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Series: GT-MAP Seminars

Please go to http://gtmap.gatech.edu or http://gtmap.gatech.edu/events/workshop-mathematics-dynamical-systems for schedule, title and abstract.

Series: GT-MAP Seminars

There is an increasing trend for robots to serve as networked mobile sensing platforms that are able to collect data and interact with humans in
various types of environment in unprecedented ways. The need for
undisturbed operation posts higher goals for autonomy. This talk reviews
recent developments in autonomous collective foraging in a complex
environment that explicitly integrates insights from biology with models
and provable strategies from control theory and robotics. The methods
are rigorously developed and tightly integrated with experimental effort with promising results achieved.

Series: GT-MAP Seminars

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.

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.