Recent content by 16universes

Excellent article. Thanks for sharing.

@MrAnchovy: Thanks. I'm going to read through this later. The equations aren't showing up on my phone so it's difficult to read. Correlation is probably a better choice of wording. I'm thinking of these abstract "processes" as operators of some kind operating on some abstract "state". The word...

Hmmm. You've raised some interesting points I haven't thought about. I need some time to think this through. I'll post my thoughts sometime in the next few days. Thanks for the help everyone.

I appreciate the help. I naively assumed that inner product had a specific definition. My experience revolves around applications to vectors in general (representing physical quantities), quantum mechanics and single variable functions in general. On some level I assumed that an inner product...

Here's one example: Suppose you were cleaning a surface. You can use soap, water, or both, before wiping down the surface. You apply water only, then wipe the surface. You then apply soap only and wipe the surface. Is the "cleanliness" of the surface equivalent to the case where you apply...

Ha I apologize. I was still caught up "seeing" the problem differently. It took some time to change how I was looking at it. But yes, you were correct. Thanks

First, I would like to thank everyone's help with this problem. I spent some time thinking about it, and realized that I probably made it more complex than it really was. After discussing the problem with my advisor, he suggested the following solution: Let ##T## be the temperature of the...

Hmmm. Interesting.

Physical processes are described with functions. Inner product as defined when discussing functions was implied. @MrAnchovy: Based on the way you respond to people on the forums, I can tell that non-mathematicians really get under your skin. I'm not a mathematician and I know haven't...

Just as we have orthogonal vectors/vector spaces/etc., we can have orthogonal functions/function spaces/etc. I'm trying to apply these concepts to physical processes. Here's a general idea of what I'm doing: Suppose you have a physical quantity you are trying to measure, ##F##, and it depends...

I had to put this problem on hold. I will post my approach/solution in the not so distant future when I get some time to work through it.

I would say L/D >> 1 I never dealt with heat transfer. Scary, I know. Jackson E&M was the majority of my experience with PDEs. I didn't get much out of it because most of the time the material was way over my head. If I can't visualize the problem and mathematics, I struggle to understand it.

After thinking about it more, my oscillation assumption was incorrect. You are absolutely right. In the steady state, heat can only be generated at the rate it can be dissipated.

I do agree with this. Which leads me to believe that I have set it up incorrectly. Before setting up any PDE, in your opinion, how should the system behave? Disregard any assumptions I have made. You have a thermistor and run constant current through it. What is its behavior?

Take a thermistor and run constant current through it. What long term behavior would you expect to see for the temperature? That's the problem I'm faced with. Now, I've set it up according to how I view the problem. Everyone has commented on how to solve the problem I've set up, but no one...