56: Chapter 56 The Sluggish Ghost

On the first page of search results, most of the literature focused on traditional tribology.

He clicked on several of the most-cited articles and skimmed the abstracts and charts at a glance.

The vast majority of these papers dealt with static contact, or low-frequency, large-slip cyclic friction.

The focus of the research was concentrated on lubricant film thickness, morphological analysis of abrasive wear, or the wear resistance of a certain new coating.

It intersected with his problem, but completely missed the mark.

What he needed to solve was the fretting and stiffness degradation of micrometer-scale or even nanometer-scale assembly surfaces driven purely by thermal stress, not gear meshing in macroscopic machines.

He downloaded two of them that were somewhat interesting in terms of mathematical modeling and continued scrolling down.

Starting from the second page, due to the search engine's weight bias, the results gradually shifted toward the design directions of precision instruments, optical platforms, and semiconductor photolithography machine bases.

Researchers in this field did not care whether parts would wear out; they only cared about one thing: the fatal impact of thermal drift on nanometer-scale measurement accuracy.

This had a massive overlap with the physical background of Jiang Lin back in the Wasteland, where he had to ensure that the yaw bearing did not undergo micrometer-level deformation under huge temperature differences, thereby preventing the resonance and disintegration of the entire tower.

He stopped what he was doing, stared at the search box at the top of the screen for a moment, readjusted his search terms, and removed the overly broad tribology vocabulary.

mechanical thermal drift

multi-material assembly

interferometric

error budget

Enter.

The page refreshed.

The third paper on the second page, that bold blue title line.

Mechanical thermal drift in high-stability interferometric displacement measurement systems: error budget and experimental validation

(Mechanical Thermal Drift in High-Stability Interferometric Displacement Measurement Systems: Error Budget and Experimental Validation)

He opened the article.

When the first page fully loaded, the first line of the author column prominently displayed a name.

Zhixing Lu (Department of Physics, Jiangcheng University)

Professor Lu Zhixing?

Jiang Lin was slightly taken aback; he truly hadn't expected to see Teacher Lu's paper here in this manner.

However, he immediately withdrew his attention and focused on the paper itself.

He directly skipped the introduction and principle overview, dragging the scrollbar to the core error budget section.

It was listed in great detail. An interferometric measurement system of this scale was wrestling with the scale of atoms.

Laser frequency drift, detector dark current noise, analog-to-digital conversion electronics background noise, thermal drift of air refractive index with temperature, vibration isolation transmissibility of the optical platform, initial alignment error of the optical path...

Professor Lu Zhixing's team dissected every conceivable source of interference like dissecting a frog.

Underneath each item were clear error propagation formulas, sensitivity coefficients, and magnitude estimations under limit conditions.

Finally, all these miscellaneous items were summarized into a system's total error budget through error synthesis formulas.

Then, they compared this budget figure with the experimental validation results they ran in the constant-temperature room in a single chart.

The two curves fit quite well, and the conclusion could be said to be extremely elegant.

But Jiang Lin did not stop there.

He read the main text word for word, dragged the scrollbar, and began reading the appendix, reading the dense tables of parameters in the appendix.

In Table A3 and Figure S4 of the appendix, he found a set of data squished into a corner.

That was the raw residual test result of interference signal stability when their experimental system underwent a complete, twenty-four-hour slow temperature cycle (rising from 20 degrees to 24 degrees, and then falling back to 20 degrees).

Staring at that set of data for a moment, he took out a piece of draft paper and wrote down several peak coordinates extracted from Appendix A3 of Professor Lu Zhixing's paper on the right side of the draft paper.

Then he organized the key numbers from the thermal cycle data he had recorded in the Wasteland and placed them side by side for comparison.

In terms of precision, the two sets of data were simply incomparable.

Professor Lu Zhixing's team used a constant-temperature vibration isolation room and a picometer-resolution interferometer; the data floor noise was as clean as a block of ice.

Meanwhile, the absolute uncertainty of Jiang Lin's data set was rougher than this interferometric data by God knows how many orders of magnitude.

If it really came down to a hard comparison of displacement precision, it had no qualification whatsoever.

But what he was comparing wasn't absolute displacement.

