TITLE:

COMPLEX NETWORKS: Connecting Equivariant Bifurcation Theory with Engineering Applications

DATE:

Friday, January 19, 2018

TIME:

3:30 PM

LOCATION:

GMCS-314

SPEAKER:

Dr. Antonio Palacios, Department of Mathematics and Statistics, SDSU

ABSTRACT:

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 eighteen years of work aimed at combining ideas
and methods from equivariant bifurcation theory to model, analyze and fabricate
novel technologies such as: ultra-sensitive magnetic and electric field
sensors; networks of nano oscillators; and multi-frequency converters.
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 the actual
design and fabrication.

HOST:

Dr. Jose Castillo

DOWNLOAD:

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