Department of Mathematics
Northeastern University

Seminar in Industrial Mathematics

• October 7, 1998
  1. "ECMI Meeting in Gothenburg" by Tom Sherman (Northeastern)
  2. Organizational Issues
• September 30, 1998
  1. "Group Study with Industry in Leiden" by Alex Martsinkovsky (Northeastern)
  2. Organizational Issues
• 4-5 pm, May 13, 1998 (Time TBA)
  Speaker: Natalia Sternberg (Clark University)
  Title: Mathematical Modeling of the Plasma and the Sheath
  Abstract: The bounded plasma problem is encountered in many applications including plasma processing, plasma chemistry, gaseous lasers, and radio frequency discharges. A universal property of a bounded plasma, independent of the method of its generation, is the existence of a sheath along the wall or the electrode. In order to understand the behavior of the plasma and sheath parameters, one has to model the plasma and the sheath separately. However, when this approach is used, the position of the plasma--sheath interface needs to be determined. There are several approaches to solve this problem, but all of them are still controversial. In the first part of the talk, we discuss how the mathematical modeling of the static bounded plasma problem helps to determine the position of the plasma-sheath interface, and to study the transition region from the plasma to the sheath. In the second part of the talk, we will introduce the dinamic sheath model and disscuss some mathematical difficulties related to this model.
• 4-5 pm, May 6, 1998
  Speaker: Misha Kilmer (Northeastern University)
  Title: Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems
  Abstract: Discrete ill-posed problems in the form of linear systems or least squares problems arise, for example, from the discretization of Fredholm integral equations and occur in a variety of applications. The matrix corresponding to a discrete ill-posed problem is ill-conditioned due to properties of the continuous operator. Since the data typically contain noise, the exact solution to such a problem often bears no resemblance to the noise-free solution. Instead, regularization methods are used to determine a solution that approximates the noise-free solution. The regularization methods replace the original operator by a better conditioned but related one to help diminish noise effects; the solution to this problem is called the regularized solution to the original problem.
  The conditioning of the new problem is controlled by one or more regularization parameters. A wise choice of regularization parameter is crucial to obtaining a useful regularized solution. For problems of large dimension, the parameter choice is not yet clearly understood, and many algorithms proposed in the literature are needlessly complicated. In this talk, we briefly survey some regularization methods and existing parameter selection techniques. We show how parameter selection techniques for the original problem can be used on an appropriately projected version of the problem obtained using iterative methods, often with little or no degradation in the overall solution. The success of these techniques and the computational savings is illustrated in examples.

• April 29, 1998
  Speaker: Gilead Tadmor (Northeastern University)
  Title: Factorization, Interpolation, Nehari and Beurling-Lax: Using Optimal Control To Establish Complex Variables Results
  Abstract: Linear time varying (LTV) systems' interpretations and proofs of some notable operator / function theoretic results will be presented (reversing the standard trend in classical control, of using transform technics to import complex--analytic results). Reviewed results will include the Nehari and Beurling-Lax Theorems characterizations of co-prime factorization, dichotomies (= stable - antistable partitions), Hilbert and Krein space isometries and classical interpolation problems.
• March 11, 1998
  Speaker: Frederick Daum (Raytheon Corp.)
  Title: Industrial Strength Nonlinear Filters with Virtual Measurements
  Abstract: This talk describes a new method to design both exact and approximate nonlinear filters. The new nonlinear filter theory generalizes the Kalman filter, and in some important applications the performance of the new filter is vastly superior to the extended Kalman filter (EKF). Unlike the EKF, the new theory does not use linearization, but rather it solves a special class of nonlinear problems exactly, based on the exponential family of probability densities. The new method uses "virtual measurements" to avoid the problem of solving a system of nonlinear PDEs, and replaces it with the off-line solution of two linear PDEs, analogous to the Hopf-Cole transformation. The basic mathematical tool is a relatively new theory called "finite sum decomposition," developed by F. Neuman.
• March 4, 1998
  Speaker: Bogdan Vernescu (Worcester Polytechnic Institute)
  Title: Modeling Electrorheological Fluids
  Abstract: In recent years the industrial interest in building controllable systems has brought the topic of electrorheological fluids back to the research community. We construct a micromechanical model for an ER fluid that enables us, via periodic homogenization, to characterize the properties that the fluid exhibits at the macroscopic scale. The rheological behavior can be interpreted as a Bingham plastic and is due to both hydrodynamic and electrostatic interparticle interactions. The effect of hydration on the ER fluid is also considered. The understanding of the underlying physics governing the electrorheological response can contribute to the engineering of better ER fluids.
• February 25, 1998
  Speaker: Joe J. Rushanan (The MITRE Corporation)
  Title: Permanents, Parallelization, Groups, and Graphs
  Abstract: About a decade ago, MITRE developed computational improvements to the problem of tracking targets in clutter. The improvements were based on relatively efficient methods for computing the permanent of a matrix. Although believed to be intractable, the permanent calculation admits to a parallel implementation on a hypercube, which trades exponential time for exponential space. This implementation led us naturally to using group representations to analyze parallel algorithms. And this analysis, in turn, leads to some questions on Cayley graphs.
  The results are joint work with Bryant York of the College of Computer Science.
• February 18, 1998
  Speaker: Tom Sherman (Dept. of Mathematics, Northeastern University)
  Title: Wavelets and Representations
  ABSTRACT: The subject of wavelets is an analytical tool a bit like Fourier analysis. It has proved to be very useful in many important applications, including signal processing, image compression, and various problems of detection. Part of what has made this such a hot topic in engineering mathematics is the existence of fast algorithms (reminiscent of the fast Fourier transform) plus great flexibility and an ability to resolve information at many different scales. On the other hand, wavelets have their own rich, quite beautiful mathematical theory which includes links to representation theory. This talk, by a non-expert, will attempt to make some of these marvels visible to other non-experts.
• February 11, 1998
  Speaker: Ken Baclawski (College of Computer Science, Northeastern University)
  Title: Formal Methods for Software Engineering Using Category Theory
  Abstract: Formal methods applied to software engineering can provide a foundation for specification and modeling environments that are more complete, consistent and unambiguous than that produced by traditional or object-oriented methods. Category theory can form the basis for a formal approach to software specification, and a formal methods system called Specware uses this approach. This talk will introduce the categories and functors that arise in software engineering. The use of category theory in this way supports software refinement, component model composability, reuse of software specifications, and specification-driven code generation.
• February 4, 1998
  Speaker: Tony Devaney (Dept. of Electrical and Computer Engineering, Northeastern University)
  Title: A Paley-Wiener Theorem for Analytic Functions on the Unit Sphere and its Application to Inverse Source and Scattering Problems
  Abstract: A Paley-Wiener type of theorem is established for entire analytic functions of a complex unit vector. The theorem provides necessary and sufficient conditions for determining whether such a function is the boundary value of the Fourier transform of a compactly supported and bounded function in R³ and has application in the problem of determing the support of a source or scattering potential from far-field data. The theorem is illustrated with an example of determning the support of a scatterer from knowledge of its scattering amplitude.
• January 28, 1998
  Speaker: Alex Schulman (GTE Labs)
  Title: Application of Operations Research Methods to Solving Network Design and Routing Problems
  Abstract: A variety of mathematical methods have been used to solve problems arising in telecommunications. The list includes queuing theory and stochastic processes, linear and nonlinear optimization, combinatorial optimization, graph theory, and other methods. The goal of this talk is to describe some of the problems that fall under the umbrella of Operations Research. In particular, I will focus on optimal network design and optimal routing, starting from problem description, formulation and possible solution methods.
• January 21, 1998
  Speaker: Boris Mirman (formerly of Digital Equipment)
  Title: Industrial Mathematics for Microelectronics: Thermo-Mechanical Reliability
  Abstract: We consider destructive processes and the application of mechanical analysis to microelectric devices. The dominant factors responsible for damaging microelectric structures are, generally speaking, different from those for conventional "macro" structures. Moreover, mechanical analysis of microstructures has a different goal than the traditional analysis. Some of these topics are considered here: specific systems of ordinary differential equations (boundary value problems) and numerical aspects of associated eigenvalue problems.
• January 14, 1998
  Speaker: Kirk Jordan (IBM T.J.Watson Research Center)
  Title: Industrial Strength Solutions
  Abstract: A discussion of mathematics and computation in an industrial setting, focussing on 3 particular case studies.