73: Chapter 73 The Battlefield of Documents

In the summer of the sixteenth year, Jiang Lin finally felt that he was qualified to go back and face that patch of mud.

Thus, he opened the long-dusty "Replicate_Biskamp_1986" project.

Armed with the rigorous "Numerical Health Check Checklist V1" on the wall, and the awe of physical multi-scales learned from Bender & Orszag, he completely overthrew and rewrote the C++ code.

This time, he no longer blindly increased the parameters.

He intentionally pulled the aspect ratio of the current sheet precisely above the instability critical threshold derived by Loureiro's theory.

At the same time, he used high-order numerical schemes to suppress numerical dissipation, ensuring that the grid resolution could perfectly resolve the inner diffusion region.

The program ran for a full twenty-three days.

Jiang Lin was not as anxious as last time; he even had the mood to overhaul the old wind turbine.

On the evening of the twenty-third day, the results came out.

Jiang Lin pulled up the animation.

On the screen, that Sweet-Parker Model current sheet, which originally looked like a noodle, suddenly bulged out a small black dot in the center during the middle of its evolution.

The zero point of the anti-parallel magnetic field, the embryonic form of the magnetic island.

Jiang Lin held his breath and didn't move.

Shortly after, the second small black dot appeared, then the third, and the fifth.

After just a dozen time steps, the entire taut current sheet was like a glass fiber subjected to extreme pressure, and its internal stress network completely collapsed.

It shattered from the inside with a bang, turning into a long string of magnetic island structures of varying sizes that swallowed each other.

The perfect nonlinear Plasmoid instability reproduced!

Jiang Lin finally saw with his own eyes in his own code that the original long noodle of the Sweet-Parker Model was not destined to despairingly slow down forever.

When it slowed to the extreme and was stretched to its physical limit, it would choose a mutually destructive shattering.

The entire huge necrotic structure continuously subdivided into countless microscopic fast reconnection regions during evolution, constantly recombined, and finally burst out with an astonishing energy release rate.

In a desperate situation, Physics found its own way out.

Jiang Lin was not intoxicated by victory; he immediately turned around and looked at the twelve items of the "Health Check Checklist" on the wall.

He began to strictly execute the full set of perturbation tests.

Increasing the grid resolution by a factor of two overall, the magnetic island chain still appeared, with minor position adjustments, but the topology remained unchanged.

This proved convergence.

Raising the Lundquist number by another order of magnitude, the magnetic islands became denser and the fragmentation more violent, consistent with theoretical predictions.

Changing the spectrum distribution of the initial perturbation, although the early evolution path had differences, the final nonlinear state reached the same goal by different paths.

After each rigorous interrogation, the magnetic island string as an overall physical phenomenon, like a piece of steel tempered through a thousand trials, stood firmly there.

Jiang Lin opened the project log and wrote the closing statement in a rigorous tone.

"This numerical result still stably exists after grid refinement and parameter perturbation, passing the twelve items of the health check list."

"However, please note: The conclusion is limited to the current two-dimensional MHD parameter interval and cannot be easily extrapolated to the high-dimensional real scale of the Wasteland sky."

"Archive Name: MR-PLM-04 (Magnetic Reconnection - Plasmoid - 04)."

Then, he walked to the north wall of the Stone House.

This wall was the place he used to draw the history map of research.

Picking up his pen, below the block of Plasmoid theory, he drew a heavy checkmark and marked it.

"Limited Credibility"

Jiang Lin looked at it and let out a long breath of turbid air.

In the seventeenth and eighteenth years, Jiang Lin's exploratory tentacles continued to extend to the microscopic level, starting to tackle collisionless reconnection and the Hall effect.

This was the zone where single-fluid MHD theory began to completely collapse.

When the plasma became extremely thin, such as in the Earth's magnetosphere or the upper atmosphere of the Wasteland, collisions between particles almost disappeared.

At this time, the assumption of treating plasma as a uniformly conductive fluid no longer held true.

Due to the vast difference in mass, electrons and ions began to part ways.

The paper of the GEM magnetic reconnection challenge was a monument that could not be bypassed.

This was a rare collective grand military parade in the academic community.

