# Analysis and extensions of Tellinen’s scalar hysteresis model

My name is Jan Kühn and I am a PhD student in the Applied Mathematics and Numerical Analysis (AMNA) working group of the University of Wuppertal. My bachelor degree was in applied science with the combination of mathematics and physics. The master degree was in mathematics with special focus on the applied side. Both degrees were obtained in Wuppertal.

My bachelor thesis was dealing with the creation of monotonic material curves, which are used for non-linear bh-curves. My master thesis already included Tellinen’s hysteresis model and combined it with uncertainty quantification. I’m currently in the last phase of my PhD, hoping to finish in a few months.

Why I became a PhD student
I like the combination of modeling physical phenomena and solving it with mathematically methods. My focus on magnetic field simulation offers me exactly that. So I wanted to expand my knowledge and dive deeper into the topic.

What if two quantities depend on each other, but this can no longer be expressed simply by an equation? This is what hysteresis is about. The current link between the quantities depends on the complete history before. Can this be numerically approximated? For magnetic hysteresis, Tellinen’s model is one of many models that try to describe the relationship between the magnetic field strength h and flux density b for ferromagnetic materials.

What I will do during my PhD
After a more detailed examination of Tellinen’s model compared to the master thesis, the next step was to extend the model. So I had to add ideas and approaches myself. And always keeping the physical background in mind.

I extended the basic model by a hysteresis loss model. These losses are dissipated as heat. So parameters were now expected to be temperature dependent. To always ensure a mathematically valid state, a thermal extension was needed. With these two extension and a combination with a heat diffusion simulation, it is now possible for me to simulate magnetic fields with temperature dependence and hysteresis.

Overall, the fine line between physical modeling and numerical realization plays an important role. No matter how good the model may be, if it cannot be meaningfully embedded in a simulation, it becomes tricky. But if the model does not describe the desired physical phenomena, you will not get anywhere. It is precisely this balancing act that accounts for a large part of my research.