He re-normalized both sets of data according to the temperature cycle period, looking only at the morphology of the rising edge, falling edge, and residual lag.

Then, he saw the thing hidden behind the noise.

The same type of hysteresis characteristic.

But.

Jiang Lin's pupils slightly constricted.

Hidden within these two vastly different sets of data was a trend so similar in morphology that it was almost glaring.

The response speed of the temperature rising edge and the response speed of the temperature falling edge were asymmetric.

In Professor Lu Zhixing's interference residual chart, during the warming phase, the residual curve climbed quite decisively, carrying the crispness of certain material deformation.

Whereas in the cooling phase, even though the temperature had already begun to recede, the residual curve dragged downward as if dragging through a mud puddle, dropping sluggishly and exhibiting an obvious phase lag and amplitude hysteresis.

This asymmetry also existed in the line chart drawn with a pencil by Jiang Lin, except it was masked by massive noise like a burr.

This asymmetry could at least be given a self-consistent explanatory path by Jiang Lin's own underconfident contact stiffness degradation model derived by himself.

During warming, the different expansion rates of aluminum and steel caused local contact stress to surge dramatically, and the asperities underwent irreversible plastic yielding.

During cooling, because plastic deformation had already occurred, the path of stress release changed, which formed a physical hysteresis loop.

The problem was that over the past fifteen years, Jiang Lin had never been certain whether the hysteresis loop in the Wasteland data was a systematic error artifact caused by his thermocouple responding too slowly, or a genuinely existing physical effect.

Looking at the draft paper, he raised his pen and drew a circle between the two sets of numbers, pulling his line of sight back to the computer screen.

He flipped the paper back to the error budget section and re-read the mechanical thermal drift paragraph word for word.

It was listed very clearly in the paper.

The static thermal expansion displacement error of the mirror mount, the repeatability precision of the mounting base, the flatness tolerance of the flange, and the amount of wobble brought by the fitting clearance of the locating pin.

Very comprehensive, belonging to textbook-level engineering troubleshooting.

But there was no dynamic angular perturbation.

More specifically, when Professor Lu Zhixing's team did the error budget, they treated the assembly structure as an ideal rigid body.

They did not analyze how the preload force of the bolts would undergo microscopic relaxation when complex assembly structures composed of multiple different metal materials experienced temperature cycles of even just a few degrees Celsius.

They did not calculate the uneven distribution of contact surface stiffness caused by this relaxation.

Nor did they deduce that this change in contact stiffness would cause the mirror mount fixing the optical lens to produce an extremely minute angular variation.

And once this angular variation, which was less than even a microradian, was mercilessly magnified by an interferometric optical path several meters long, it would be equivalent to a periodic, hard-to-eliminate low-frequency displacement residual on the final detector.

Jiang Lin leaned against the back of the chair and closed his eyes.

He re-ran every formula in the paper and every line of derivation on his own draft paper in his mind like 3D modeling.

Confirming that no preconditions were misread, and confirming that no obvious breakpoints were temporarily found.

He opened his eyes, picked up his pen, and rapidly wrote three lines at the bottom of the draft paper.

1. In the error budget of this paper, mechanical thermal drift only dealt with static displacement, missing the dynamic angular perturbation under thermal cycling.

2. The temperature response asymmetry in the Appendix A3 data was the ghost of this omitted item; they could not explain this ghost within the budget framework.

3. My model, if correct, happened to fill this blank and explain this asymmetry.

However, this "if it is correct" needed validation.

Before the ironclad laws of science, no matter how perfect an unverified logical chain was, it was just a pile of exquisite ash.

He needed validation.

And the most direct and brute-force way, naturally, was to find someone who had the right equipment in hand, ready-made data, and enough professional background to understand what he was talking about, letting his model undergo a real, hard-hitting test.

The Key Laboratory of the School of Physics at Jiangcheng University where Professor Lu Zhixing was located had the kind of high-precision interference data he needed, and most likely also possessed the top-tier measurement equipment of the kind he dreamed of touching.

Without hesitation, Jiang Lin moved the mouse and opened the computer's built-in email client.

New email.

In the recipient field, he typed letter by letter the school work email ending in .edu.cn left below the signature page of Professor Lu Zhixing's paper.

