Wellen und Fronten in der Mathematik : Wasserwellen und weitere Beispiele wandernder Wellen

Wasserwellen faszinieren Menschen seit den frühen Kulturen. Wir geben einen kurzen Abriss der mathematischen Theorie der Wasserwellen und ihrer Entstehung. Aus mathematischer Sicht sind Wasserwellen sogenannte “traveling waves”, welche auch für die Feststoffverbrennung und die Verbrennungssynthese von Bedeutung sind, auf deren Musterbildung wir kurz eingehen. Schließlich beschreiben wir Erweiterungen der traveling waves auf allgemeinere Konzepte wie pulsating waves und transition waves, die gegenwärtig in unserer Arbeitsgruppe untersucht werden.

Water waves have been intriguing humans since the early civilizations. We briefly discuss the origins of the mathematical theory of water waves and its development in the 19th century, concluding our first section with research on “Stokes conjecture” as an example of recent research on water waves. Water waves are special examples of so-called travelling waves and fronts. In our second example we consider models of smouldering combustion and self-propagating high-temperature synthesis (SHS). In experiments and simulation, the planar combustion front becomes unstable and fingers or screw-like fronts arise. In the regime of high activation energy, we point out a fascinating relation to a model of the freezing of super-cooled water. Similar models appear in the modelling of growing bacteria in a petri dish. In the last section we describe the mathematical framework of travelling waves, beginning with planar waves and extending definitions to pulsating waves and transition waves, and hinting at even more general waves, which are currently one of the research topics in our group.



Citation style:
Could not load citation form.


Use and reproduction:
All rights reserved