Nine top international research groups, bringing their respective proud nine completely different numerical codes, calculated the same preset reconnection problem.

The paper's conclusion was extremely glaring, as if it had slapped single-fluid MHD hard across the face.

No matter what flashy numerical methods you used, as long as your Physics equations included the Hall effect, the reconnection rates calculated by all codes would ultimately and startlingly converge to a similar fast reconnection value.

Conversely, if you stubbornly used only single-fluid MHD, even if your code was written to perfection, the result would without exception tragically slide back to the desperate slow road of the Sweet-Parker Model.

If it were reading textbooks in the past, Jiang Lin would only see a dry sentence summarized in the textbook.

"Studies show that the Hall effect becomes exceptionally important in small-scale diffusion regions and is the key mechanism triggering fast reconnection."

But Jiang Lin now was a veteran who had developed antibodies against this textbook style.

He didn't look at the praise in the main text at all and turned directly to the appendix.

Like a harsh prosecutor, he used a magnifying glass to compare the grid parameters, boundary conditions, initial perturbation types, and numerical dissipation schemes set by the nine research groups.

After looking at it for a week, he understood.

The results of the GEM challenge were of course extremely great; it was a turning point in history.

But it was not the ultimate truth.

What it truly proved was that within that cage of special initial perturbations and boundary conditions jointly agreed upon by the nine groups, the Hall effect was the ruler.

If you changed to another boundary, or another three-dimensional turbulent environment, could the Hall effect still be so immediate?

No one dared to guarantee it.

Jiang Lin walked to the research history map on the north wall and drew a circle around the GEM challenge.

"Strong evidence, but the qualifying conditions are very clear and cannot be arbitrarily generalized and extrapolated."

This was already an extremely high evaluation Jiang Lin could give.

What truly plunged Jiang Lin into a long silence was another paper.

Burch, J. L., et al. (2016). Electron-scale measurements of magnetic reconnection in space.

Published in "Science".

This was a miracle in the history of human observation.

The MMS satellite formation.

Four expensive satellites formed a tight tetrahedral array, with a distance of only a mere few kilometers between the satellites.

This was practically face-to-face in the vast space.

Like four delicate silver needles, they plunged headfirst into the Earth's magnetopause.

Then, directly in space, they caught that legendary electron diffusion region that only existed on paper and in supercomputers.

That was a microscopic physical structure with a scale of only tens of kilometers.

To catch a glimpse of it in this fleeting space, humanity burned billions of dollars in funding and deployed top-tier aerospace engineering technology just to get this data chart.

At night.

Jiang Lin sat at the table in the Stone House, staring at the phase space distribution map with tetrahedral coordinates in the paper.

He looked at it for a very, very long time.

His Observation Point A and Observation Point B, coupled with a moving observation line, formed a maximum observation baseline of a pathetic 2.5 kilometers.

Low-light cameras, civilian magnetometers, anemometers, homemade time benchmarks...

These things could record the Wasteland sky and tell him the red band was not an illusion, but they could never send him into the subtle electron diffusion region dozens of kilometers high in the upper atmosphere.

He wanted to use observations on the Wasteland to verify the Hall electric field?

It was simply impossible.

He wanted to capture the real-time microscopic particle distribution of fast reconnection like MMS?

That was daydreaming.

He wanted to plunge into the magnetopause like four probes?

Don't even think about it in this lifetime.

The technological barriers of aerospace engineering, detector arrays, and in-situ observations lay between him and that layer of truth.

However, Jiang Lin did not feel humiliated or unwilling like a passionate manga protagonist.

After all, it wasn't his first time recognizing the cruelty of boundaries.

He got up, opened the door, and walked out of the Stone House.

It was the depth of winter. The Wasteland sky presented a sickly grayish-blue.

That year-round faint light-red band in the low northern sky did not appear tonight, seemingly blocked by heavy radiation clouds.

wind turbine no. 2 was rotating slowly and persistently on the spire.

Jiang Lin stood under the tower with his hands in the pockets of his windbreaker for a full half hour until white frost formed on his eyelashes.

Returning to the Stone House, he opened his notebook and wrote on the newest page.

