Nonlinear dynamics

Tuesday, May 2, 2017 - 11:00am - 12:00pm
Quan Nguyen (Vietnam National University)
In this talk, we present a method for transmission stabilization and robust dynamic switching for colliding soliton sequences in perturbed broadband waveguide systems. We show that dynamics of soliton amplitudes in N-sequence transmission can be described by N-dimensional Lotka-Volterra (LV) models, where the form of the LV model depends on the nature of the perturbation term. We study the stability and bifurcation analysis of the equilibrium points to stabilize soliton-sequence propagation and to achieve the transmission switching of the soliton sequences.
Monday, May 11, 2015 - 3:35pm - 4:00pm
Robert Lipton (Louisiana State University)
Geological formations comprised of oil shale are often quasi-brittle. Higher fidelity modeling beyond linear elastic fracture mechanics provides an opportunity to capture the effects of the process zone and softening near crack tips inside these materials. In this talk we present a non-local, nonlinear, cohesive continuum model of peridynamic type for assessing the deformation state inside a quasi-brittle formation. Here interaction forces between material points are initially elastic and then go unstable and soften beyond a critical relative displacement.
Wednesday, June 2, 2010 - 2:15pm - 3:00pm
Russ Tedrake (Massachusetts Institute of Technology)
Keywords: locomotion, motion planning, verification, control, robotic birds,

Abstract: Locomotion in fluids (and on terrain) often involves complex nonlinear
dynamics and non-trivial notions of stability including limit cycles
and dynamically stable maneuvers. In this talk I will describe some
new algorithms for automatically verifying stability (via a Lyapunov
function) and estimating regions of attraction for dynamic nonlinear
Tuesday, October 8, 2013 - 3:15pm - 4:05pm
Konstantin Mischaikow (Rutgers, The State University Of New Jersey )
It is a classical result that Newton's method converges rapidly to a nondegenerate zero if the
Tuesday, December 4, 2012 - 9:00am - 9:50am
Panayotis Kevrekidis (University of Massachusetts)
In this talk, we 'll start by reviewing some of the developments on nonlinear
dynamical lattices of the discrete nonlinear Schrodinger type. We will explore
ideas of continuation from the so-called anti-continuum limit, in order to
identify discrete solitons and their stability in 1d lattices, as well as
discrete vortices and more complex entities (such as vortex cubes) in two-dimensional and three dimensional case examples. Time-permitting we will
present some extensions of these nearest-neighbor lattices to longer range
Monday, March 11, 2013 - 3:00pm - 3:30pm
Henk Dijkstra (Rijksuniversiteit te Utrecht)
Results will be presented of a study on the interaction of noise and nonlinear dynamics
in a quasi-geostrophic model of the wind-driven ocean circulation. The recently developed
framework of dynamically orthogonal field theory is used to determine the statistics of
the flows which arise through successive bifurcations of the system as the ratio of forcing
to friction is increased. Focus will be on the understanding of the role of the spatial and
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