Schedule:
- Unless otherwise noted, all talks will take place in the third floor
seminar room of Chauvenet Hall.
- Click on the title to see the abstract of the
individual talks (if javascript is enabled).
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Monday, September 15, 2008,
12:00 noon Dr. Eric M. Bollt (Clarkson
University)
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How Can I Say that A “Toy” Model
Reminds Me of My Observations?
A Dynamical Systems Perspective of Modeling and Comparing
Non-Conjugate Systems-- Mostly Conjugate
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abstract: We address a fundamental modeling
issue in science as related to the field of dynamical
systems: when is a model of a physical system a “good”
representation? Conjugacy provides a means to define if
two systems are dynamically equivalent; it is the
central equivalence relationship in the field of
dynamical systems. However, it cannot cope with systems
which are not dynamically identical. What then to do
with the common scientific practice of modeling, whereby
we build heuristic and phenomenological models which
“remind” us of the true system?
We develop mathematical technology to decide when
dynamics of a toy model are like dynamics of the
physical system. When applied to non-conjugate dynamical
systems, we show that a fixed point iteration scheme
yields a limit point, that is a function we call a
“commuter” — a non-homeomorphic change of coordinates
translating between dissimilar systems. This translation
is true to the concepts of dynamical systems in that it
matches systems within the language of their orbit
structures. We introduce methods to compare
nonequivalent systems by quantifying a defect of the
commuter function’s failure to be a homeomorphism - an
approach that better respects the dynamics than any
traditional comparisons based on normed linear spaces.
Our discussion addresses a fundamental issue — how does
one make principled statements of the degree to which a
“toy model” might be representative of a more
complicated system. We highlight our methods with a
lower-ordered models of more complicated systems. |
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Wednesday, October 22, 2008,
12:00 noon Dr. Michal Branicki (University
of Bristol)
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An Adaptive Method for Computing Invariant Manifolds
in Non-Autonomous, Three-Dimensional Dynamical Systems
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abstract: I'll discuss a computational method for determining the geometry of
three-dimensional invariant manifolds in non-autonomous dynamical systems which can be applied
to analyze the geometry of invariant manifolds in three-dimensional, time-dependent fluid flows.
Snapshots of such invariant manifolds, representing the manifold geometry at some time instant
during the flow evolution, are given by two-dimensional surfaces. The developed method can be
used, in particular, to determine the geometry of stable and unstable invariant manifolds of
certain hyperbolic trajectories which are important in understanding the global, Lagrangian
structure of unsteady 3D fluid flows. In this context the proposed method represents the first
step towards the extension of `lobe dynamics' and the `invariant manifold' approach to the
Lagrangian transport in unsteady 3D fluid flows (outstanding issues will be discussed). The
computational procedure employs an automatic mesh refinement which is coupled with adaptive
vertex redistribution. A variant of the advancing front technique is used for remeshing,
whenever necessary. Such an approach allows for computationally efficient determination
of highly convoluted, evolving geometry of invariant manifold snapshots in unsteady flows.
I'll show that the developed method is capable of providing detailed information on the
evolving Lagrangian flow structure in three dimensions over long periods of time. |
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Tues/Wed, Oct. 28/29, 2008,
12:00 noon Dr. Steve Wiggins (University
of Bristol)
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The Dynamical Systems Approach to Lagrangian Transport: Fronts and
Eddies in Realistic Ocean Models
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abstract: In this talk I will briefly review the dynamical systems approach to
Lagrangian transport, with particular emphasis on recent theoretical
and computational results that allow the application to realistic
ocean models. I will then apply this approach to a study associated
with fronts and eddies in the Mediterranean Sea. First, I must discuss
the notion of Lagrangian fronts and eddies and their relation to
hyperbolic trajectories and their stable and unstable manifolds. After
this, then show how the Lagrangian description allows for a detailed
spatio-temporal description of transport. This barely scratches the
surface of possible mathematical and physical analyses for such
systems and I will conclude by discussing further directions and
problems. |
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Monday, March 9, 2009,
3:45 pm Dr. J. Edgar Parker (James Madison University)
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Polynomial Projection and Modified Picard Iteration:
Using Classical Methods in Modern Computing Environments
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abstract: An overview of the theory surrounding polynomial projection,
which enables the use of numerical schemes consequent to modifying the Picard iteration
on a broad class of initial value ODE’s with analytic solutions is given. Projection of
the n-body problem and aspects of the numerical scheme that have particular utility for
spiking neural network simulations will be illustrated.
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Monday, March 16, 2009,
2:00 pm Dr. Olga Korotkova (University of Miami)
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Random electromagnetic beams for atmospheric applications
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abstract: We will discuss potential applications of random (stochastic)
electromagnetic beams for optical systems operating through clear-air
turbulent atmosphere. Our analysis is purely analytical, based on rigorous
propagation theory of random light, with few results obtained by computer
simulations. The primary goal will be investigation of possible use of
polarization properties of random beams for quality improvement of signals
in LaserCom systems and returns in active LIDARs. In particular, our
preliminary results regarding LaserCom systems show that the use of
polarization domain of beams propagating in the atmosphere may lead to
significant reduction in optical scintillation and the possibility of
controlling power loss at the same time. On the other hand we will show
that polarization properties of the returned random beams in active LIDARs
may be effectively used in target recognition problem, providing with
reach content about the size, curvature, surface roughness, etc. of the
target.
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Friday, March 27, 2009,
3:45 pm Dr. Ben Fine (Fairfield College)
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CAISS-Stat - An All Purpose Graphical Interface Statistics Program
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abstract: CAISS - Stat is a graphical interface driven Statistics package developed at City College in New York.
It is designed to be both a full service statistical analysis application as well as a teaching tool.
For the experienced it can be utilized to analyze a wide array of statistical data sets and
testing situations and at the same time employing an extremely easy to use interface. For students
of Statistics it provides an easy to learn and easy to operate method to explore statistical data
sets and obtain online textbook explanations of procedures. Further the operation of CAISS-Stat will
guide the student through the exploratory analysis. Its extremely easy learning curve makes CAISS-Stat
an ideal statistical package for research workers who need to obtain statistical results quickly and
understand what is being done without being bogged in learning a complicated Statistics program.
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