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Series: GT-MAP Seminars

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

Series: GT-MAP Seminars

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

Series: GT-MAP Seminars

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).

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.

Series: GT-MAP Seminars

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.