Abstract: Some open challenges for wind waves and nature's natural patterns
I plan to talk to you about several of the challenges that I am currently wrestling with in research projects. The first set of challenges have to do with the waves on windswept seas. How is energy transferred from wind to waves and how is that energy redistributed throughout the spectrum? In nonlinear systems, in general, the closure of the set of moment equations that describe the statistics is unclosed but for weakly nonlinear dispersive waves one finds a natural closure. What are the consequences of that closure? What are the open questions? The second set of challenges have to do with patterns that arise both in nature and the laboratory, generally from instabilities, (e.g. the buckling patterns one sees on compressed elastic shells, the rich mosaics of patterns you see on sunflowers, in convection patterns). One would like to understand the circumstances under which various shapes such as rolls, squares, hexagons, Fibonacci patterns are seen. One would like to understand how one might go about describing their behaviors in mathematical terms by what are called order parameter equations. One would like to understand possible connections between optimal packing and preferred pattern arrangements. One would like to know if there is a role machine learning can play in the formulation of order parameter equations.
The talk will be informal. Interruptions and questions and discussions are welcome. There is no end goal other than provoking interest.