1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Functional Derivative of Long Range Dipole Interaction Energy

  1. Oct 6, 2013 #1
    1. The problem statement, all variables and given/known data

    Dear all, Good day.

    I am currently working on the phase field modeling of ferroelectrics. For this reason, I need to find functional derivative of an expression as presented in attached picture 1.

    Then in picture 2, it shows the final form of equation that I am supposed to arrive at.

    2. Relevant equations

    I am stuck at line P in attached picture 5. Looking at the equation in line P, if I can include only the exponentials in the integral d^3g, then I can change them to 2*Dirac's delta, and the multiplication of dirac's delta with P' leads to P and performing Fourier transform, I can get the form as shown in attached picture 2. However, I doubt if I can do so because n is a function of g. Can anyone please help me on this? I have been breaking my head trying to figure this out for two days.

    3. The attempt at a solution

    My attempt on the question is as attached in picture 3, 4 and 5.

    As shown in attached picture 3, line A, B, C, D is how I started. I bring the unit vector n into the integral of P because it is not a function of r, then I separate exponential into cos real part and sin imaginary part. This is to get rid of the magnitude operator.

    Then in attached picture 4 and 5, from line E to P is how I am trying to find the functional derivative of F dip wrt P1. I am stuck at line P.
     

    Attached Files:

    • 1.jpg
      1.jpg
      File size:
      20.7 KB
      Views:
      69
    • 2.png
      2.png
      File size:
      69.3 KB
      Views:
      64
    • 3.jpg
      3.jpg
      File size:
      21.3 KB
      Views:
      63
    • 4.jpg
      4.jpg
      File size:
      34 KB
      Views:
      62
    • 5.jpg
      5.jpg
      File size:
      40.3 KB
      Views:
      63
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Functional Derivative of Long Range Dipole Interaction Energy
Loading...