Speaker: Bernard Deconinck (University of Washington)
636
Science and Engineering
Offices (SEO)
3:00 PM
Title: Cnoidal wave solutions of the KdV equation are
linearly stable.
Abstract: Going back to considerations of Benjamin (1974), there
has been significant interest in the question of stability for the
stationary periodic solutions of the Korteweg-deVries equation, the
so-called cnoidal waves. In this paper, we exploit the squared-eigenfunction
connection between the linear stability problem and the Lax pair for the
Korteweg-deVries equation to completely determine the spectrum of the
linear stability problem for eigenfunctions that are bounded on the real
line. We find that this spectrum is confined to the imaginary axis,
leading to the conclusion of spectral stability. An additional
completeness argument allows for a statement of linear stability.
636 Science and Engineering Offices (SEO) 5:00 PM
Title: The Gaussian random walk, sampling Brownian motion, and the Riemann zeta function
Abstract: We consider the Gaussian random walk (one-dimensional random
walk with normally distributed increments), and in particular the
moments of its maximum M. Explicit expressions for all moments of M are
derived in terms of Taylor series with coefficients that involve the
Riemann zeta function.
We build upon the work of Chang and Peres (1997) on P(M=0) and Bateman's
formulas on Lerch's transcendent. Our result for E(M) completes earlier
work of Kingman (1965), Siegmund (1985), and Chang and Peres (1997).
The maximum M shows up in a range of applications, such as sequentially
testing for the drift of a Brownian motion, corrected diffusion
approximations, simulation of Brownian motion, option pricing,
thermodynamics of a polymer chain, and queueing systems in heavy
traffic. Some of these applications are discussed, as well as several
issues open for further research. This talk is based on joint work with
A.J.E.M. Janssen.
field trip to *Chicago Mercantile Exchange*(CME,http://www.cme.com/)
on Monday, Nov.5, 2007. We can gather at 8 at SEO and
leave around 8:30. Hopefully, we can come back around 11am.
Please reply to qzhen2[at]uic[dot]edu for registration.
Graduate Student Colloquium
"An introduction to
dynamical bifurcation theory and its applications"
Speaker: Chun-Hsiung Hsia (UIC)
636 Science
and Engineering Offices (SEO)
3:00 PM
ABSTRACT
"In the talk, we introduce the concepts and the machinery of
bifurcation theory. Bifurcation theory studies the qualitative changes
of the solutions for a system of equations while the control parameters
of the equations vary. In this talk, we start with algebraic equations
and ordinary differential equations to demonstrate the basic idea of
bifurcation theory. We present different types of bifurcations including
steady-state bifurcation, Hopf bifurcation and attractor bifurcation. We
will conclude this talk by showing applications."
-
October
10, 2007 Wednesday
(Joint with Applied Math. seminar)
"High-order
methods for high-frequency acoustic and electromagnetic scattering
simulations"
Speaker: Fernando Reitich (University of Minnesota)
636 Science
and Engineering Offices (SEO)
4:00 PM
ABSTRACT
"In this talk we will present some new algorithms that have
been recently developed for the solution of electromagnetic and
acoustic scattering problems and that are aimed at overcoming the
limitations of state-of-the-art scattering solvers. We will begin with
a brief review of the techniques most commonly used for the numerical
simulation of scattering experiments, highlighting their advantages
and shortcomings. In addition to providing a context for the
presentation, the review will motivate the continued need for
algorithms that can tackle these problems efficiently, especially at
high frequencies, without sacrificing accuracy and
error-controllability. In this connection, we shall first introduce a
novel approach to the rigorous numerical solution of the
integral-equation formulation of (surface) scattering problems in the
high-frequency regime. As we will show, this scheme can deliver
error-controllable answers without the need to discretize on the scale
of the wavelength of radiation, and it therefore holds significant
promise for applicability in a variety of configurations; examples
from implementations of this approach in the context of bounded,
unbounded (periodic) and multi-scale scattering surfaces will be
presented. As we shall explain, these high-frequency integral-equation
solvers possess the additional advantage that they seamlessly reduce
to more standard schemes as the frequency decreases. Moreover, at the
other end of the spectrum, the algorithms are based on the use of a
geometrical optics (GO) ansatz (or of the related physical optics or
geometrical theory of diffraction approximations) for the unknown
surface currents and, thus, they naturally connect with classical
approximate high-frequency solvers. With regards to the latter,
time-permitting, we shall further review some recent developments on
the numerical solution of the GO model itself, and we shall present a
new (Eulerian) high-order accurate procedure for the solution of its
phase-space formulation that is based on spectral and discontinuous
Galerkin approximations."
-
August
30, 2007 Thursday
The UIC Student Chapter
of SIAM (Society for Industrial and Applied
Mathematicians) invites you to enhance your mathematics education by
exploring applications of mathematics in industry!
The first meeting of the SIAM student chapter will be held on
Thursday,
Aug. 30th, 4:00PM at SEO 636.
We will schedule our Fall term field trip, discuss your interested
plan
and announce upcoming events.
Of course with
refreshment :)
-
Feburary
8, 2007 Thursday
"
MASSAGE: Collaborative Visualization Using Mobile Display Clusters
"
Speaker: Xun Luo (Motorola Labs/UIC)
636 Science
and Engineering Offices (SEO)
4:00 PM
ABSTRACT
"
There has been a notable increase in consumer use of mobile devices. In the mean time, the rate of improvements on individual device displays has lagged behind those for computing and storage on the same devices. This talk presents the Mobile ASsembled Scalable Adaptive Graphics Engine (MASSAGE), a specialized middleware for ollaborative visualization using the displays from a cluster of mobile devices. MASSAGE dynamically organizes a group of mobile devices within proximity in an ad-hoc manner, into a network that consists of one rendering node and multiple synchronized display nodes. The physical displays of all the display nodes subsequently form a larger virtual display, and are able to be used transparently by applications on the rendering node. MASSAGE is light-weight, bandwidth-efficient and native OS-independent. Our experimental result indicates that even limited by a star connection over Bluetooth wireless local links, this approach has been successfully shown to scale to support interactive-rate streaming on 1x2, 1x3, 1x4 and 2x2 tiled configurations, with over 90% network capacity utilization. MASSAGE is now being extended to support higher bandwidth wireless local links, and peer-to-peer connection with co-existence of multiple rendering nodes. MASSAGE could be used as stand-alone cluster. It is also able to be integrated into mobile grids as a means of display service. Details of related research, under a larger framework called PACE (Personal Augmented Computing Environment), can be found at http://www.cs.uic.edu/~xluo.
"
|
