Cooling Pipes - Henry Ho

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Hello,

I'm still searching for a solid topic to work upon, however, I thought of something along the lines of organizing random data/patterns. This is influenced by my interest in tetris, anagrams, and sudoku. For example, tetris: organizing random building blocks of four; function generators for data points: creating a suitable function for a set of 'random' datum.

Perhaps the easiest thing to do would be to program a function generator, but I want this to be more interactive. The interactiveness should make the program somewhat practical, allowing us to use it as a form of a data organizer.

I've defined some loose rules:
- The data/pattern would be random within some parameter.
- The data/pattern must have one solution.
- There must be multiple ways to arrive at the solution.
- Those ways can be compared in terms of time efficiency.

This sounds fairly simple. If you're only allowing identical square blocks, and all four have to share at least one face with at least one other block, then the number of topographically unique arrangements is only -- let's see -- five, if reflections are not allowed. Then each one can be rotated through 90, 180 or 270 degrees to give a total of 15 possible different shapes. If you label the squares with unique colors you just multiply by the number of ways 4 objects can be rearranged: 4! = 24. So there are 15*24 = 360 such objects. Choosing one at random is equally simple. I have a bias that Physics is generally more fun than games, but I am happy to be shown counterexamples. One that I think is eminently programmable is go; it would be neat to see if the computer could "discover" such patterns as "two eyes" or "zigzag flight" on its own and use them strategically the way human players do. An analogous task for the computer would be to program it to solve Tetris in real time; but I think most Tetris games already have that built in as a sort of screensaver, so all you'd have to do is get the sources, and/or write your own and show how yours is better. -- Jess 15:15, 20 September 2008 (PDT)

(I thought my editing option was disabled, so I sent an email. It works fine now.)

My math professor recently enlightened me on the application of matrices involving graphics. I was wondering if there was a way to plot 3D objects in space using matrices, then building a program that will organize the objects efficiently. However, that would mean one of the rules I've defined, 'There must be only one solution to the data/pattern', may have to be dismissed...

I'm afraid I have no idea what you mean by "plot(ting) 3D objects in space using matrices," sorry! -- Jess 22:21, 20 September 2008 (PDT)

In a way, this would be like Tetris, but at a 3D level - which would make the game much harder, but at the same time, more practical. I was hoping this program would allow people to build machines and equipments that would be much more efficient and sustainable. I know this is probably too ambitious now, but perhaps there IS a better design for accelerators, nuclear power plants, solar panels, etc.

I must be missing the point entirely; how would 3D Tetris (which is readily available, just Google "3D Tetris") help you build better accelerators etc.? I can see how it might help bricklayers, but that can't be what you mean. -- Jess 22:21, 20 September 2008 (PDT)

To put it shortly, I can design a program similar to 3D tetris, which shouldn't be extremely difficult since I have references online, and have a computer 'play' the game as efficiently as possible. The hard part would be assigning a 'nature' to the blocks.

For example, a cube would be a brick, a straight block would be a pipe, an L-shaped block would be a bent pipe. If I can set the end faces of those 'pipes' to always touch another face, I can basically build a long pipe. Furthermore, if I can set an interface where the idea would be to carry 'water' from one place to another (similar to the classic water pipe game), the program should be able to design the most efficient path.

Now, if I can extend the 'nature' of those blocks to more complex ones, such as magnets, mirrors, and etc, then the program should (theoretically, if I do it correctly) be able to build an efficient solution to a presented problem. Of course, I do not intend to do that in this course; however, if I can build the skeleton of this program, I would be quite satisfied.

So basically, the program should be able to solve an engineering problem efficiently if you give it a specific problem, materials, and the nature of those materials. I will NOT be going for something as complex as an accelerator, but perhaps a water pipe system would be my goal.

I am still confused. Is the idea that the solution of the Tetris game is isomorphic to the solution of a topological construction, so that when a "player" solves the game s/he is also optimizing the construction? Or does the computer itself find an optimal solution and the Tetris version is just a visualization scheme? Or...?? It is not at all clear to me that the topological challenges of Tetris could even in principle be isomorphic to any but a very narrow class of engineering problems. What am I missing here? -- Jess 07:40, 24 September 2008 (PDT)

I've changed plans considerably, I'm now going for something along the line of thermodynamics and entropy. I was actually motivated by a question on entropy from high school. The question was something like this, 'If a refrigerator was left running with its door opened in a closed room, would the entropy of the air in the room change?' The answer was 'no', and it had to do with how a refrigerator functions.

Actually I'd guess 'yes' because the refrigerator is drawing power from elsewhere (either from the wall socket or from burning propane if it's one of those types) and that power ends up dissipated into the air of the room, so the air eventually heats up. -- Jess 09:39, 5 October 2008 (PDT)

Although that question had no relevance whatsoever with my idea, but it sparked a few ideas:

• Cooling pipes: Would a turbulent flow or a laminar flow be more efficient in terms of cooling a body of water? Or, how will the density of the surrounding liquid affect the efficiency of the pipe?

This is relatively simple, I think. Just for the sake of a visually appealing final presentation, I think you'll want to ask questions for which the answers are more spatio-temporal than "yes" or "no", so you can make cool plots or animations. Also one gets more of a feeling for "what's going on" from such graphics, if they are well done. For instance, you could start with a pipe full of fluid at rest in thermal equilibrium with the surrounding fluid and then "turn on" a flow of cold fluid in the pipe and see what happens to the temperature of the surrounding fluid, using false-color representation of temperature. This would require real-time solutions of the heat equation, which is real computational physics. Or you could numerically simulate the propagation of a heat pulse, to "show" the Green's function for the heat equation. Or you could just show the final steady-state temperature distribution for various geometries and various conditions -- this is more like what you proposed above, and could still be "visually impressive" in false colors. -- Jess 09:39, 5 October 2008 (PDT)

• Entropy (I): To simulate the change in entropy during a closed nuclear explosion?? (This idea is still underdeveloped, I'm hoping you guys can give me some leads). I've also thought about measuring entropy change during a particle collision in an accelerator. I'm not sure how hard it will be to simulate a change in entropy visually, or if that is even possible.

Wow, these are interesting ideas. But make sure you start with a very rigorous definition of "entropy" from Statistical Mechanics, otherwise it would be extremely difficult to even state the question unambiguously. See e.g. my little intro to Thermal Physics. -- Jess 09:39, 5 October 2008 (PDT)

• Entropy (II): To find the rate of entropy change when a closed system is exposed to its surroundings. For example, the difference between a tiny slit and a basketball hoop.

This could also evolve into something interesting if you are careful to explain exactly what you mean; but I am utterly mystified by your example! -- Jess 09:39, 5 October 2008 (PDT)