The sound of the keyboard rang crisply in the room.

The first paragraph of the email.

He stated flatly that he had read the paper and, after carefully analyzing the residual data of Appendix A3, discovered a striking feature.

The asymmetry of the temperature response rising edge and falling edge.

He pointed out bluntly that this phenomenon, obviously bearing hysteresis characteristics, had no corresponding reasonable explanation in the main text's practically perfect error budget checklist.

Writing up to here, Jiang Lin paused for a moment.

He didn't want to sound like a contrarian, so he added a sentence: "I would like to know whether this feature was intentionally categorized as background noise in your group's data processing because its magnitude was evaluated as insignificant, or if the current theoretical framework has not yet covered this part?"

The second paragraph.

He had to throw out his own chips.

Stating that he was currently independently researching a related problem: the contact stiffness evolution mechanism of multi-material assembly structures under thermal cycle alternating loads.

...

"I also observed a similar trend in my own experimental data," Jiang Lin typed this line on the keyboard with a trace of self-mockery in the corners of his mouth.

The equipment cobbled together with scrap metal in the Wasteland, viewed from his current standards, was practically prehistoric stone tools.

"However, because my measurement conditions were extremely rough, the system's data noise was too large, and the signal-to-noise ratio was insufficient to support strict quantitative analysis. I am currently unable to determine whether that hysteresis asymmetry is a real microscopic physical effect or a systematic artifact brought by my crude measurement means."

He confessed his shortcomings without any concealment.

"Therefore, I would like to venture to ask whether Professor Lu's team's experiments in the constant-temperature room have independently and repeatedly verified this asymmetric feature?"

The third paragraph.

To prove that he wasn't some baseless amateur scientist, Jiang Lin listed several key numbers from his own Wasteland data set.

Thermal cycle period, temperature gradient, and estimated contact surface preload decay percentage.

He articulated clearly the reasons why he believed these two sets of data could be compared under the same physical framework.

Essentially, they were both static joint interfaces formed by multi-metal materials through bolt preloading. In the sense of thermo-mechanical coupling and contact mechanics, they obeyed the same type of equations.

...

After finishing the last line, Jiang Lin carefully read the email from beginning to end, changed two expressions that might cause ambiguity, changed "will inevitably lead to" to "has a high probability of inducing", making the tone appear more objective.

Then, he moved the cursor to the send button and clicked.

He didn't know if Teacher Lu would reply.

University professors received countless emails every day, and emails like this from an unknown address that immediately discussed corner-and-cranny data in the appendix had a high probability of being ignored as spam.

If he could get a response, that naturally would be the best opening.

If there was no reply, he would have to find other paths.

For example, figuring out a way to contact a testing agency, paying for a commissioned test, or buying second-hand parts himself to hand-craft a measuring instrument in his garage.

This would be extremely time-consuming.

...

Building B of the School of Physics at Jiangcheng University, nine-forty-seven in the evening.

Most areas of the entire building had plunged into darkness, with only a scattering of laboratory windows still transmitting a cold white light.

At the end of the third-floor corridor, Professor Lu Zhixing's office door was half-open.

On the spacious desk, several printed all-English peer review comments, a stack of experimental data record books held together by clips, and a few reimbursement forms that hadn't had invoices attached yet were spread out messily.

Two or three discarded optical polarizers with somewhat damaged edges were casually pressed onto the corners of a few sheets of A4 paper, refracting a cold, eerie blue halo around their edges under the illumination of the desk lamp.

Professor Lu Zhixing sat in front of the computer, his eyes covered with fine bloodshot veins.

On the computer screen was the peer review comment email forwarded three days ago by the editorial office of Physical Review Letters.

This email, especially the sprawling comments from the second reviewer, Professor Lu Zhixing had read back and forth no less than four times over the past few days.

That was a peer with viciously sharp insight.

In his comments, the other party did not deny the novelty of their high-stability interferometric measurement scheme, nor did he question the derivation of the core interference formulas.

What truly stuck this paper—upon which high hopes were pinned—was a section of residual data that their own team was well aware of, but explained insufficiently cleanly and neatly.

The reviewer's original words were extremely sharp.

