Understanding Hysteresis Curves: Mathematical Modeling for Nonlinear ODEs

[mhill]

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.

 

[pam]

Since B(H) is not a single valued function, or any simple function, of H, you cannot do what you are trying.

 

[charng]

I am fascinated by the concept of hysteresis curves and the potential for mathematical modeling to help us understand and predict their behavior. The proposed model, with a nonlinear ODE representing the relationship between magnetic field strength (H) and magnetic flux density (B), shows promise in capturing the complex and dynamic nature of hysteresis curves.

However, it is important to note that while mathematical models can provide valuable insights and predictions, they are not a perfect representation of the real world. There are many factors that can affect the behavior of hysteresis curves, such as material properties, environmental conditions, and experimental setup. Therefore, it is crucial to validate any mathematical model with experimental data to ensure its accuracy and applicability.

That being said, if we can provide a model of a nonlinear ODE that accurately represents the relationship between H and B, we can indeed deduce the hysteresis curve mathematically. This would allow us to study and analyze the behavior of hysteresis curves in a more systematic and quantitative manner, leading to a better understanding of their underlying mechanisms.

In conclusion, the idea of using mathematical modeling to understand hysteresis curves is a promising one, and I am eager to see further research and developments in this area. By combining theoretical models with experimental data, we can gain a deeper understanding of hysteresis and its implications in various fields such as materials science, engineering, and physics.