Dynamical systems and PDE's
Organizers - Dr. Michael Ward (UBC), Dr. Dmitri Pelinovski (McMaster), Dr. Luciano Buono (UOIT)
Plenary speaker: Antonio Palacios, SDSU.
Connecting Dynamical Systems Theory with Engineering Applications
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 seventeen years of work aimed at combining ideas and methods from dynamical systems and 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 vibratory gyroscopes systems. Under normal conditions of operation, the model equations can be reformulated in a Hamiltonian structure and the corresponding normal forms are then derived. Through a normal form analysis, we investigate the effects of various coupling topologies and unravel the nature of the bifurcations that lead a ring of gyroscopes of any size into and out of synchronization. The synchronization state is particularly important because it can lead to a significant reduction in phase drift, thus enhancing performance. The Hamiltonian approach can, in principle, be readily extended to other symmetry related systems.
Antonio Palacios received his Ph.D. in Mathematics at Arizona State University under the guidance of Prof. Dieter Armbruster. He was a postdoctoral fellow in Physics at the University of Houston under the guidance of Prof. Michael Gorman and then in Mathematics under the supervision of Prof. Marty Golubitsky. He joined the Math Department at San Diego State University in 1999 and has been a full professor since 2008. His research interests are in modeling complex nonlinear systems. In particular, multidisciplinary nonlinear systems that interface with Biology, Engineering, and Physics. Over the past fifteen years he has been collaborating with the Applied Chaos and Dynamics Group at the Space and Naval Warfare (SPAWAR) Center, San Diego to design and fabricate innovative technologies. A common theme of his work is to combine dynamical systems theory, symmetry, equivariant bifurcation theory and computational methods to model, analyze, predict and control the behavior of Complex Nonlinear Systems. A fundamental principle is to mimic what nature does best: to create symmetric networks of tightly interconnected artificial cells, i.e., devices, with collective optimal responses. He holds fifteen U.S. Patents for works that include: highly sensitive, biologically-inspired, networks of magnetic and electric field sensors; networks of energy harvesting systems with increase power output; arrays of vibratory gyroscopes with reduced phase drifts; and networks of superconducting loops for designing the next generation of antennas and radar systems.