"In the long-term stability test presented by the authors in Figure S4, there is a low-frequency drift with a period of about forty minutes and an amplitude at the sub-nanometer level. Notably, this drift exhibits an obvious response asymmetry on the temperature rising and falling edges. The authors simply classified it into the systematic error margin in the error analysis and glossed over it, which is not rigorous. It is recommended that the authors supplement control-variable stability experiments and provide an exact physical source explanation for this low-frequency drift, otherwise it will seriously weaken the reliability claim of the measurement system."

The most troublesome thing was that this forty-minute drift did not exist in isolation.

It was superimposed on the grand backdrop of the twenty-four-hour temperature cycle, like a layer of small-period ripples.

Every time the temperature control system entered the minor adjustment interval, it would appear. But it was neither strictly synchronized with the air conditioner's output temperature nor matched with the platform's vibration spectrum.

This was precisely what the reviewer was most dissatisfied with.

Professor Lu Zhixing tilted his head back against the mesh backrest of the ergonomic chair, rubbed his throbbing temples hard, and let out a long sigh.

The place this article truly wanted to charge into PRL for wasn't the interferometer itself, but rather that they used this system to push the stability of low-frequency displacement readouts to a magnitude sufficient to support next-generation weak-force measurement experiments.

He was thirty-nine years old this year, standing in the awkward age of being neither here nor there in this academic circle where seniority was taken extremely seriously.

As an associate professor and young PI at the School of Physics of Jiangcheng University, he nominally leaned under the well-funded provincial-ministerial key laboratory of academic giant Professor Wang Heng, responsible for one of the sub-branches of high-stability interferometric measurement.

Such days of living under someone else's roof were not pleasant.

If this article could be successfully published in PRL, it would be the hardest and most impregnable stepping stone for his subsequent applications for national talent projects, coping with the college's tenure evaluation, and securing renewal funding for his own independent sub-project.

If this paper got rejected or fell through, it wouldn't exactly mean the sky was falling and he'd be packed off to leave immediately.

But the rhythm of this already slow-moving sub-project in his hands would be completely disrupted.

Yin Hang, the PhD student working under him, would have to push back the paper he planned to use for graduation.

At next month's mid-term project report for the Key Laboratory, his PowerPoint slides would look terrible.

And Professor Wang Heng would definitely not give him a pleasant look.

The problem was, the data was indeed stuck.

Stuck in an awkward limbo.

That damn low-frequency drift was like an extremely fine glass splinter stuck in the web of a finger—invisible and intangible, but agonizingly painful whenever the error budget table was touched.

"Advisor Lu?"

The office door was knocked twice, and the PhD student Yin Hang walked in with a bird's nest of hair and an exhausted look on his face.

"How is it? Are the results from the adaptive filtering running any better?" Professor Lu Zhixing straightened his posture, picked up the completely cold coffee on his desk, and took a sip.

Yin Hang shook his head with a wry face and handed over a few newly printed charts: "No good. I just ran two new versions of Kalman Filtering. The curve is a bit smoother, but that low-frequency envelope is still there and can't be removed. I still maintain that the problem lies in the size of the filtering window and the dark noise model of the detector itself."

Professor Lu Zhixing took the charts, glanced at them, and his brows knitted tightly together.

The other two core members in the laboratory had also had a rough time these past few days.

Meng Che, who was in charge of hardware assembly and was a man of few words, had already locked himself in the constant-temperature room, re-measured the ripple of the laser power supply twice, and confirmed that the power supply was as clean as purified water.

Yao Siyu, who was in charge of data organization, guarded tens of gigabytes of temperature monitoring records and checked them for three full days and nights, stubbornly failing to find any strict phase correspondence between that forty-minute-cycle drift and the temperature fluctuations of the air conditioning system.

They ruled out the thermal noise of the photoelectric detector, rechecked the working status of the air-bearing optical isolation table, and repeatedly aligned the ambient temperature, platform vibration spectrum, and raw interference signal.

As a result, none of them were clean enough.

Mathematical filtering was like adding a beauty filter to a face covered in pimples; you could make the curve look visually pleasing, but you couldn't make the low-frequency residual lurking in the underlying Physics process truly disappear.

Reviewers weren't fools and could see right through it at a glance.

