- #1
lucerne
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I wish to know why and how does hysteresis occur from a purely mathematical perspective, using analytical functions and multivariable calculus. Thank you!
A mathematical explanation of hysteresis?
- Context: Graduate
- Thread starter lucerne
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Discussion Overview
The discussion centers on the mathematical explanation of hysteresis, exploring its occurrence and characteristics through analytical functions and multivariable calculus. Participants examine the interplay between mathematical models and physical phenomena associated with hysteresis.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant expresses a desire to understand hysteresis from a purely mathematical perspective, emphasizing the use of analytical functions and multivariable calculus.
- Another participant argues that a purely mathematical perspective is impossible due to the necessity of incorporating physics, as not all phenomena exhibit hysteresis.
- A different viewpoint suggests that hysteresis can be mathematically described by a cubic or higher degree odd dependence in the phase plane, detailing a specific behavior of the system as it transitions between states.
- One participant notes that hysteresis encompasses a variety of physical phenomena across different fields, prompting a request for clarification on the specific area of interest.
Areas of Agreement / Disagreement
Participants do not appear to reach a consensus, as there are competing views on the necessity of incorporating physics into the mathematical explanation of hysteresis and the specific contexts in which hysteresis occurs.
Contextual Notes
The discussion highlights the complexity of hysteresis, indicating that its mathematical modeling may depend on specific physical contexts and assumptions that are not fully resolved in the conversation.
- #2
Vanadium 50
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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.
- #3
HallsofIvy
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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.)
- #4
Studiot
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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?
So if you would like to tell us which area you referring to please?
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