"The MMS satellite formation spent money I could never get in several lifetimes to see a microscopic world I could never see with my mortal eyes."

"What I can do is start from that structure they have already confirmed to exist at the summit and push backward. If such a strong electron diffusion region really happens in the high altitude above my head, during its downward radiation process, will it leave some kind of macroscopic projection at the foot of the mountain in my old camera, on this 2.5-kilometer-long baseline, and in this red band of the night sky?"

"I can't see the snow at the summit clearly."

"But if an avalanche happens at the foot of the mountain, and I map the debris distribution of the avalanche in the mud, that is also a kind of surveying and mapping. Deducing the microscopic from the macroscopic is the only path I can take."

After writing these paragraphs, he walked to the north wall and made an unprecedented special mark next to that shining paper by Burch 2016.

Then he wrote beside it.

"Untouchable High Point"

And noted a line of small characters below.

"This is the star I use to orient myself in the dark night, even though I know that is definitely not a place this physical body of mine can reach."

His heart was as still as stagnant water.

In the spring of the nineteenth year, the Wasteland welcomed a rare period of calm with no sandstorms and no acid rain.

But Jiang Lin ushered in the third major stagnation of his research career.

This stagnation was more desperate than the previous two.

The previous two times, whether it was the C++ code crashing or the algebraic derivation of asymptotic matching being impenetrable, were at least within the scope of Physics and engineering.

As long as time was spent, a foothold could always be found.

But this time, he was stuck in front of a theoretical literature about the mathematical rigor proof of Plasmoid instability.

The paper attempted to prove from the perspective of pure mathematical partial differential equation analysis that under certain limit theorems, the rupture of magnetic islands was inevitable.

Then Jiang Lin found himself turned into an illiterate.

Every line of inequality transformation in this paper seemed familiar when taken apart.

But he couldn't read it at all.

He was completely unable to understand the terrifying weight belonging to the modern mathematical system truly borne behind those symbols.

The article was filled with such vocabulary.

Sobolev norm estimates, global existence of weak solutions, a priori energy inequalities, improvement of spatial regularity...

These words, Jiang Lin had vaguely seen when self-studying Advanced Mathematics and functional analysis.

He could only barely recite the definition of inner product space or completeness on scratch paper.

But when these dry definitions were forcibly stuffed into an extremely complex nonlinear MHD system of equations, used as bricks to push a thirty-page long proof chain forward, Jiang Lin clearly felt for the first time that he was standing outside the door of a towering, smooth iron wall reaching into the clouds.

With his strong algebraic foundation, he could mechanically verify whether a certain integral inequality in the paper was scaled correctly.

But he couldn't judge at all why the author had to jump from the space on the left to the space on the right.

Why use a weak convergence here, and a compactness theorem there?

Why must this bridge of logic be built this way?

Mechanical verification could only prove that he didn't calculate this step of the arithmetic problem incorrectly.

It could completely not prove that he understood this huge and precise set of higher-level mathematical tools.

That night, Jiang Lin sat in front of the screen, looking at the paper full of integral signs, and shook his head with self-deprecation.

He decisively closed the literature reader.

In the root directory of the workstation, create a new folder.

[Sobolev_Energy_Methods]

Then, he skillfully brought up three legendary books in the field of pure mathematics that were famous enough to make countless graduate students go bald.

Evans's "Partial Differential Equations".

Brezis's "Functional Analysis, Sobolev Spaces and Partial Differential Equations".

Temam's "Navier-Stokes Equations: Theory and Numerical Analysis".

The icons of the three e-books were lined up on the desktop, like three moss-covered stumbling blocks pressing down on his threshold to truth.

Jiang Lin opened a new page in his paper notebook and wrote heavily:

[This is the closest I have ever been to independently and rigorously proving a theorem in the field of magnetic reconnection in mathematics.]

[Yet, pathetically, I found myself lacking a complete set of modern mathematical tools for building bridges.]

[Stop talking nonsense and go learn how to build the tools first.]

For the next year and a half, the rhythm inside the Stone House in the Wasteland became so monotonous it was almost self-abasing.

