CHAPTER 503: CHAPTER 160: SENIOR BROTHER, LET’S DO SOMETHING BIG THIS TIME

Due to the project Brother Liu is in charge of, Qiao Yu often goes to learn about some laboratory matters this week.

Then he discovered a lot of complaints about the laboratory being overly mystical, with all sorts of bizarre and supernatural things emerging.

For example, even when all experimental conditions are consistent, the success rate is higher in the morning than in the afternoon; the reaction on rainy days feels different from sunny days; using chemical vapor deposition to grow molybdenum disulfide requires constant personnel changes, otherwise it won’t grow at all...

This is enough to show that many unknowable stories continue happening in the laboratory, so when Qiao Yu thinks, it’s not just Liu Hao’s issue he’s considering, but many other problems as well.

For example, how exactly this laboratory mysticism is generated. Is there a way to transform mysticism into science?

For this reason, during this period, he has truly read many review papers on chemistry. Then his thinking was limited.

Now he found this review paper on arXiv, the author signed as Albert C.J. Luo, affiliated with the Mechanical Engineering department at Southern Illinois University Edwardsville.

Qiao Yu hasn’t really heard of this university, but from the name, it can be seen that this professor should be an overseas Chinese.

The main focus of the paper is discussing the introduction of a generalized modal axiomatic system into complex dynamic systems, exploring the possibility of optimized modal geometry solutions to key problems in nonlinear systems.

There was a passage in the paper that Qiao Yu particularly liked.

"The complexity of dynamic systems, such as chemical reaction networks and material self-assembly, makes traditional research methods difficult to analyze high-dimensional nonlinear behaviors. The introduction of a generalized modal axiomatic system provides the possibility to apply geometric tools to dynamic system research.

Mapping dynamic system states to modal space, using modal distance and modal convolution, quantifying the relationships between different variables, capturing functional hotspots, thereby providing a unified description from dynamic behavior to geometric patterns..."

Truly, after seeing this paper, Qiao Yu’s mind was suddenly activated.

Why didn’t he think that his set of mathematical axiomatic systems could be applied?

And once his thinking opened up, Qiao Yu’s ideas started sprouting like bamboo shoots after the rain.

After all, the person who understands how this axiomatic system operates in this world the most is Qiao Yu himself.

Although he designed this axiomatic system to solve number theory problems, it’s evident that this framework can solve more than just number theory problems.

Specifically regarding the challenges faced by Liu Hao’s project, the mutual coupling of multivariate variables, the significant impact of weak intermolecular forces on performance, but showing as nonlinear, with complex parameter optimization...

So once mapped, the nonlinear effects of different molecular interactions on gel performance can be analyzed using modal distance paired with existing data.

The parameter problem can be defined as finding the region with the highest modal density in modal space, representing the optimal experimental conditions.

Map the self-healing behavior of the material as periodic distributions on the modal path, finding hotspot areas with low repair efficiency...

Theoretically feasible?

With this idea, Qiao Yu wasn’t even concerned about reading the paper Senior Brother Chen sent. Instead, he directly opened the software to start designing a mathematical model for the laboratory.

Currently, the three most important parameter states in the lab are reaction time, molecular interaction amount, and material response intensity, represented by α, β, and γ, respectively.

So the mapping formula is r=(α,β,γ).

Add a weight factor within, and after analyzing the laboratory results, give a specific value.

Then directly using the definition of modal distance: d_M(r_1, r_2) can be directly expressed as:

Next is to assess the cumulative contribution of nonlinear effects, this part needs to use modal convolution, similarly using a formula, directly obtaining:

Analyze the high-density areas in the space through this formula, thus finally obtaining the objective function for optimization goals:

Clearly, function X in the optimization formula represents the lab parameters to be optimized.

Of course, this is just a general formula.

After spending a few hours working through the formula, Qiao Yu carefully thought about his idea again.

He feels there’s no problem in mathematics, but he’s not sure if it can guide Brother Liu’s project yet.

After all, this is just a concept, but fortunately he still has some bundled data from the lab on hand.

The only problem is, this involves a lot of complex calculations. To say nothing of him or Professor Lu, both believe Liu Hao’s project group currently lacks sufficient data.

But the "insufficient" mentioned here is from a mathematician’s point of view, meaning there’s not enough data to reveal certain patterns, not that the total amount of data is insufficient. In fact, the total amount of data accumulated over half a year is still considerable.

Now the way Qiao Yu is handling the issue, in technical terms, is to search for the most representative low-dimensional projection in high-dimensional modal space, reducing dependency on full data, and try to discover potential patterns from these scattered data.

By minimizing the value of d-m, he finds the most regular path, and according to modal hotspots, guides subsequent experimental designs, and supplements the range of key parameter data with new laboratory data.

This method is actually a bit clumsy, although leveraging supercomputing, it requires someone who understands this scheme to adjust each weight parameter based on existing data.

It’s not too difficult, but it takes a lot of time. In the past, Qiao Yu would have just worked on it quietly, after all, making it work could be lucrative.