@article{castle_2021, title={Developing Non-Calculus Service Courses That Showcase the Applicability of Mathematics}, volume={7}, ISBN={["978-3-030-61719-6", "978-3-030-61716-5"]}, ISSN={["2199-305X"]}, DOI={10.1007/978-3-030-61717-2_4}, abstractNote={Students often take precalculus or college algebra as a terminal math course, leaving them with the impression that mathematics lacks real meaning. As applied mathematicians, we are well-poised to intervene and design inspiring general education courses that reveal the utility of mathematics. In this paper, we share experiences working with faculty from a range of disciplines to develop a two-course sequence that explores mathematical concepts by answering questions that matter to our student population.}, journal={IMPROVING APPLIED MATHEMATICS EDUCATION}, author={Castle, Lucas}, year={2021}, pages={51–64} }
@article{bociu_castle_lasiecka_tuffaha_2020, title={Minimizing drag in a moving boundary fluid-elasticity interaction}, volume={197}, ISSN={["1873-5215"]}, DOI={10.1016/j.na.2020.111837}, abstractNote={Our goal is to minimize the fluid vorticity in the case of an elastic body moving and deforming inside the fluid, using a distributed control. This translates into analyzing an optimal control problem subject to a moving boundary fluid–structure interaction (FSI). The FSI is described by the coupling of Navier–Stokes and wave equations. The control is inherently a nonlinear control, acting as feedback on the moving frame. Its action depends on the flow map of the domain, which is itself defined through the dynamics of the problem. A key ingredient in the optimal control problem is represented by the long time behavior of the forced dynamics, which was an open problem in the field. Our main results include existence of solutions for all times with small distributed sources and small initial data, as well as existence of optimal control for the problem of minimization of drag in the fluid.}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Bociu, L. and Castle, L. and Lasiecka, I and Tuffaha, A.}, year={2020}, month={Aug} }