Like a lonely mathematical believer, he plunged headfirst into the abstract topological world constructed by Evans and Brezis.

Evans pressed him into the mud of partial differential equations and rubbed him against it repeatedly.

There, Jiang Lin's worldview was reshaped.

Previously, a solution to an equation meant calculating an expression with x and t, such as u(x, t) = sin(x - ct).

Physics intuition told him that waves propagated this way.

But in Evans's world, for nonlinear equations, whether a solution existed was by no means explicitly writing out a formula.

That was a narrow bridge pieced together by countless extremely fragile logics.

Step one: first construct a series of smooth approximate solutions.

Step two: use extremely delicate a priori estimates, such as multiplying a certain term by the equation itself and then integrating by parts, to prove that a certain energy of these approximate solutions was controlled.

Step three: use the boundedness of this energy to lead to weak convergence.

Step four: use the compactness theorem to extract a strongly convergent subsequence from the weakly convergent sequence.

The final step: let the limit quantity take the limit, proving that this shadow-like limit actually satisfied the original equation.

Every step on this bridge, as long as a single inequality scaling missed even a tiny error, would cause the entire bridge to collapse instantly.

There was no room to muddle through.

Jiang Lin truly understood for the first time why a mathematical energy inequality that seemingly had no Physics significance could possess such enormous power.

It could determine whether an entire family of approximate solutions was qualified to survive to the other shore of the limit.

And what stuck him the longest was the Sobolev embedding theorem in Brezis.

Previously, it was just a few poorly formatted theorems in textbooks.

Now, in Jiang Lin's eyes, it had turned into a strictly stratified border map of the Wasteland.

"In this world, if you want to possess a certain privilege, you must exchange it with another resource."

Jiang Lin drew diagrams on his handwriting tablet and muttered to himself.

With different spatial dimensions, different differentiability indices k, and different integrability indices p, the spatial properties you could embed into were entirely different.

Even if you fell short by just a tiny bit of index and crossed that line, mathematics would mercilessly throw a divergent counterexample at you, telling you that this path was blocked.

Jiang Lin was an extremely stubborn person.

He spent a full two months deriving all the commonly used embedding theorems under high-dimensional and low-dimensional cases, arranging them into a huge table.

In this table, behind every embedding theorem, he stubbornly attached a counterexample he constructed himself or found in books.

That huge table full of counterexamples was later taped by him to the north wall of the Stone House.

It was not to show off learning.

It was to remind himself of one sentence every time he looked up.

In front of nonlinear equations, regularity was never a wish you could have just because you wanted it.

It was a condition you had to trade your life for.

Brezis completed the chassis of his functional analysis.

Weak convergence, compactness, dual space, reflexive space...

These terms used to be like a pile of lifeless specimen names in his mind.

After reading Brezis, they came alive and turned into sharp scalpels in his hands.

Jiang Lin could finally understand which segment of weight those abstract words in previous proof articles were bearing within the entire logical chain.

Strong convergence was the limit of solid gold and silver.

But strong convergence was too hard to obtain.

So settling for second best, weak convergence only gave you a vague shadow.

And the compactness theorem was the magic hand responsible for re-condensing those vague shadows into touchable entities within certain specific low-order spaces.

Could this re-condensed entity be brought back into the original nonlinear equation?

That depended on whether your initial a priori energy estimate in the first step was done correctly and whether it leaked.

Linked ring by ring, it was breathtakingly beautiful.

Coming to Temam's Navier-Stokes equations.

This was already the Bible of fluid mechanics.

Although the Navier-Stokes equations were not MHD containing a magnetic field, they possessed extremely similar mathematical skeletons.

Incompressible condition.

Annoying nonlinear convection term.

Diffusion term responsible for smoothing everything out.

As well as that extremely rigorous Leray-Hopf weak solution construction method ranging from a priori estimates to Galerkin approximations, and then to compactness lemmas, ultimately obtaining weak solutions.

Late at night on the day Jiang Lin read the proof of the existence of the Leray-Hopf weak solution, wind turbine no. 2 outside was emitting a steady low whistle.

He closed his eyes, and in his mind were no longer color images run by code, but abstract spaces intertwining with one another.

