850 MPa, the stress curve will drop by 0.15 MPa ahead of schedule." Zhao Peng stopped and looked up at Da Yong.
Zheng Nan also turned his head.
"Then at 852 MPa, the material will completely fracture," Da Yong continued.
The lab was silent for a few seconds.
Zhao Peng looked at Da Yong, then at Zheng Nan.
"You figured that out?" Zhao Peng asked.
"Um."
Da Yong nodded.
Zhao Peng didn't say anything more and turned his gaze back to the screen.
"Let's give it a try."
Press the left mouse button with your index finger.
The tensile testing machine is started.
A low, mechanical hum emanated from the vacuum chamber.
On the screen, the green real-time stress curve starts from the origin of the coordinate axis and steadily climbs to the upper right.
None of the three spoke.
All eyes were fixed on the green line on the screen.
Over time, the metal inside the cavity is subjected to increasing tension.
The curve gradually rises.
500 MPa.
600 MPa.
700 MPa.
Zhao Peng's breathing became heavier, and his body involuntarily leaned forward, almost touching the monitor.
Zheng Nan stood to the side, gripping the back of the chair tightly with both hands.
800 MPa.
The green line remains a perfectly straight diagonal line.
840 MPa.
845 MPa.
848 MPa.
Da Yong stood still, his hands in his pockets, his expression unchanged.
The moment the vertical coordinate of the green line jumps to 850.
The green line on the screen, which had been smoothly rising, suddenly dipped downwards.
An extremely conspicuous burr.
Zhao Peng gasped sharply.
His eyes were fixed on the extent of the collapse.
0.15.
Exactly.
next second.
The green line struggled upwards a little longer.
It reached the 852 mark.
"Clang!"
A crisp yet muffled cracking sound came from inside the vacuum chamber.
The green line on the screen plummeted instantly, dropping to zero.
The material is broken.
The laboratory was deathly silent.
The only sound is the humming of the cooling fan after the tensile testing machine stops running.
Zhao Peng's hand was still frozen on the mouse.
Zheng Nan slowly released his grip on the back of the chair and turned to look at Da Yong.
His eyes were filled with shock, as if he had seen a ghost.
"Holy crap!"
After holding it in for a long time, Zheng Nan finally uttered two words.
Zhao Peng turned his chair around and looked at Da Yong.
"Dayong, what... what did you use to calculate that just now?"
Zhao Peng's voice sounded a little strained.
Dayong took his hand out of his pocket and patted the old notebook.
"We eliminated the useless micro-variables and created an approximate model."
Zhao Peng stood up.
"Walk."
"Where to?"
"Go to Teacher Liu's office."
Zhao Peng's tone was somewhat urgent.
"Take your notebook with you."
It was an afternoon in mid-May.
Sunlight streamed through the window into Professor Liu's office.
Professor Liu sat on the mahogany sofa, holding a cup of freshly brewed green tea in his hand.
Zhao Peng and Zheng Nan stood to one side.
Dayong sat on the single sofa opposite Professor Liu.
The coffee table has been emptied.
Da Yong untied the rubber band and slowly spread out the huge coordinate paper covered with red and blue dots on the dormitory floor on the coffee table.
Because it was rolled for too long, the edges of the paper curled up a bit.
Dayong took the two ashtrays from the table and placed them on the corner.
On the drawing, more than eighty scattered points converge into a perfectly smooth curved surface under a specific coordinate mapping.
Dayong took the notebook out of his pocket and turned to the page with the phenomenological equations written on it.
Hand it to Professor Liu.
Professor Liu put down his teacup and took the notebook.
He put on his glasses and looked down at the page.
The only sound in the office was the ticking of the clock on the wall.
Professor Liu looked at it for a long time.
After looking at the formulas in my notebook, I went to look at the graph paper spread out on the coffee table.
His gaze shifted back and forth between the formulas and the drawings.
"Did you derive this formula yourself?"
Professor Liu looked up at Dayong.
Da Yong nodded.
Professor Liu placed his notebook on the graph paper.
"You haven't taken into account the microscopic dislocation density and slip system at all."
Professor Liu pointed to the formula.
