Seminars and Colloquia by Series

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.
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.  
Friday, December 2, 2016 - 15:00 , Location: Skiles 006 , Prof. David McDowell and Shouzhi Xu , GT ME and MSE , Organizer: Sung Ha Kang

Talk by Shuozhi Xu,

Title: Algorithms and Implementation for the Concurrent Atomistic-Continuum Method.

Abstract: Unlikemany other multiscale methods, the concurrent atomistic-continuum
(CAC) method admits the migration of dislocations and intrinsic
stacking faults through a lattice while employing an underlying
interatomic potential as the only constitutive relation. Here, we
build algorithms and develop a new CAC code which runs in parallel
using MPI with a domain decomposition algorithm. New features of the
code include, but are not limited to: (i) both dynamic and
quasistatic CAC simulations are available, (ii) mesh refinement
schemes for both dynamic fracture and curved dislocation migration
are implemented, and (iii) integration points in individual finite
elements are shared among multiple processors to minimize the amount
of data communication. The CAC program is then employed to study a
series of metal plasticity problems in which both dislocation core
effects at the nanoscale and the long range stress field of
dislocations at the submicron scales are preserved. Applications
using the new code include dislocation multiplication from Frank-Read
sources, dislocation/void interactions, and dislocation/grain
boundary interactions.

Crystal plasticity modeling is useful for considering the influence of anisotropy of elastic and plastic deformation on local and global responses in crystals and polycrystals. Modern crystal plasticity has numerous manifestations, including bottom-up models based on adaptive quasi-continuum and concurrent atomistic-continuum methods in addition to discrete dislocation dynamics and continuum crystal plasticity. Some key gaps in mesoscale crystal plasticity models will be discussed, including interface slip transfer, grain subdivision in large deformation, shock wave propagation in heterogeneous polycrystals, and dislocation dynamics with explicit treatment of waves. Given the mesoscopic character of these phenomena, contrasts are drawn between bottom-up (e.g., atomistic and discrete dislocation simulations and in situ experimental observations) and top-down (e.g., experimental) information in assembling mesoscale constitutive relations and informing their parameters.
Friday, November 18, 2016 - 12:00 , Location: Skiles 006 , Luca Dieci and Sung Ha Kang , GT Math , Organizer: Sung Ha Kang
This is an information session about research opportunities related to GT MAP activities.  If you are a math graduate student, please join for free pizza as well.
Friday, October 21, 2016 - 15:00 , Location: Skiles 006 , Prof. Julian Rimoli , GT AE , Organizer: Sung Ha Kang
Most available techniques for the design of tensegrity structures can be  grouped in two categories. On the one hand, methods that rely on the  systematic application of topological and geometric rules to regular polyhedrons have been applied to the generation of tensegrity elementary  cells. On the other hand, efforts have been made to either combine  elementary cells or apply rules of self-similarity in order to generate  complex structures of engineering interest, for example, columns, beams and  plates. However, perhaps due to the lack of adequate symmetries on  traditional tensegrity elementary cells, the design of three-dimensional  tensegrity lattices has remained an elusive goal. In this work, we first  develop a method to construct three-dimensional tensegrity lattices from  truncated octahedron elementary cells. The required space-tiling  translational symmetry is achieved by performing recursive reflection  operations on the elementary cells. We then analyze the mechanical response  of the resulting lattices in the fully nonlinear regime via two distinctive approaches: we first adopt a discrete reduced-order model that explicitly accounts for the deformation of individual tensegrity members, and we then utilize this model as the basis for the development of a continuum approximation for the tensegrity lattices. Using this homogenization method, we study tensegrity lattices under a wide range of loading conditions and prestressed configurations. We present Ashby charts for yield strength to density ratio to illustrate how our tensegrity lattices can potentially achieve superior performance when compared to other lattices available in the literature. Finally, using the discrete model, we analyze wave propagation on a finite tensegrity lattice impacting a rigid wall. 

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