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Talks in the Department of Mathematical Sciences (Fall 2006)
- Dept. of Mathematical Sciences Seminar
Richard O. Moore, New Jersey Institute of Technology
Wednesday, November 29, 2:45-3:45pm in Room RI-222
Title: Pulse interactions in self-heated parametric gain devices
Abstract: Parametric gain devices such as optical parametric
oscillators (OPOs) operated at high average power have been seen
to exhibit interesting dynamics resulting from the changing modal
properties due to self-induced heating. The heating introduces a
linear spatial coupling between different modes through the
refractive index in addition to the nonlinear coupling through
the parametric gain medium. We study the interaction of pump and
signal fields in the context of a particular mean-field limit of
the degenerate OPO equations, where the dynamics can effectively
be reduced to a finite-dimensional representation. Depending on
their relative sign and position, the optical fields and their
``thermal aprons'' are seen to merge to form new stably bound
multi-bump solutions that are rendered amenable to analysis
through a disparity in spatial decay scales.
- Dept. of Mathematical Sciences Seminar
Arup Mukherjee, Montclair State University
Wednesday, November 15, 2:45-3:45pm in Room RI-222
Title: Liquid Crystals: Elastic Continuum Models and Analysis
Abstract: Liquid crystals are a phase of matter with both liquid and solid
crystal properties. For instance, a liquid crystal (LC) may flow like a
liquid, but have the molecules in the liquid arranged and/or oriented
in a crystal-like way. Using ideas from Calculus as building blocks, we
will build up a elastic continuum model for nematic (rod-like) liquid
crystals (NLCs) and analyze the model to understand the viscoelastic
response of NLCs to applied external fields and boundary effects. The
talk is designed to introduce students to the subject and indicate how
mathematical models and analysis play a crucial role in understanding
the behavior of LCs. Some open problems appropriate for student
research will be presented.
- Dept. of Mathematical Sciences Seminar
Crystal Dahlhaus, Student, Montclair State University
Advisor: Youngna Choi
Wednesday, November 8, 2:45-3:45pm in Room RI-222
Title: The Mathematics of Refinancing
Abstract: Financing describes a method of raising funds or capital. Many
people finance an asset and pay for it in installments, as opposed to
paying a sum up-front. The cost of financing is the interest expense.
Banks charge an interest rate on the loan. This motivates people to
scout for and obtain the lowest interest rate possible. Even after a
loan is taken, people look towards refinancing in order to achieve an
even lower interest rate. This research models the effects of
refinancing at lower interest rates. Mathematically, we show that the
point in time that is most beneficial to the borrower for refinancing
depends on the terms left on the loan and the percent decrease in the
interest rate. We take into account the refinancing fees in the model.
Also, we look at how the refinanced loan will be contracted. We use
examples from the two most common financing types in the United States,
automobile and real estate loans. For example, should the borrower
always refinance if there is a lower interest rate? Can various fees
make the refinancing at lower interest rate worse than the original
loan? This research helps to arrive at the answers to these questions.
- Dept. of Mathematical Sciences Seminar
Dr. Leah Shaw, US Naval Research Lab, Washington, DC
Wednesday, October 25, 2:45-3:45pm in Room RI-222
Title: Synchronization in small delay-coupled networks of lasers
Abstract: An approach to achieving coherent power is to synchronize many individual
devices, such as lasers. However, for most coupled laser systems,
synchronized behavior is typically not stable. Results are presented for
small networks of delay-coupled oscillators, including semiconductor
lasers and fiber ring lasers. Delay systems are infinite dimensional
dynamical systems and can display complex behavior. Behavior can include
delay synchronization, in which there is a constant phase difference
between the oscillators. We show that modifying the architecture by
adding self-feedback loops in the system stabilizes the in-phase
synchronized solution.
- Provost’s Series on University Learning and Teaching
Professor Jeanette Norden, Vanderbilt University
Wednesday, October 18, 3:00-4:00pm in University Hall 1070
Title: What Great Teachers Do: Fostering Intellectual and Personal Development
- Dept. of Mathematical Sciences Seminar
Dr. Michael Huber, Muhlenberg College
Wednesday, October 11, 2:45-3:45pm in Room RI-222
Title: Will Poisson Pitch the Next No-Hitter? Modeling Rare Baseball Events
Abstract:
Three sets of rare baseball events pitching a no-hit game,
hitting for the cycle, and turning a triple play offer
excellent examples of events whose occurrence may be modeled as
Poisson processes. That is, the time of occurrence of one of
these events doesnt affect when we see the next occurrence of
such. With a colleague at the United States Military Academy, I
have modeled occurrences of these three events in Major League
Baseball for data from 1901 through 2004 including a refinement
for six commonly accepted baseball eras within this time period.
Model assessment was primarily done using goodness of fit
analyses on inter-arrival data. I will share our analysis of
these events and discuss student projects with other rare events
as well.
- Dept. of Mathematical Sciences Seminar
Dr. Aihua Li, Dept of Mathematical Sciences, MSU
Wednesday, September 20, 2:45-3:45pm in Room RI-222
Title: Certain Matrix Equations
Abstract: Solving matrix equations is a classical mathematics problem
that challenges many research areas. The focus of this talk
is on the matrix equation X2AX = XAX, where both A and X are
square matrices and X is the variable matrix to be solved
for. The talk will start with the background of this
equation and traditional methods to determine the existence
of nontrivial solutions and how to obtain them if any.
Furthermore, a symbolic algorithmic method to solve the
equation, which uses the Gröbner Basis techniques, will be
introduced. This method provides an additional algebraic
tool to solve multivariable polynomial systems and matrix
equations.
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