Connecting Equivariant Bifurcation Theory with Bio-inspired Engineering Systems

Friday, April 20, 2018 - 12:15pm


Antonio Palacios
Department of Mathematics
San Diego State University


The advent of novel engineered or smart materials, whose properties can be significantly altered in a controlled fashion by external stimuli, has stimulated the design and fabrication of smaller, faster, and more energy-efficient devices. As the need for even more powerful technologies grows, networks have become popular alternatives to advance the fundamental limits of performance of individual devices. Thus, in the first part of this talk we provide an overview of biologically-inspired ultra-sensitive
magnetic and electric field sensors.

In the second part of the talk, we discuss more recent work on networks of coupled crystal oscillators as an alternative for developing an inexpensive precision timing device. At the National Observatory in Washington D.C., time is measured by averaging the times of an uncoupled ensemble. The measurements show a scaling law for phase-error reduction as 1/square-root(N), where N is the number of crystals in the ensemble. Preliminary results suggest that rotating wave patterns can significantly reduce phase error, with a scaling law that follows a 1/N curve. We use symmetry-based methods to classify all possible patterns of oscillations, which should guide engineers into future design and fabrication.