"I can't figure it out; there are too many variables."
Da Yong was very calm.
"So you just created a parameter out of thin air?"
"right."
"I don't need to know exactly how many atoms are cracked inside. Before this batch of titanium-aluminum alloy fractures, the release pattern of internal potential energy is fixed. As long as irrelevant external variables are filtered out, this pattern can be quantified."
Dayong pointed to the curved surface on the drawing.
"Professor Liu, as long as we apply this formula and input the current tensile rate, the fatigue fracture critical point of this batch of materials under any environment can be accurately predicted in advance."
Professor Liu leaned back on the sofa.
He took off his glasses and slowly wiped them in his hand.
He looked at Dayong sitting opposite him.
There is no sophisticated microscopic theoretical derivation, nor rigorous mathematical tensor analysis.
There was only a crumpled coordinate sheet and three lines of formulas that had been cut down to their core.
For the military's general assembly project team, the most troublesome issue over the past six months has not been whether this batch of materials is tough enough.
The real question is when this batch of materials will suddenly stop.
Metal fatigue prediction is a critical weakness in the development of aero-engines.
Although Da Yong's model looks somewhat crude, in engineering applications, once it is written into the underlying code of the detection equipment, it becomes a ready-made military-grade fatigue early warning system.
"Zhao Peng".
Professor Liu suddenly spoke.
"Yes, teacher."
Zhao Peng quickly responded.
"Have you saved the test data from the 120th group?"
"Saved."
"Organize the data and put it together with the previous hundred or so sets of data."
Professor Liu put his glasses back on.
"Give me a complete report by tomorrow morning."
"OK."
Professor Liu turned to look at Dayong.
"Da Yong".
"Teacher Liu."
Da Yong sat up straight.
"Leave this formula and this drawing with me."
Professor Liu pointed to the coffee table.
"OK."
Da Yong nodded.
I'm going to the capital tomorrow.
Professor Liu picked up his teacup and took a sip of water.
"There's a meeting for a project progress report."
Professor Liu looked at Dayong, his tone becoming very serious.
"Don't go anywhere these next few days, just stay at school and keep your phone on."
"it is good."
Professor Liu waved his hand.
"Alright, you guys go back now. Zhao Peng, get the report done quickly."
Zhao Peng and Zheng Nan led Da Yong out of the office.
In the corridor.
Zheng Nan let out a long sigh of relief and patted Da Yong on the shoulder.
"Dayong, you're really going to be something else."
Zheng Nan lowered his voice and said.
Da Yong scratched his head and smiled, without saying anything.
He went down the stairs.
Stepping out of the lab building, it was already dark outside, but the streetlights were on.
Dayong walked alone on his way back to the dormitory.
The feeling of pressure on my chest and difficulty breathing that I had for the past three months is completely gone.
He felt his steps were very light.
Back in the dormitory building, I went up to the second floor.
Pushing open the door to room 215, I saw the lights were on inside the dormitory.
Chen Zhuo sat in front of his computer, the screen displaying lines of complex symbols.
Hearing the door open, Chen Zhuo stopped knocking and turned around.
Dayong walked to his desk, pulled out a chair, and sat down.
"Xiao Zhuo."
Da Yong shouted.
"Um."
"I've figured it out."
Da Yong turned around, looked at Chen Zhuo, and said calmly, without any particularly excited expression.
Chen Zhuo looked at him.
"What did you use to calculate it?" Chen Zhuo asked.
"Cut off the useless ones," Da Yong said.
Chen Zhuo nodded, a gentle smile appearing on his lips.
He turned around and put his hands back on the keyboard.
"Congratulations."
Chen Zhuo's voice came through the clatter of the keyboard.
Dayong leaned back in his chair.
He glanced at the few dusty theoretical physics books on the corner of the table.
I stood up and stuffed them all back to the bottom of the bookshelf.
He took the basin and towel.
"I'm going to take a shower."
Da Yong called out to Chen Zhuo's retreating figure, opened the door, and went inside.
The sound of running water came from the bathroom.
Chen Zhuo sat in front of the computer and continued typing his article.
May is halfway over.
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