What annoyed Professor Lu Zhixing the most right now was precisely this point.

If this drift was purely random electrical noise, there would be a complete set of electronics denoising methods to deal with it.

If it was simply environmental temperature drift, there should be a clear, delay-free linear correspondence with the records of the laboratory temperature monitoring probe.

Yet it happened to be stuck in the middle ground.

It behaved like some kind of real physical existence that, after being mashed up by massive analysis software, still stubbornly remained near the baseline.

It had inertia and hysteresis.

"Alright, go back and rest first, and look at it tomorrow." Professor Lu Zhixing threw the charts on the desk and waved his hand.

"Okay, Advisor Lu, you should go back early too." Yin Hang felt as if he had been granted amnesty and hurriedly slipped out.

There were already few people in the corridor outside the office, occasionally accompanied by one or two sounds of vacuum pump pumping coming from who knows which laboratory.

Professor Lu Zhixing irritably grabbed the phone on the desk, originally just wanting to open WeChat to reply to a few harmless messages in the department's work group.

But when his fingertips brushed across the notification bar at the top of the screen, he saw a red envelope icon pop up in the background of his bound school email.

A new email.

The sender was an unfamiliar digital email address with no signature.

But that bolded title was like a bolt of lightning, instantly striking Professor Lu Zhixing's somewhat chaotic brain and causing his sliding fingertips to stop abruptly.

[A question regarding the asymmetry of temperature response in Appendix A3 of your paper]

Professor Lu Zhixing's pupils dilated abruptly, and his heart skipped a heavy beat.

Which bored reader was this sending a nitpicking email again?

He immediately clicked open the body of the email.

Before he had even finished reading the first paragraph, Professor Lu Zhixing's body leaned forward uncontrollably, almost pressing against the phone screen.

Because the other party pointed out in a somewhat cold engineering tone: "The responses of the rising and falling edges of the temperature in your Appendix A3 are asymmetric. Moreover, in the main text, your treatment of mechanical thermal drift only stops at calculating the static expansion displacement of the mirror mount and the installation repeatability of the base. You completely failed to further analyze whether the redistribution of the preload path at the assembly interface of multiple materials during the thermal cycle might cause continuous dynamic angular disturbances to the optical mirror mount."

Professor Lu Zhixing, who slowly straightened his body, developed a fine layer of goosebumps on his back and eagerly continued reading downwards.

In the second paragraph, the other party calmly mentioned that they were researching an engineering problem related to underlying principles.

The evolution of contact stiffness in multi-material assembly structures under thermal cycles. The other party even mentioned plastic rheology and hysteresis loops.

In the third paragraph, the other party candidly listed several sets of experimental data that appeared extremely rough, or even rudimentary.

The other party explicitly stated that their measurement conditions were limited, the noise in the data was very large, and they dared not use it as quantitative ironclad evidence, but could only use it as a reference for the direction of physical evolution.

Seeing this, Professor Lu Zhixing's initially somewhat guarded psychological defense was completely shattered.

The other party's last sentence was even like a heavy hammer, striking his most fragile nerves over the past few days.

[I do not think that the two sets of data already match in terms of precision, but I would like to ask: Has the asymmetry of the rising edge/falling edge in your group's experiment undergone independent replication? Is it possible that it is a physical inevitability caused by changes in contact stiffness under thermal cycling?]

Professor Lu Zhixing's hand holding the phone was sweating slightly.

The place asked about by this person on the other side of the screen was precisely the direction he was most reluctant to admit and least wanted to thoroughly investigate in his subconscious these past few days.

Micro-motion of mechanical paths.

Relaxation of bolt preload.

Thermal cycle hysteresis.

Contact stiffness degradation.

These terms were too unrefined, too biased towards traditional mechanical engineering.

They weren't pretty enough, not Quantum Mechanics enough, and not suitable to be put in the abstract of a PRL paper to brag about as high-end highlights.

Subconsciously, as someone working in optics, he always treated mechanical structures as rigid carriers, ignoring the fact that they actually had life and breath at the microscopic level.

But Physics experiments were ruthless.

It wouldn't prevent these mechanical effects from phantom-like manifesting in the residuals of the detector just because they weren't pretty or quantum.

