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Chapter 378: Chapter 300: Strange Curve

This was what Problem A asked the contestants to do.

Li Dong read quickly.

He could mentally construct the framework of each paper—its abstract, model assumptions, solution process, numerical results, and conclusion—almost at a single glance.

The first ten papers were all more or less the same in their approach.

They all handled geometric shading by sweeping a discrete grid, applied textbook formulas for optical efficiency, and finally, fed everything into a genetic algorithm or particle swarm to run.

To put it bluntly, they all safely and steadily followed the few mainstream paths laid out in the field’s public literature.

The work was solid, but that’s all it was—solid.

Li Dong flipped through the papers one by one, marking down scores as he went.

When he got to the eleventh paper, Li Dong’s hand paused.

The paper’s abstract wasn’t anything special.

But as he flipped to the second page, to the first section, Li Dong noticed something different.

This team hadn’t taken the mainstream discrete grid approach.

It treated the entire mirror field as a continuous field approximation in a polar coordinate system, with the heat absorption tower as the pole.

In their model, the thousands of mirrors were no longer treated as individual small mirrors.

Instead, they became a continuous ”mirror surface density field” that varied with the polar angle and polar radius.

The cosine efficiency, shadow blocking, atmospheric attenuation, and truncation efficiency at every point in this field could be written as a set of analytical expressions in terms of the polar angle and polar radius.

Li Dong had never seen this kind of approach in any published literature.

He read on.

This team had managed to formulate the entire field’s annual average power output as a double integral.

The physical meaning of each term in the integrand was crystal clear, and each term could be analytically decomposed.

When it came to the optimization section, they hadn’t used any heuristic algorithms.

They directly applied the variational method to that double integral.

The resulting Euler-Lagrange Equations corresponded precisely to the local conditions for the optimal distribution of the mirror surface density field.

And that optimal distribution yielded a very elegant shape that decreased monotonically with the polar radius.

It was almost identical to the parameterized annular arrays produced by traditional numerical optimization.

But this paper had derived it using the variational method, with just pen and paper.

Finally, they even added a section using a Monte Carlo simulation on a small scale to verify the deviation of the analytical solution.

The deviation was controlled to within two percentage points.

Li Dong reread the paper from beginning to end.

He let out a quiet ’Whoa’ in his mind.

’This approach is interesting.’

’At its core, this method isn’t really mathematical modeling. It’s physics.’

’This team treated the entire Fixed Sun Mirror Field as a continuous medium.’

’This move... is incredibly unconventional.’

Li Dong gave it a very high score on the evaluation sheet.

Then he set that paper aside.

...

The sound of pages turning filled the room for the entire afternoon.

Around five in the afternoon, the judges finally began to put down their pens one by one.

Zhang Wenping looked up.

”Everyone finished?”

Several of them nodded.

”Then let’s start comparing notes.”

”Old Min, let’s start with you.”

...

Min Ziqiang cleared his throat.

He pulled a paper from the stack on his desk.

”For Problem A, this is the paper I’ve picked with the highest score.”

He read out the temporary identification number from the cover page.

Then he ran everyone through the paper’s core approach.

”For the shadow-blocking portion, this team didn’t use a discrete grid.”

”They went with vector ray tracing. The shadow domain of each mirror was calculated entirely using analytical ray-polyhedron intersections.”

”Their calculations were nearly two orders of magnitude faster than the conventional grid method, and the precision was also a notch higher.”

Min Ziqiang paused for a moment.

”What surprised me the most was in the optimization section. They divided the entire Fixed Sun Mirror Field into three layers.”

”They applied a special treatment to the innermost layer, adding an asymmetrical offset angle specifically to mitigate the cosine losses around noon near the summer solstice.”

”It was a brilliant move.”

”I ran the numbers myself, and it increased the annual average optical efficiency by about 0.7 percentage points.”

”This one is my top pick.”

He paused, then added another sentence.

”The kids who wrote this also have a very solid engineering implementation.”

”The code runs cleanly.”

Several people in the room nodded.

At this moment, Wen Jingxing spoke up.

”...The one on my desk, I’m guessing it’s from the same university as the one Old Min has, right?”

He read out the temporary identification number from the cover.

Min Ziqiang was taken aback.

He looked down to check.

”Hmm, the numbers are only a few digits apart. They should be from the same university.”

He looked up, his eyes narrowing slightly.

”Old Wen, is the approach in your paper similar to the one I described?”

Wen Jingxing nodded.

”This paper goes a bit deeper on the vector ray tracing part than the one Old Min has.”

”They directly formulated the entire field’s reflected light cone as a probability density on the cross-section at the top of the tower.”

”The truncation efficiency is no longer calculated mirror by mirror. Instead, it’s integrated directly from this probability density.”

”For the shadow-blocking part, they used a hierarchical AABB (Axis-Aligned Bounding Box) acceleration structure.”

”This technique further accelerated the Monte Carlo convergence speed significantly.”

”Moreover...”

”In their final section, they added a robustness analysis for year-round extreme insolation conditions.”

”This part is what I value most in this paper.”

”The kids who wrote this paper have gone beyond simply solving the problem.”

”They’re thinking in terms of real-world engineering.”

The robustness analysis for year-round extreme insolation conditions that Wen Jingxing mentioned actually meant...