Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bounds of Integration for Random Oriented particle

  1. Jun 15, 2015 #1
    In the Stoner-Wohlfarth model, a uniaxial, non-interacting particle is cooled to very low temperature with no exposure to an external field. Therefore, the orientation of each particle is random, if you have a group of particles. In their paper, they integrate such that:
    [tex]\langle \cos (\Theta )\rangle =\int_0^{\frac{\pi }{2}} \sin (\Theta ) \cos (\Theta ) \, d\Theta[/tex]

    I am having a hard time understanding why they only integrate from 0 to pi over two, instead of 0 to pi. Can anyone shine any enlightenment on this?
     

    Attached Files:

  2. jcsd
  3. Jun 15, 2015 #2

    fzero

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    A copy of the paper can be found at http://spin.nanophys.kth.se/spin/stoner-wohlfarth.pdf There's a lot of discussion around Fig. 4 where they talk about how the symmetries of the problem allow them to reproduce the solutions everywhere in parameter space from the region ##0 \leq \theta,\phi \leq \pi/2##.
     
  4. Jun 16, 2015 #3
    That helped me tremendously - thank you!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook