Department of Mathematics, Northeastern University

Industrial Mathematics

• 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.