For the first time, he felt that when facing a system of nonlinear partial differential equations that could not yield analytical solutions, humanity was not limited to numerical simulation alone.

Pure mathematics provided a more aloof and ruthless path.

Although you could not calculate its exact appearance, you could use a chain of energy inequalities to force it into a dead corner bit by bit.

This approximation was not complete taming, because the solution might still undergo singularity blow-up locally (Blow-up, Millennium Prize Problems).

But this set of chains could at least guarantee that within a certain specific spatial category, it could not run amok at will.

In the winter of the twentieth year, when the first heavy snow sealed the doors.

Jiang Lin turned the last page of Temam.

The three legendary books were finally finished reading.

Inside that [Sobolev_Energy_Methods] folder, it was already stuffed with thousands of pages scanned by his phone—his own exercise calculations, overthrown counterexamples, and functional space relationship diagrams drawn like strategic maps.

He did not immediately return to that Plasmoid rigorous proof paper that had blocked him outside the door.

Instead, he stood up and walked to the north wall.

Beside the research history map on the left that occupied more than half of the wall, he newly carved out a dedicated rectangular area with a pen.

[Mathematical_Toolbox (Mathematical Arsenal)]

Then, he listed line by line below the three sets of heavy weapons he had forged over the past decade to cross the barriers.

[1. Numerical PDE Higher-Order Theory and Verification — Used for interrogating machines.]

[2. Asymptotic Matching and Singular Perturbation — Used for crossing scales.]

[3. Sobolev Spaces and Nonlinear Functional Energy Methods — Used for forging chains.]

After writing these three lines, he walked back to the workbench and opened the notebook, which was already on its third volume.

On the penultimate page, he wrote a passage extremely similar to the one five years ago, but with a world of difference in confidence.

[For Plasmoid classes and MHD nonlinear rupture problems, the underlying mathematical tools have all been fully reserved.]

The first time he wrote similar words was after reading Bender & Orszag.

At that time, he only vaguely felt that he might be able to derive something by copying the pattern.

But this time, it was no longer a maybe.

He clearly saw a path that was extremely narrow but completely feasible.

That was a path leading from the most macroscopic current sheet breakup, passing through the boundary layer of asymptotic matching, and ultimately leading to giving strict weak solution constraints using functional energy methods.

He did not start running on this path immediately.

Because of the current lack of observational data, it was not yet worth mobilizing this heavy firepower to engage in theoretical spinning in place.

But he knew that these two lines—the red band observation in the Wasteland sky and this set of ultimate mathematical weapons on the wall—had each lit up in his heart.

If the timing matured, they would inevitably converge roaringly at the exact same extremely dangerous singularity.

In the twenty-first and twenty-second years, Jiang Lin cast his gaze toward two branches in the field of magnetic reconnection that were extremely massive and closely connected to industry.

Turbulent reconnection and fusion device tearing modes.

He first read the foundational work on turbulent reconnection: Lazarian, A., & Vishniac, E. T. (1999). Reconnection in a weakly stochastic field.

Before this, all the models Jiang Lin had read were striving to find a special microscopic geometric mechanism to accelerate reconnection.

But the Lazarian-Vishniac (LV99) theory directly flipped the table.

Because the core idea of the LV99 theory was extremely wild.

If the magnetic field in the plasma itself was in a state of highly chaotic turbulence, then under huge macroscopic scales, countless tiny, born-and-dying small-scale reconnection events would occur simultaneously.

Because the magnetic field lines wandered in three-dimensional space like a ball of tangled hemp, the contact points where they intersected increased exponentially.

The overall reconnection rate naturally became faster.

The most fascinating and terrifying aspect of this theory was that.

It didn't care at all what the underlying single microscopic mechanism actually was.

Whether you were the Sweet-Parker Model or the Hall effect, under macroscopic statistical averaging, all those microscopic details were smoothed out by turbulent effects.

It directly redefined magnetic reconnection from a single geometric event that needed to be precisely dissected into a statistical phenomenon composed of massive random events.

When textbooks wrote about turbulent reconnection, they always glossed over it with a stroke, giving a reconnection rate formula proportional to turbulence intensity and calling it a day.

