Homework Statement
By analogy with an electric quadrupole, one can devise a simple model for a magnetic quadrupole
that consists of two small parallel loops with currents circulating in opposite senses and that are
separated by a small distance. Consider two magnetic dipoles of equal dipole...
I'm trying to combine several contour plots together onto the same graph in gnuplot. I know that I can just do something along the lines of
splot "file1.dat" u 1:2:3 w lines, "file2.dat" u 1:2:3 w lines
set contour base
set no surface
set view 0,0
However, when I do that, the data from...
I agree with lotm. This is, philosophically speaking, a controversial subject area. However, the orthodox mathematical theory -- and, indeed, the one I know best -- is that described by the Kolmogorov axioms.
Sorry it's taken me a while to respond. I've been pretty busy with grad school. At any rate, we want to define something like:
L_V T=[V,T]
or
L_V T=VT-TV
for all tensors T and any vector V where L is the lie differential operator. Now, ordinarily, the lie derivative acting on a tensor is...
I did, but I did so by defining a new commutator. Turns out that you actually can do all lie derivatives as commutators so long as you properly define what it means for a tensor to act on a vector (I proved this and, if people are interested, I can post something more explicit later.) After you...
Yes, I'm aware of the related Millenium Problem. At any rate, does anyone have any information connecting ergodicity and psuedo-randomness for other systems? That seems intriguing to me.
I've been trying to get a grasp on Lie Derivatives. I understand that we can represent a lie derivative acting on a vector as a commutator. What do I do when I act a lie derivative on a tensor? Can I still just write out the commutator?
I was thinking about the non-linear Navier-Stokes equation this morning and was briefly browsing a text on the subject. I'm aware that one popular approach to dealing with turbulence is to take averages and look at correlators (which, in turn, can be related to field theory.) Now, one thing...
Ha, that's so obvious! Thanks!
How do I mark this thread as "Solved"? I tried looking under "Thread Tools" but I didn't see an option for doing that...
Homework Statement
This is from "Equilibrium Statistical Physics" by Plischke and Bergerson, problem 1.1:
"Consider a Carnot engine working between reservoirs at temperatures T1 and T2. The working substance is an ideal gas obeying the equation of state [ PV=Nk_BT ], which may be taken to be...
I actually solved this problem today. The connector from the external circuitry to the DAQ on the back of the computer wasn't tight enough, so the ground wasn't actually being properly connected. Why the signal saturates when there's nothing connected beats the hell out of me.
At any rate...
I'm trying to use an accelerometer to take measurements. I have it physically wired to my computer's DAQ board (a NI 6025E). According to the manual, pin 1 is ground and pin 3 is analog input 0. Therefore, this is where I have the output from my accelerometer going. I checked the signal at those...