The field of MEMS, Micro-Electro-Mechanical Systems, is the branch of microelectronic engineering dedicated to building microscopic machines on computer chips. The field emerged with the refinement of chip fabrication methods. Over the past twenty years, it has evolved from an academic novelty into a useful industrial enterprise. MEMS accelerometers trigger automobile airbags, MEMS micromirror arrays display HDTV images, MEMS sensors measure blood pressure through IV lines, and MEMS fluid pumps produce pictures in ink jet printers. In this talk, David Ross will introduce the field of MEMS from a mathematician's perspective. He will discuss some of his modeling work on MEMS energy harvesters and ink jet printheads. In connection with ink jet printing, he will discuss one model in detail.
Experiments with bi-layer MEMS microbeams show that the resonant frequencies of such beams depend non-monotonically on temperature. At low temperatures, the beams' fundamental frequency decreases with increasing temperature; at high temperatures, this frequency increases. Ross will present a mathematical model that explains this unexpected phenomenon. The model is expressed as a nonlinear PDE. He will show how numerical solutions of this PDE helped identify the cause of the non-monotone behavior, and he will describe several open mathematical questions.