But when Jiang Lin bit the bullet and chewed through the original manuscripts of LV99 and subsequent developments, he felt a deep sense of incongruity.

The research route of turbulent reconnection was the one among all reconnection theories that least resembled traditional theoretical Physics, and instead most resembled engineering statistics.

It didn't care about local details; it only cared about the overall power spectrum and statistical ensemble.

This was actually very similar to what Jiang Lin had been doing on the Wasteland for over twenty years.

His observation equipment was extremely crude, and the signal-to-noise ratio of a single photo was very low.

He relied on the stacking of a large amount of low-quality data and statistical averaging over time series to barely squeeze out a little credible auroral red band signal.

The train of thought was identical.

Logically speaking, he should have felt affectionate toward this theory.

But he couldn't read on.

Because in order to give a rigorous mathematical proof of the LV99 theory, later comers mobilized two sets of tools even more unfamiliar to him than Sobolev spaces.

To continue delving into this line, he could not bypass turbulence statistics, random fields, scale cascades, or even certain languages borrowed from statistical field theory and renormalization groups.

These were ultimate killer weapons directly borrowed from condensed matter Physics and quantum field theory.

Jiang Lin leaned back against the chair back, looking at the renormalization group flow equations on the screen.

In his toolbox, there was no reserve whatsoever for these two things.

Statistical field theory required extremely high partition function integration techniques.

Renormalization groups required understanding fixed points and critical exponents under scale transformations.

To patch together these two sets of tools on the Wasteland without the guidance of a mentor, and reach a level where he could independently derive and calculate them himself, Jiang Lin pondered silently in his heart.

It would require at least three brick-sized books at the level of Quantum Field Theory.

It would require at least three to five years of pure catch-up time.

But that was still not the most troublesome part.

To take a step back, even if he spent five years becoming an expert in the renormalization group, so what?

In the LV99 theory, wanting to predict the reconnection rate required inputting several key microscopic parameters.

The local turbulent injection scale, the anisotropic turbulent power spectrum index, and the small-scale Alfvén Mach number.

Jiang Lin turned his head to look outside.

What was the data he could acquire?

It was that civilian magnetometer on the ground, which could only read out a total magnetic field vector after attenuation through tens of kilometers of the atmosphere.

It was utterly impossible for him to acquire the high-altitude in-situ turbulent power spectrum of the area where that red band was located.

This was a dead end.

Jiang Lin weighed it in front of the workstation for a whole afternoon.

Patch it, spend five years, and obtain a set of dragon-slaying arts.

Not patch it, for the huge branch of turbulent reconnection, he could only remain at the superficial level of understanding formulas summarized by others in review articles, forever unable to personally step into the field to verify them.

Finally, he stood up and walked to the [ Mathematical _ Toolbox ] area on the north wall.

Picking up a pen, below the previous three tools, he wrote down the fourth one very forcefully.

[ 4 . Statistical Field Theory and Renormalization Group Methods — Actively choose not to patch. ]

Then he added a line of red annotations below.

[ Reason: The time cost of acquiring this tool is too high. And even if completed, it is absolutely impossible to use it to independently verify any of my ground Wasteland observation data. ]

[ This is not shrinking back or giving up, this is an acknowledgment of the boundaries of real Physics, knowing when to stop avoids danger. ]

After writing this passage, Jiang Lin did not have a trace of regret in his heart.

This was a composure belonging to a mature person that could only be possessed after crossing countless mountains.

He knew what he could change, and even more, he knew what he could not change.

Immediately following that, in the second half of the twenty-second year, Jiang Lin quickly skimmed a large number of papers on tearing modes in tokamak devices.

Tearing modes.

This was one of the instabilities that gave physicists dedicated to controlled nuclear fusion the biggest headache.

It would tear open the magnetic surfaces in the extremely high-temperature plasma ring, leading to the collapse of confinement.

When Jiang Lin put the equations of the tearing mode and the equations of spatial magnetic reconnection together for comparison, he couldn't help but smile.

Essentially, they were the exact same Physics.

