1. Limited time only! Sign up for a free 30min personal 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!

What is diffusion tensor?

  1. Dec 1, 2009 #1
    Hi all:
    Does anyone explain why we call diffusion as the second rank tensor variable? I understand Based on the tensor definition, we know tensor expresses the relationship between input vector and output vector. How about diffusion? what is its input vector? what is its output vector? thanks in advance

    xf
     
  2. jcsd
  3. Dec 1, 2009 #2

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor
    2016 Award

    The diffusion tensor (or the related Oseen mobility tensor) are used to allow the material to be anisotropic. The diffusivity varies with location and direction.

    The current use of diffusion tensor comes from MRI (diffusion tensor imaging), but the concept was developed for colloidal solutions.
     
  4. Dec 1, 2009 #3
    Thank you. Could you tell me what the meaning of each component of diffusion tensor matrix is ? For example, what do off-diagonal terms represent? What do diagonal terms represent?
    thanks
     
  5. Dec 2, 2009 #4

    Andy Resnick

    User Avatar
    Science Advisor
    Education Advisor
    2016 Award

    The diagonal components are translational diffusivities/mobilities. I think the off-diagonal components correspond to rotational mobility/diffusion.
     
  6. Dec 2, 2009 #5
    Thanks. I do not really understand your answer. After I search the internet and get some explanation, for diffusion tensor matrix, each component of matrix represents an apparent diffusion coefficient. These diffusion coefficient are not real diffusion coefficient. After we calculate the eigenvalue of the matrix, we can get true and objective diffusion coefficient which is independent of coordinate frame selection. I am not sure these explanations are correct or not. Anyway thank you. Andy Resnick

    xf
     
  7. Dec 3, 2009 #6

    Mapes

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The diagonal components represent flux in some direction caused by a concentration gradient in that same direction. The off-diagonal components represent flux in some direction caused by a concentration gradient in another direction (which is less intuitive).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: What is diffusion tensor?
Loading...