Fernando Guevara Vasquez, Professor, University of Utah
1 – 2PM
Friday Feb 3, 2017
POB 6.304
Abstract
Consider a compressible fluid that is subject to a standing acoustic wave. Particles within the fluid are subject to an acoustic radiation force and tend to move to minima of the associated potential. In many cases, these minima coincide with the nodal sets of the standing wave, which are solutions to the Helmholtz equation. We present two methods for solving the control problem of finding the settings for transducers lining a reservoir (i.e. boundary conditions), necessary to best approximate a desired particle pattern within the reservoir. In the first method, a discretized version of the control problem is reduced to finding the smallest eigenvalue of a matrix. In the second method, we use an approximation result of functions by entire solutions to the Helmholtz equation to give an efficient and explicit solution to the control problem. An application of this principle is to fabricate selectively reinforced composite materials, where the matrix is a photo-cured polymer and the inclusions are carbon nanotubes.