They were not the same problem, yet they shared the same class of Physics core: magnetic topology changes, magnetic energy release, fluid/electromagnetic coupling, and the strong constraints of boundary conditions on the evolutionary path.

What was the only difference?

Boundary conditions.

Magnetic reconnection in Solar Flares and the Earth's magnetopause occurred in a vast open space with nearly free boundaries.

Whereas the tearing mode in a tokamak was locked tightly inside a closed doughnut with a strong toroidal magnetic field, a conductive metal wall, and complex geometric curvature.

The boundaries were completely different, but the core Physics engine was the same.

Not far away, wind turbine no. 2 was rotating steadily in the wind.

This entry-level commercial wind turbine he had bought had been modified, repaired, and tuned by him countless times.

On the foundation nearby lay the wreckage of the disassembled old wind turbine.

The old wind turbine had been handcrafted by him during his fifth Wasteland, with many parts coming from the wreckage of the Wasteland World.

Two wind turbines.

One was a product of high industrial standards, and one was a defective handmade geek product of the Wasteland.

Their shapes were completely different, their craftsmanship was worlds apart, and their origins had nothing to do with each other.

But they were both doing the same thing: converting the kinetic energy of the wind into electrical energy.

The core Physics laws they followed had the exact same ancestor.

The fluid dynamics incidence calculation of the wind, the decomposition of blade angle of attack and lift-drag, Faraday's law of electromagnetic induction inside the generator, the rectifier bridge converting AC to DC, and finally the storage battery energy storage.

This entire set of Physics processes was absolutely valid for both wind turbines.

The reason they looked different and behaved differently was simply because the boundary conditions under which they were concretely implemented were different.

The relationship between Solar Flares and tokamak devices.

The relationship between space plasma and laboratory plasma.

Just like the relationship between wind turbine no. 1 and wind turbine no. 2.

Jiang Lin turned around and created a brand-new, and also the final summative folder in the workstation.

Named: [ Same _ Physics _ Different _ Boundaries (Homologous Physics and Heterogeneous Boundaries) ]

He did not put any papers inside.

He just created a text document named README . md inside and wrote a sentence.

[ There is always only one core engine, and the myriad forms of all things in the world are all transformed by the differences in boundary conditions. ]

On the last day of the twenty-second year, December 31st.

The Wasteland ushered in an extremely rare bitterly cold night.

The temperature plummeted, but the sky was unusually clear without a trace of clouds.

Inside the Stone House, Jiang Lin turned off all the screens. The only illumination was the camping lamp overhead.

He stood in front of the north wall.

The entire huge north wall had already been densely crawled over by his research history map.

That was the territory he had conquered inch by inch over a full ten years.

Class A core paper intensive reading, accompanied by hand-derived formulas and reproduction verification, eighty-two pieces.

Class B key paper thread combing, four hundred and twenty-one pieces.

Class C extensive reading and index database archiving, four thousand and thirty-six pieces.

Every slightly important article had been marked by Jiang Lin on the wall with lead wires and labels.

What was marked was not how great the conclusions of the papers were.

What was marked was what their most fragile assumptions were, how many insurmountable order-of-magnitude barriers separated them from the phenomena he could observe on the Wasteland, and which family tree with the same core but different boundaries they belonged to.

The marks on this wall were eclectic and varied, not looking like a scholar's knowledge tree at all.

It looked more like a theater map drawn by a veteran who had been through countless battles.

Green mark: [ Limited Credibility ].

Those nonlinear structures like Plasmoids that he had reproduced himself using rigorous PDE codes.

Yellow mark: [ Partially Verifiable ].

Logical closed loop, but experimental conditions as harsh as the GEM Challenge.

Red mark: [ Completely Unverifiable ].

Castles in the air that are mathematically self-absorbed and physically completely ungrounded.

Blue mark: [ Refuted by Counterexamples ].

Old theories that had been solidly overthrown by higher-dimensional simulations or observations.

Black mark: [ Mathematically Self-Consistent But Physically Isolated ].

Purple mark: [ Misinterpretations by Later Generations ].

Annotations forcefully added by later generations of textbooks; the original author did not hold this view back then, such as Parker's original intention.

