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!

A mathematical explanation of hysteresis?

  1. Oct 20, 2012 #1
    I wish to know why and how does hysteresis occur from a purely mathematical perspective, using analytical functions and multivariable calculus. Thank you!
     
  2. jcsd
  3. Oct 20, 2012 #2

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor

    Since some phenomena and materials experience this and some don't, a "purely mathematical perspective" is impossible. Some physics will need to enter the problem.
     
  4. Oct 20, 2012 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    From a purely mathematical point of view, hysteresis results when there is a cubic (or higher degree odd) dependence. If, in the phase plane (y versus dy/dt) y has a cubic dependence on dy/dt and we have the central part (in red in the graph below) unstable, then as x approaches 2 from below, it jumps to the other blue branch, going from 2 up. But as we come back down, x will stay on that section until it gets down to x= -2 before it jumps to the branch. (The x-axis is vertical in this graph.)
    hysteresis.jpg
     
  5. Oct 20, 2012 #4
    Hysteresis refers to an number of unrelated physical phenomena (and to some related ones) in mechanical systems, digital electronics, elasticity, electromagnetism to name but a few.

    So if you would like to tell us which area you referring to please?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A mathematical explanation of hysteresis?
Loading...