Friday, December 1, 2017 - 14:00 , Location: Skiles , TBA , GT Math , Organizer: Sung Ha Kang
Friday, November 10, 2017 - 15:00 , Location: Skiles 006 , Prof. Fumin Zhang , GT ECE , Organizer: Sung Ha Kang
Modeling and predicting urban crime – How data assimilation helps bridge the gap between stochastic and continuous modelsFriday, October 20, 2017 - 15:00 , Location: Skiles 006 , Prof. Martin Short , GT Math , Organizer: Sung Ha Kang
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.
Thursday, August 17, 2017 - 09:00 , Location: Klaus 2447 , Various Speaker , Different units of GT , Organizer: Sung Ha Kang
The workshop will launch the thematic semesters on Dynamics (Fall 2017) and Control (Spring 2018) for GT-MAP activities. This is a two-day workshop, the first day focusing on the theme of Dynamics, and the second day focusing on the theme of Control. There will be light refreshments throughout the event. The workshop will be held in the Klaus building Room 2447. More information at http://gtmap.gatech.edu/events/gt-map-workshop-dynamics-and-control
Thursday, August 10, 2017 - 10:54 , Location: Klaus 1447 , Various Speakers , From various places , Organizer: Sung Ha Kang
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
Tuesday, May 9, 2017 - 10:00 , Location: Skiles 006 , Speaker list and schedule can be found at http://www.math.gatech.edu/hg/item/589661 , Organizers: Shui-Nee Chow, Wilfrid Gangbo, Prasad Tetali, and Haomin Zhou , Organizer: Haomin Zhou
This workshop is sponsored by College of Science, School of Mathematics, GT-MAP and NSF.
The goal of this workshop is to bring together experts in various aspects of optimal transport and related topics on graphs (e.g., PDE/Numerics, Computational and Analytic/Probabilistic aspects).
Friday, April 14, 2017 - 16:00 , Location: Skiles 006 , Alexander H. Chang , GT ECE , Organizer: Sung Ha Kang
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.
Friday, April 14, 2017 - 15:00 , Location: Skiles 006 , Patricio A. Vela , GT ECE , Organizer: Sung Ha Kang
Robotic locomotive mechanisms designed to mimic those of their biological counterparts differ from traditionally engineered systems. Though both require overcoming non-holonomic properties of the interaction dynamics, the nature of their non-holonomy differs. Traditionally engineered systems have more direct actuation, in the sense that control signals directly lead to generated forces or torques, as in the case of rotors, wheels, motors, jets/ducted fans, etc. In contrast, the body/environment interactions that animals exploit induce forces or torque that may not always align with their intended direction vector.Through periodic shape change animals are able to effect an overall force or torque in the desired direction. Deriving control equations for this class of robotic systems requires modelling the periodic interaction forces, then applying averaging theory to arrive at autonomous nonlinear control models whose form and structure resembles that of traditionally engineered systems. Once obtained, classical nonlinear control methods may be applied, though some attention is required since the control can no longer apply at arbitrary time scales.The talk will cover the fundamentals of averaging theory and efforts to identify a generalized averaging strategy capable of recovering the desired control equations. Importantly, the strategy reverses the typical approach to averaged expansions, which significantly simplifies the procedure. Doing so provides insights into feedback control strategies available for systems controlled through time-periodic signals.
Friday, February 17, 2017 - 15:00 , Location: Skiles 006 , Prof. Alper Erturk , GT Mechanical Engineering , Organizer: Sung Ha Kang
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.
Modeling and Control of hybrid systems and systems with delay, with applications from population dynamics to post-Newtonian gravitation.Friday, January 27, 2017 - 15:00 , Location: Skiles 006 , Prof. Erik Verriest , GT ECE , Organizer: Sung Ha Kang
This talk contains two parts. First I will discuss our work related to causal modeling in hybrid systems. The idea is to model jump conditions as caused by impulsive inputs. While this is well defined for linear systems, the notion of impulsive inputs poses problems in the nonlinear case. We demonstrate a viable approach based on nonstandard analysis. The second part deals with dynamical systems with delays. First I will show an application of the maximum principle to a delayed resource allocation problem in population dynamics solving a problem in the model of a bee colony cycle. Next I discuss some problems regarding causality in systems with varying delays. These problems relate to the well-posedness (existence and uniqueness) and causality of the mathematical models for physical phenomena, and illustrate why one should consider the physics first and then the mathematics. Finally, I consider the post Newtonian problem as a problem with state dependent delay. Einstein’s field equations relate space time geometry to matter and energy distribution. These tensorial equations are so unwieldy that solutions are only known in some very specific cases. A semi-relativistic approximation is desirable: One where space-time may still be considered as flat, but where Newton’s equations (where gravity acts instantaneously) are replaced by a post-Newtonian theory, involving propagation of gravity at the speed of light. As this retardation depends on the geometry of the point masses, a dynamical system with state dependent delay results, where delay and state are implicitly related. We investigate several problems with the Lagrange-Bürman inversion technique and perturbation expansions. Interesting phenomena (entrainment, dynamic friction, fission and orbital speeds) not explainable by the Newtonian theory emerge. Further details on aspects of impulsive systems and delay systems will be elaborated on by Nak-seung (Patrick) Hyun and Aftab Ahmed respectively.