[grads] [Sem-coll] AM Dept. Colloquium & Seminar April 2 & 4

[Joe Millham]

Greetings all,

Please join the Applied Mathematics Department for the following
seminar and colloquium.  Please note the special time and location of
this week's colloquium.  Graduate students are strongly encouraged to
attend.

**Discrete Applied Mathematics Seminar **
Iyad Kanj - Depaul University
"On the Induced Matching Problem"
Wed. April 2, 4:00 pm -  E1 245
See abstract below
 ----------------------------------------------------------

AM Department Special Colloquium
James Glimm - SUNY-Stony Brook; President, American Mathematical Society
"Macro/Micro Perspectives for Turbulent Mixing Large Scale and Atomic
Scale Mixing Properties"
Fri., April 4, 12:45 pm -  Wishnick 113
See abstract below


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Iyad Kanj - Depaul University
"On the Induced Matching Problem"
Wed. April 2, 4:00 pm -  E1 245
We study extremal questions on induced matchings in several natural
graph classes. We argue that these questions should be asked for
twinless graphs, that is graphs not containing two vertices with the
same neighborhood. We show that planar twinless graphs always contain
an induced matching of size at least n/40 while there are planar
twinless graphs that do not contain an induced matching of size
(n+10)/27. We derive similar results for outerplanar graphs and graphs
of bounded genus. These extremal results can be applied to the area of
parameterized computation. For example, we show that the induced
matching problem on planar graphs has a kernel of size at most 40k
that is computable in linear time; this significantly improves the
results of Moser and Sikdar (2007). We also show that we can decide in
time O(91k + n) whether a planar graph contains an induced matching of
size at least k.

This is joint work with Michael Pelsmajer, Marcus Schaefer, and Ge Xia.
 ----------------------------------------------------------


James Glimm - SUNY-Stony Brook; President, American Mathematical Society
"Macro/Micro Perspectives for Turbulent Mixing Large Scale and Atomic
Scale Mixing Properties"
Fri., April 4, 12:45 pm -  Wishnick 113

Numerical approximation of fluid equations are reviewed. We identify
numerical mass diffusion as a characteristic problem in most
simulation codes. This fact is illustrated by an analysis of fluid
mixing flows. A main problem for such flows is to sort out the
distinct effects of small and large scale mixing.
    We study both large scale and atomic scale mixing properties for
classical hydrodynamic instabilities and mixing flows. The instability
is driven by acceleration directed across a density discontinuity in
the fluid. Assuming small scale initial perturbations of the
interface, a highly complex mixing zone develops when acceleration is
applied to the fluids. This simple sounding mixing flow has been
notoriously difficult to predict. Standard simulations may give
results differing from experiments by factors of two or more. We
ascribe these differences to numerical artifacts in the simulations,
specifically numerical mass diffusion.
         A number of additional startling conclusions have recently
emerged. For a flow accelerated by multiple shock waves, we observe an
interface between the two fluids proportional to Delta x^-1, that is
occupying a constant fraction of the available mesh degrees of
freedom.  This result suggests (a) nonconvergence for the mathematical
problem or (b) nonuniqueness of the limit if it exists, or (c)
limiting solutions only in the very weak form of a space time
dependent probability distribution.
         The cure for this pathology is a regularized solution, in
other words inclusion of all physical regularizing effects, such as
viscosity and physical mass diffusion. Once this is done, the solution
appears to depend on the ratio of the coefficients in these terms,
such as the Schmidt number, or if the solution is under resolved, on a
numerical and code dependent Schmidt number.



Thank you, and see you there,
Joe


-- 
Joe Millham
Administrative Assistant
Department of Applied Mathematics
Illinois Institute of Technology
10 W. 32rd St.
Chicago IL 60616
312.567.8984
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