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!

Variation Formulations of Physical Laws: The Correct Formulation

  1. Oct 1, 2013 #1
    Source of Question
    J.N. Reddy states in Finite Element Method: "Variational forms of the laws of continuum physics may be the only natural and rigorously correct way to think of them. While all sufficiently smooth fields lead to meaningful variational forms, the converse is not true: There exists physical phenomena which can be adequately modeled mathematically only in a variational setting; they are nonsensical when viewed locally"

    My Question
    What are some examples of physical phenomena that can be adequately modeled mathematically only in a variational setting and why are they nonsensical when viewed locally?
     
  2. jcsd
  3. Oct 1, 2013 #2

    UltrafastPED

    User Avatar
    Science Advisor
    Gold Member

    Some approaches are "mean field theories" which result in very smooth fields - Maxwell's equations in matter are an example. But when you look at the microscopic sources of the fields (atoms and molecules, etc) their appear to be discontinuities ... hence you cannot meet the usual requirements for differentiability so that you can carry out the variational principle.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Variation Formulations of Physical Laws: The Correct Formulation
Loading...