Free boundary methods and non-scattering phenomena

We study a question arising in inverse scattering theory: given a penetrable obstacle, does there exist an incident wave that does not scatter? We show that every penetrable obstacle with real-analytic boundary admits such an incident wave. At zero frequency, we use quadrature domains to show that there are also obstacles with inward cusps having this property. In the converse direction, under a nonvanishing condition for the incident wave, we show that there is a dichotomy for boundary points of any penetrable obstacle having this property: either the boundary is regular, or the complement of the obstacle has to be very thin near the point. These facts are proved by invoking results from the theory of free boundary problems.

Utilization of direct forcing immersed boundary methods for the optimization of inertial focusing microfluidics

Inertial focusing microfluidics have gained significant momentum in the last decade for their ability to separate and filter mixtures of particles and cells based on size [1-3]. However, the most important feature is that the separation is passive, without the need for external forces. At the heart of inertial focusing is the balance between counteracting lift forces: shear and wallinduced lift. Shear-induced lift is a product of the curvature of the fluid flow and the rotation of the particle in the flow, while wall-induced lift is generated by the disturbance of the fluid by the particle near a wall. This phenomenon was first observed by Segre and Silberberg for the focusing of particles in a pipe, and was later extended to the focusing of cells and particle in rectangular channels [4]. Taking advantage of inertial focusing we explore particle capture utilizing an expanded channel microfluidics chip design. By expanding a small region of the straight channel microvortices form in the well, which allows for size selective trapping of particles.