Can anyone suggest a good, concrete example of using "chaos theory" to solve an easily understood engineering problem?
I'm wondering if there is a an answer of the following sort:
"We have a high level objective to design a system that does XYZ. To achieve this objective, we propose the following design D. If we look at the low level physics of our design, we see that the dynamics are nonlinear and exhibit "chaotic" behavior, but we can categorize the chaotic behavior as of being type ABC. Because we are able to understand that the chaotic dynamics are of the specific type ABC, although we can't make precise statements about every aspect of the system, we are still able to make the following "high-level" claims. And using those claims, we have designed a system in which,although certains parts are behaving "chaotically," the system still performs our desired objective XYZ very effectively."
I'm not looking for answers of either the following sort:
"Looking at the underlying physics we see that the dynamics are chaotic, but we can also see that if we introduce a mechanism EFG into our design, we can see that it will "dampen" the chaotic behavior and then leave us in a place where we can find a good solution."
or
"Looking at the underlying physics, we can see that certain aspects might be chaotic, but it turns out for the following reasons R1, R2, etc that underlying chaos has no bearing on our high level objective and we can create a solution in which we do not need to worry about the chaotic aspects."
An ideal answer might be something like "even though it's clear that this wing design is going to create a lot of turbulence, we can see that the turbulence will have a certain "structure", and thinking about this "structure" just a little bit, we can see that it's going actually work in our favor and greatly increase fuel efficiency." And course the problem is that it seems so implausible that turbulent flow ever works out this way -- rather it is something that is meant to be stamped away at all costs, but I imagine there must be some other example out there.
I find most texts on nonlinear dynamics/chaos very reasonable in their mathematical development of why chaos occurs, and how it has certain structure, but while I find myself able to see ways of avoiding chaos or even ignoring it, I don't have a good idea of how I could use my knowledge of it's structure directly to my advantage.
thanks!
