Adrien Semin develops mathematical models to describe the propagation of sound waves. He is postdoctoral fellow in the Department of Mathematics, Technische Universität Berlin.

## »If nature could be written in equations, there would be no more surprises«

**Why do we need mathematical models to study natural phenomena? **

Modelling and simulations are often less time-consuming and expensive than real experiments. And in some cases, it would simply not be feasible to conduct a real experiment and make observations. For example, if we wanted to understand the aerodynamics of an aeroplane in flight, it would be very difficult to see or measure air behaviour in a real experiment. The same applies to sound waves, which is what I am trying to model. I am working on a Navier–Stokes equation that describes acoustic waves in the presence of fluids. My goal is to understand how waves are propagated at different length scales. I'll give you an example: if we have a turbine chamber which is one metre long with small holes of one millimetre in diameter, there will be perturbations near these small holes. But they will not happen in the same way on a larger scale, if the holes are ten times that size, for example. The patterns will be different. Our idea is to derive a mathematical model that fits both scales.

**What about wave type? Does it make a difference in simulations?**

When mathematicians think about wave propagation, it makes no difference whether we are talking about water waves, sound waves, or light waves. The theoretical models, the geometry, and even our observations can vary, but the mathematics behind them always stays the same. So the techniques we use to develop the model also remain relatively constant.

**How close do models come to real phenomena? **

Not especially close, I would have to say. To describe a complex physical phenomenon like the flow of water in a turbine chamber, we have to break it up into a series of different mathematical problems. We start with simplified equations that only include a limited number of parameters, for example the size of the turbine chamber. We cannot create a complete model that accounts for all possible parameters of the phenomenon we are studying. That would be mathematically impossible. Our models can offer little more than approximations. This is fine, as long as we apply a given model within our explicit range of parameters. However, we will start to have problems when we try to transfer a model to a new set of parameters. Reality is far too complex to be described in mathematical terms. On the other hand, if nature could be written in equations, there would be no more surprises. That would make my job as a scientist far less exciting.

*This page will not be updated after the end of the fellowship.*

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