Henok Mawi, Ph.D., a Howard University assistant professor of mathematics, received a National Science Foundation Research Award for $275,509.

The award will support the project titled “Research Initiation Award: Mathematical Modeling on the Geometric Optics Problem of Refraction.” The objective of the research is to investigate some mathematical models that originate from geometrical optics and to answer questions pertinent to the synthesis of refracting surfaces that are capable of redirecting light rays of a given intensity from a point source onto a given set of direction or target, which has a prescribed intensity.

The synthesis of such optical surfaces starts at careful application of laws of optics and energy conservation and naturally leads to a highly nonlinear mathematical model. The mathematical analysis uses techniques that interweave the mathematics of mass transportation theory, calculus of variations as well as nonlinear partial differential equations of Monge–Ampère type. The numerical aspect of study of the model focuses on obtaining efficient computational methods and simulating some models of these surfaces. The geometric set up of the model—together with the analytical studies—will provide a means of obtaining an algorithm that will help to compute the solution numerically.

The research has numerous potential applications in the design of efficient optical devices, which range from free-form lenses to reflector antennas and medical imaging machines.

Mawi is an associate professor in the department of mathematics in the College of Arts and Sciences. His research is in partial differential equations and involves investigation of mathematical models that can be described using these equations. He earned his Ph.D. from Temple University and was a postdoctoral fellow at the Mathematical Sciences Research Institute in Berkley, California.