And that black star: [ Untouchable High Point ].

Every lead wire, every color block, every line of annotation was permeated with the smell of gunpowder from generations of top physicists fighting, compromising, and self-overturning in this extremely esoteric field.

To the right of this theater map was that [ Mathematical _ Toolbox ] written full of his painstaking efforts.

Quietly lying inside were the three major weapons of numerical analysis, asymptotic matching, and Sobolev spaces, as well as that striking line of red text.

The renormalization group that was temporarily and actively abandoned.

In front of the workbench, Jiang Lin leaned back against the chair and quietly looked over the entire wall.

He looked at it for a full half hour.

Then he opened the diary program of the workstation and solemnly typed out the annual summary for the twenty-second year, which was also the ultimate summary of these ten years.

[ Summary of the Twenty-Second Year ]

[ Past Ten Years Data Report: 82 Class A core papers intensively read. 421 Class B key papers sorted out. 4036 Class C index archived. ]

[ Three underlying mathematical weapons catch-up completed. Based on reality boundaries, one actively abandoned. ]

[ The pedigree map of the research history has crawled all over the north wall. ]

Enter, line break.

[ Ten years ago, which was when I had just deleted all those second-hand textbooks, I thought I was learning what magnetic reconnection was. ]

[ Now, after these ten years, looking at these color labels all over the wall, I finally know what I truly learned in these ten years is why this field has not been completely solved to this day. ]

[ I have learned what assumptions are fragile, what mechanisms are imposed, what mathematics is forced, and what observations are out of reach. ]

[ In this subject attempting to reveal the universe's most core energy release laws, to truly move toward the answer, you must first know which pits your predecessors died in. Knowing why it has not been solved is a ghost gate that anyone trying to approach the truth must wade through step by step before seeing the answer. ]

[ I have walked in this ghost gate for a full ten years. ]

[ If you ask me now how close I am to the ultimate answer? I honestly answer, perhaps still a hundred thousand miles away. ]

[ But, I know another thing. ]

[ I am much, much closer to the realm of knowing what I truly do not know. ]

[ In this desolate Wasteland World, this is enough. This gave me an anchor point so I wouldn't go mad when facing the full sky of stars. ]

[ This ten-year-long paper deduction and historical mapping can officially come to an end. ]

Save, close program.

Jiang Lin turned off the power of the workstation host, walked to the door of the Stone House, and pushed open the wooden door.

The bitterly cold air rushed in instantly, and Jiang Lin involuntarily shuddered.

He zipped his cold-weather suit up to the very top and walked into the night.

Outside, wind turbine no. 2 was rotating steadily in the night wind, like a loyal sentinel.

Looking along the lines, Observation Point A and Observation Point B in the distance each lit up an extremely faint green power indicator light in the dark like fireflies.

He raised his head and looked at the low altitude in the north.

Tonight, the sky was extremely clear.

But that light red bright band that he dreamed of did not appear.

Jiang Lin was not disappointed.

Because it was right there, starting from the seventieth day of his sixth return to the Wasteland, from the moment he first captured its abnormal contour in the lens, it had always been right there.

During those full ten days and nights when he gnawed on those eighty-two Class A core papers in the Stone House, that red band, that great high-altitude tear, had never truly left this scarred sky.

It just had its own temper and sometimes didn't come out.

Jiang Lin stood straight in the biting night wind and took a deep breath of cold air.

Then he turned around and returned to the Stone House.

He knew what he was going to do tomorrow.

The blueprint of theory had been drawn, and the knife of mathematics had been sharpened. Textbooks gave Sweet's long noodles, Petschek gave the gorgeous X-type, Plasmoid gave the fragmented magnetic island chain, Hall gave the departure of electrons and ions, and turbulence gave the fog of statistics.

But these were, after all, model images compromised and abstracted on supercomputers and scratchpads.

What Jiang Lin wanted to see was not models.

What he wanted to see was the real magnetic field macroscopic wreckage left behind by nature, the host with infinite computing power, every time the red band shone on this Wasteland that had suffered a real disaster.

Tomorrow, redeploy the observation baseline network.

Go capture the truth belonging to the Wasteland itself.