Bryan J. Glaz : The Quasi-Periodic Intermittency Attractor and a Fractional Calculus Perspective of Generalized Spectral Decompositions for Nonlinear Dynamical Systems
Complex, nonlinear dynamical systems are pervasive across many Army relevant scientific disciplines, including turbulence, robotics, and reconfigurable active matter. Typically, our engineering objectives are to control the
dynamics. However, our inability to achieve these objectives for a variety
of high-dimensional dynamical systems is due to a lack of mathematical tools
to describe underlying salient, particularly when it comes to control of
such systems. This talk focuses on the Koopman theoretic based spectral
decomposition perspective for extracting these features.
In the first part of the talk, we demonstrate how external forcing (e.g.
control) can be accounted for in the form of a parametric term added to the
Koopman operator of the unforced system. By using the simple fluid dynamics
example of streamwise oscillating flow over a cylinder, we establish an
analogy with parametrically excited Hopf bifurcations. Quite unexpectedly,
we happened upon a peculiar phenomenon that is not quite chaotic, not quite
quasi-periodic, and not quite intermittent. We establish the theoretical
underpinnings for this phenomenon, that we name Quasi-periodic Intermittency
and we discuss the implications across a variety of physical systems. In the
second part of the talk, a fractional calculus perspective of complexity
will be introduced to generalize Koopman based spectral decompositions to
systems with memory as a first step toward dealing with truly complex
systems. The analysis leads to modes whose temporal behavior is anomalous
and lacks a characteristic scale. The approach we propose may uncover
inherent memory effects that would otherwise be obscured by conventional
spectral methods.
The talk will conclude with a discussion of new follow-on research thrusts
ranging from control for adaptive, reflexive robotic mobility to
self-organized adaptation and reconfiguration of active matter systems. In
addition, opportunities for students (undergraduate and graduate) and
faculty to engage with the U.S. Army Research Laboratory will be discussed.
- Category: Nonlinear and Complex Systems
- Duration: 01:24:45
- Date: October 25, 2017 at 11:55 AM
- Tags: seminar, CNCS Seminar (MEMS Fall Seminar Series)
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