Professor Lu Zhixing put down his phone, slowly turned his head, and looked back at the residual curve on the computer screen that had tortured him for three days.

That low-frequency drift with hysteresis characteristics was still there.

Quiet and stubborn, it was like a geological fracture that had always existed but had never been named by them.

After a long time, Professor Lu Zhixing violently grabbed the keyboard, hit Enter to wake up the screen, and opened the email system on the computer side.

Beginning to reply word by word.

...

At 6:00 a.m. the next morning, the morning mist of Jiangcheng had not yet dissipated.

Jiang Lin sat up from bed on time, and the first thing he did after putting on his clothes was to habitually grab the phone placed by the bedside and open the email client.

In the inbox, an unread new email was impressively lying there.

Sender: Professor Lu Zhixing.

Subject: Re: A question regarding the asymmetry of temperature response in Appendix A3 of your paper.

Time: 1:22 a.m. early this morning.

Jiang Lin's eyes lit up slightly, he settled on the edge of the bed, and opened the email.

Professor Lu Zhixing's reply was very long, sprawling over four major paragraphs, and between the lines exuded the excitement and straightforwardness unique to late-night scientific researchers.

In the first paragraph, Professor Lu Zhixing frankly acknowledged that the asymmetry mentioned in the email genuinely existed and could basically rule out pure detector measurement artifacts.

The team had conducted repeated verification on this up to five times in past constant temperature control experiments, and the conclusion was very stable.

But he candidly explained why they didn't delve deeper at the time.

Because in their initial error budget framework, a certain amount of redundancy had already been left for this type of unpredictable mechanical drift.

And under the evaluation at that time, the additional nanoscale displacement impact brought by this asymmetry happened to fall within that margin range.

In order to rush the paper's progress, they chose not to deal with it for the time being.

The tone of the second paragraph took a sharp turn.

He said that he was now very interested in the contact stiffness evolution model mentioned in Jiang Lin's email.

Professor Lu Zhixing wrote: "If your model can indeed explain that asymmetric hysteresis response from the perspective of underlying mechanical micro-motion, it won't just be an engineering empirical judgment, but may provide us with a new physical troubleshooting direction."

In the third paragraph, Professor Lu Zhixing asked very directly.

"How does your contact stiffness evolution model specifically parameterize the process of redistributing macroscopic preload among microscopic asperities?"

To enable Jiang Lin to answer in a targeted manner, Professor Lu Zhixing also tossed out a specific question.

He cautiously provided a simplified description of a structure: in the core area of their optical experimental setup, to fix the beam splitter, there was an aluminum alloy-stainless steel combined adapter plate.

Prior to this, the entire team had always treated it as a perfect rigid connection, and had never seriously analyzed its microscopic mechanical behavior under minor environmental thermal cycles.

He wanted to see what specific derivations and parameter performances would result if Jiang Lin's model were applied to this specific structure.

By the fourth paragraph, Professor Lu Zhixing's tone became somewhat curious.

He asked under what extreme conditions the set of data mentioned in Jiang Lin's email—though rough but matching in trend—was measured, what obsolete measuring tools were used, and what the bottom line of calibration precision actually was.

...

Jiang Lin read it word for word without getting up to wash up; he sat straight at the desk, opened his laptop, and created a new Word document.

Facing the gradually brightening morning light outside the window, he spent nearly three hours writing an ultra-long reply email of about 2,500 words.

In the email, he disassembled his simplified model using solid mechanics and heat conduction equations.

He described in detail how to equivalently model microscopic surface roughness as a spring array, how to introduce the difference in linear expansion coefficients of different metals, and how to use yield criteria to calculate the irreversible loss of stiffness caused by plastic deformation.

After finishing the core derivation, Jiang Lin carefully read through this long letter.

He paused slightly at the end where the cursor was blinking, and then added a paragraph.

"As I mentioned before, given my current conditions, I cannot find a sufficiently precise measurement environment with traceability benchmarks to quantitatively verify several nonlinear coefficients in this model. This is my biggest predicament at present."

