October 2011
10 posts
Well I failed that exam!
Or so I assume. But not in the bad way. The class is ridiculously over my head and I’m going to keep trying to catch up part of the way. If I have to drop it, I’ll just drop it. As long as I feel like I’m learning cool stuff and making some kind of movement towards finding a specialty and they’re not taking my stipend away, grad school is going as planned!
Sure gives...
Distributions
are fucking marvelous.
Linear Algebra
For those of you playing along at home, I’m now trying to work on a dimensional analysis problem, which are supposed to be easy but which I didn’t understand when we did them on the last homework. I think it’s because my linear algebra is rusty. So here are some linear algebra facts:
You can think of a matrix as a function that takes in a vector and outputs a different...
Next up, distributions
But not in the probability sense! I’m apparently learning to take derivatives of functions that I’ve always been told weren’t differentiable. Because apparently now differentiability is not the point. It’s all about integration, baby.
I’ve been told before that integration is a mathematically deeper, more fundamental concept than differentiation, even though they...
So you've got this viscous fluid...
and this inclined plane. We align some coordinate axes with the plane so that the x direction is downward along the plane, the y direction in perpendicular to the plane, and the z direction is determined by the x and y. The plane goes on forever in all directions because this is MATH and we do what we want. There’s a layer of the viscous fluid on the plane. The layer also goes on...
More on Stress from Wikipedia
Ok, I think stress is “the intensity of internal forces” in a body. So maybe in my current example, the external forces are gravity pulling all of the fluid down the inclined plane, and some friction acting on the bottom “layer” of the fluid, the part that’s in contact with the plane. The internal forces are the…friction, right? between different...
“The stress tensor sigma_ij can be expressed as the sum of two other stress...”
– Well that’s a relief. (from Wikipedia)
Alright, Navier-Stokes
I’m trying to do applied math for the first time pretty much ever. The problem I’m trying to understand is about a viscous fluid on an inclined plane “governed by the Navier-Stokes equations.” Yikes! First step, I have to learn what all the words mean.
One of the words is “stress tensor,” which is a pun on my current situation.
