How Applied Math Labs Shape Research (and Teaching)
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How Applied Math Labs Shape Research (and Teaching)
Applied mathematics has always been experimental, though our experiments look different from those in physics or biology. In math labs, such as those at Courant, MIT, UCLA, UNC, and Arizona, we study problems such as fluid–structure interactions, falling bodies, and pattern formation with a mathematician’s perspective: we simplify the problem, quantify it, and choose boundary conditions carefully. We set up problems that can be reduced to two-dimensional or axisymmetric cases, focus on the leading-order dynamics, and build experiments that match the models. Classic examples include flapping flags and foils, falling spheres, bouncing droplets, and valveless pumps, where controlled experiments reveal nonlinear instabilities, transitions between flow regimes, and scaling relations. To tackle these problems, we rely not just on theory but on the art of modeling and the development of new numerical methods. In this talk I will show how new mathematics is inspired and generated when lab work, numerics, and theory are developed together, and reflect on how this experimental approach enriches teaching and student training.