Georgia Institute of Technology College of Sciences

Data assimilation is a powerful tool for combining mathematical models with real-world data to make better predictions and estimate the state and/or parameters of dynamical systems. In this talk I will give an overview of some work on models for predicting urban crime patterns, ranging from stochastic models to differential equations. I will then present some work on data assimilation techniques that have been developed and applied for this problem, so that these models can be joined with real data for purposes of model fitting and crime forecasting.

GT MAP sponsored "Workshop on Dynamical Systems" to mark the retirement of Prof. Shui Nee Chow. Full day August 10- 11. After nearly 30 years at Georgia Tech, Prof. Shui Nee Chow has officially retired. This workshop will see several of his former students, post-docs, and friends, coming together to thank Shui Nee for his vision, service, and research, that so greatly impacted the School of Mathematics at Georgia Tech. The workshop will be held in the Klaus building Room 1447. More information at http://gtmap.gatech.edu/events/workshop-dynamical-system

Robotic snakes have the potential to navigate areas or environments that would be more challenging for traditionally engineered robots. To realize their potential requires deriving feedback control and path planning algorithms applicable to the diverse gait modalities possible. In turn, this requires equations of motion for snake movement that generalize across the gait types and their interaction dynamics. This talk will discuss efforts towards both obtaining general control equations for snake robots, and controlling them along planned trajectories. We model three-dimensional time- and spatially-varying locomotion gaits, utilized by snake-like robots, as planar continuous body curves. In so doing, quantities relevant to computing system dynamics are expressed conveniently and geometrically with respect to the planar body, thereby facilitating derivation of governing equations of motion. Simulations using the derived dynamics characterize the averaged, steady-behavior as a function of the gait parameters. These then inform an optimal trajectory planner tasked to generate viable paths through obstacle-strewn terrain. Discrete-time feedback control successfully guides the snake-like robot along the planned paths.

The first part of this talk will review our recent efforts on the electroelastodynamics of smart structures for various applications ranging from nonlinear energy harvesting, bio-inspired actuation, and acoustic power transfer to elastic wave guiding and vibration attenuation via metamaterials. We will discuss how to exploit nonlinear dynamic phenomena for frequency bandwidth enhancement to outperform narrowband linear-resonant devices in applications such as vibration energy harvesting for wireless electronic components. We will also cover inherent nonlinearities (material and internal/external dissipative), and their interactions with intentionally designed nonlinearities, as well as electrical circuit nonlinearities. Electromechanical modeling efforts will be presented, and approximate analysis results using the method of harmonic balance will be compared with experimental measurements. Our recent efforts on phononic crystal-enhanced elastic wave guiding and harvesting, wideband vibration attenuation via locally resonant metamaterials, contactless acoustic power transfer, bifurcation suppression using nonlinear circuits, and exploiting size effects via strain-gradient induced polarization (flexoelectricity) in centrosymmetric elastic dielectrics will be summarized. The second part of the talk, which will be given by Chris Sugino (Research Assistant and PhD Student), will be centered on low-frequency vibration attenuation in finite structures by means of locally resonant elastic and electroelastic metamaterials. Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration/sound attenuation. Typically, bandgap analyses and predictions rely on the assumption of waves traveling in an infinite medium, and do not take advantage of modal representations commonly used for the analysis of the dynamic behavior of finite structures. We will present a novel argument for estimating the locally resonant bandgap in metamaterial-based finite structures (i.e. meta-structures with prescribed boundary conditions) using modal analysis, yielding a simple closed-form expression for the bandgap frequency and size. A method for understanding the importance of the resonator locations and mass distribution will be discussed in the context of a Riemann sum approximation of an integral. Numerical and experimental results will be presented regarding the effects of mass ratio, non-uniform spacing of resonators, and parameter variations among the resonators. Electromechanical counterpart of the problem will also be summarized for piezoelectric structures.