"If your laboratory has the opportunity and willingness to use your relatively reliable interferometric measurement equipment to conduct a set of targeted control experiments—for example, under controllable minor thermal cycle conditions, separately measuring the stiffness evolution in the normal and tangential directions of that aluminum-steel composite contact surface, as well as the tiny displacement response caused thereby—I would very much like to know the real data feedback."

"It is not necessarily required to shut down specifically to design large-scale experiments; if your daily discarded data records have similar residual characteristics, they can also be used as a comparison."

...

Professor Lu Zhixing's reply came extremely fast.

About an hour later, just as Jiang Lin finished breakfast, his phone vibrated.

This time Professor Lu Zhixing didn't write a long essay, nor did he send complete drawings, but instead attached an encrypted PDF in the email.

Inside the attachment was a desensitized structural parameter description. The description deleted the overall layout of the experimental setup and key optical path details, retaining only parameters sufficient for preliminary magnitude estimation: material combinations, connection methods, bolt specifications, target torque ranges, contact surface roughness requirements, and several equivalent geometric dimensions.

Professor Lu Zhixing wrote at the end of the email.

"It is inconvenient to send more complete drawings and raw data via email. If your model can still give clear predictions under this set of simplified parameters, we can make an appointment to discuss it in person."

Jiang Lin looked at these mechanical parameters, which could not be more familiar, and only felt the blood all over his body accelerate its flow.

He grabbed paper and pen and began calculating.

Substituting the desensitized parameters given by Professor Lu Zhixing into his contact stiffness evolution model, he made a quick preliminary estimation.

Half an hour later, he typed the core conclusion of the estimation into an email and sent it back.

In the email, he rigorously pointed out that in his estimation.

The thermal expansion coefficient and Young's modulus of the materials were based on reliable manuals.

But the true asperities distribution of the initial contact surface could only be empirically estimated based on Ra 0.8, processing methods, and common surface spectra. The uncertainty of this parameter was very large, and a conservative estimate would bring at least 15% or more fluctuation, or even higher.

Finally, he provided a prediction that could be directly tested by experiments.

"If this mechanism holds true, then the residual curve should not be completely synchronized with the ambient temperature monitoring records, but will exhibit a stable phase shift relative to the temperature curve. The offset depends on the thermal diffusion time constant jointly determined by the aluminum alloy, stainless steel, contact interface thermal resistance, and the assembly geometry dimensions."

"At the same time, if the bolt tightening sequence is changed during reassembly, or a stricter cross-graded preload process is used, the amplitude of this low-frequency drift should undergo repeatable changes."

"In other words, it should not only be related to the ambient temperature, but also to the assembly history."

"The above is not a conclusion, but merely a testable consequence given by the model."

Email sent.

This time, Jiang Lin only waited ten minutes.

Professor Lu Zhixing's latest reply popped up on the screen.

This email was as short as just a few sentences, exuding an inability to sit still with urgency.

"The phase shift feature you mentioned is indeed present in our raw data. Our entire group has been stuck here for three weeks and has never found its physical source."

"Would it be convenient for you to come to Jiangcheng University to talk in person?"

Jiang Lin looked at these two lines of words on the screen and let out a long breath.

"Yes."

Professor Lu Zhixing replied almost instantly and attached a mobile phone number.

"Tomorrow morning at nine o'clock, in the lobby of Building B of the School of Physics at Jiangcheng University, do you find that convenient?"

...

Having determined the time and place, Jiang Lin began to reorganize everything he needed to bring to tomorrow's meeting.

He took out the handwritten organized version of the contact stiffness model derivation and arranged it by chapter.

From physical assumptions to microscopic force analysis, and then to the integration of macroscopic equations.

He made dense annotations in red pen on the side.

Which parameters came from classic textbooks, which estimated values were forcibly set based on Wasteland experience, and where the confidence interval of the measured values lay.

Whenever he encountered places where he himself had no confidence in his heart and the derivation was not rigorous enough, he would never conceal it; he directly drew a big circle with a red pen and put a question mark on it.

Next was the organized version of that set of thermal cycle data.

Drawing the axes and arranging the data points in strict chronological order.

Finally, he pulled out a clean sheet of A4 paper.

For tomorrow's meeting, he wrote a separate explanatory abstract similar to a project proposal, outlining his core conjectures and the argumentation bottlenecks currently encountered.