Understanding Hysteresis Curves: Mathematical Modeling for Nonlinear ODEs

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SUMMARY

The discussion focuses on the mathematical modeling of hysteresis curves, specifically the relationship between magnetic field strength (H) and magnetic flux density (B). A proposed nonlinear ordinary differential equation (ODE) is presented: \(\frac{dB}{dH}= B^{r}- (1/B)\). Participants emphasize the complexity of deriving a single-valued function for B(H) due to its inherent nonlinearity, indicating that a straightforward mathematical deduction of the hysteresis curve is not feasible.

PREREQUISITES
  • Understanding of nonlinear ordinary differential equations (ODEs)
  • Familiarity with magnetic field concepts, specifically magnetic flux density
  • Knowledge of hysteresis phenomena in physics
  • Basic calculus, particularly differentiation techniques
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  • Study the implications of non-single-valued functions in physical systems
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Physicists, engineers, and mathematicians interested in the mathematical modeling of hysteresis phenomena and nonlinear dynamics in materials.

mhill
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the idea is , if we have the magnetic field strength (H) and magnetic flux density (B) so we represent the 'hysteresis cycle' to be B(H)=B my question is could we deduce mathematically the hysteresis curve ?? for example if we can provide a model of a nonlinear ODE so

\frac{dB}{dH}= B^{r}- (1/B)

or something similar, i would be interested in the differential equation satisfied by B=B(H) thanks.
 
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Since B(H) is not a single valued function, or any simple function, of H, you cannot do what you are trying.
 

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