Department of Mathematics,
Northeastern University
Industrial Mathematics
Past Talks in 1999:
May 19, 1999: Note Special Schedule!
Speaker: Louis Rossi (UMass Lowell) 12:00-1:00 pm: Lunch Discussion of UMass Lowell's Industrial Math Program 1:00-2:00 pm: "Some Results on the Existence of Two-dimensional Rotating,
Viscous Vortical Structures"
Abstract:
Two-dimensional coherent, vortical structures play a key role in many
atmospheric, oceanographic and industrial processes. Many varieties of
these structures have been observed in nature, laboratory experiments and
numerical studies. For instance, vortex monopoles, referred to as gyres by
oceanographers, can persist for years in the oceans. More surprisingly,
fluid that is stirred vigorously is known to relax rapidly into vast regions
of irrotational flow punctuated by vortex monopoles, dipoles and sometimes
tripoles and other structures. Over the past two decades, considerable
effort has been dedicated to the understanding the evolution and fate of
coherent vortical structures. One of the key processes in monopole and
tripole formation and evolution is the mixing of vorticity within the
vortical structure. Mixing across streamlines leads to rapid
axisymmetrization of vortex structures, but strong nonlinearities can
inhibit mixing in structures such as the vortex tripoles. Recently, my
colleague James Graham-Eagle and I have proven that there are no
self-similar solutions possessing these self-sustaining nonlinearities.
Since coherent structures must be self-similar, this result suggests that
tripoles are evanescent and that the only rotating, viscous coherent
structure is the monopole.
May 12, 1999
Speaker: Marshall Slemrod (Univ of Wisconsin)
Title: The Chapman Enskog Expansion for Gas Dynamics
Abstract:
A popoular idea in differential equations with two distinct time scales is
eliminate the fast time flow dynmaics in favor of a reduced order system
evolving on the slow dynamics. This idea has been used in many contexts
(Tichinov's theorem, method of averaging, etc.) but its origins seem to go
back to the classical Chapman-Enskog expansion of rarefied gas dynamics.
This talk with survey this area and show how the idea of stability is
crucial to understanding the classical expansion.
May 5, 1999
Speaker: Steven Johnson (MIT)
Title: Photonic Crystals: Theory and Applications
April 21, 1999
Speaker: Jack Warga (Northeastern University, retired)
Title: Necessary Conditions Optimal Control
Abstract: This is a continuation of the presentation in March
April 14, 1999
Speaker: Tom Sherman (Northeastern University)
Title: Songs from the heart
Abstract: Using spherical harmonics to
locate cardiac abnormalities
April 7, 1999
Speaker: Alexander Bratus (Moscow State University, visiting Worchester Polytechnic)
Title: Mathematical models of interaction between pollution and environment
Abstract:
Various mathematical problems of interaction between live nature and
pollutant are considered. It is known that live nature can absorb
pollutant up to a certain limit (threshold value). Experiments show that
the dependence between the emitted quantity of pollutant and
the remaining quantity has a certain shape if the chimney emits a single
burst of pollutant. If some quantity of pollutant is emitted regularly,
we get an iterative process for the sequence of functions which
describes the dependence between the emitted and the remaining
quantities of the pollutant. It is proved that this process has a limit
and its main properties are investigated. Based on this, a conceptual
differential model is considered. The differential model makes it
possible to obtain a distributed model in the plane and in space.
Taking into account the diffusion of pollutant and the distributions
of plants we obtain a system of three semi-linear parabolic equations.
I will present results of a numerical modeling based on monitoring
by Moscow Institute of Forest Ecology.