[+] Team 1: Chemical/Mechanical Planarization in Semiconductor Manufacturing

**Mentor** Leonard Borucki, Motorola- Cameron Connell, New York University
- Hala Jadallah, Indiana University
- Jianbo Li, University of Kentucky
- Peter Park, California Institute of Technology
- Boris Petracovici, University of Illinois at Urbana-Champaign
- David Zeigler, Texas A & M University

Chemical/mechanical polishing utilizes a liquid slurry containing very fine particles to planarize the surface of a wafer. The slurry coats the top of the wafer and is pressed between the wafer and a flexible circular rotating pad. The surface of the pad in contact with the slurry is not smooth, but contains grooves and is "conditioned" so that the entire surface contains small scratches. The conditioning process greatly affects the polishing performance. So does the pressure applied to the pad.

The liquid in the slurry is formulated to have a slight etching effect. As the slurry flows over the wafer surface, the suspended particles abrade the surface and the liquid in the slurry etches the abraded area. The process is somewhat like using a rotary buffer to polish the finish on a car. The overall objective is to understand how the achievable flatness is related to the many variables that might be controlled in the process, for example the pressure on the pad, the rotation speed, the sizes of the particles in the slurry, the pad conditioning, the chemistry of the liquid used in the slurry, etc.

[+] Team 2: Problems in Computer Security

**Mentor** John Hoffman, Secure Computing Corporation- Ruth Auerbach, University of Maryland
- Natalyia Kerbel, University of Minnesota, Twin Cities
- Molly Megraw, Johns Hopkins University
- Robert Osburn, Louisiana State University
- Sachindev Shetty, Arizona State University

The area of mathematics/computer security that the problem will be from is an area known as Non-Interference. For the development of highly secure systems, it is crucial that all information flows through the system are understood. In particular, covert channels or unexpected information flows can be particularily damaging to a secure system which is attempting to maintain a high level of confidentiality. (For example, a top secret process should not under normal situations be able to send or otherwise signal any information to a secret process.) Non-Interference is a mathematical technique that allows a system model to be analyzed for these kinds of information. Traditionally these non-interference techniques or theorems have been stated in a hierarchical (POSet based) fashion. That is, they have emphasized a military approach where information is labelled "top secret" or "secret" and no information from "top secret" is allowed to flow to "secret". Recently there have been attempts to generalize this approach, to allow information to flow between processes in a non-hierarchical (non partially ordered set) way. The problem will be to examine this new framework, and to work some small examples to gain an understanding of this approach and to validate whether or not in can be used to actually analyze real systems.

[+] Team 3: Computer Simulation of Intracardiac Electrogram Sensing

**Mentor** Shirley Min, Medtronic- John Alford, University of Houston
- Nick Cogan, Montana State University
- Charles Miller, University of Notre Dame
- Seth Patinkin, Indiana University
- Bradford Peercy, The University of Utah
- Noah Rosenberg, Stanford University

The project will lead students step by step from understanding the electrogram sensing problems to mathematical formulation and solution. At the beginning of the workshop, an overview of the mathematical modeling and the importance in tachyarrhythmia research of implantable cardioverter and defibrillator industries will be given. Then the background and the existing models of the sensing will be reviewed. Mathematical description of the problem will be developed and the surface integral equations will solved by numerical methods i.e. Method of Moment. Other alternative approaches such as Finite Element Analysis will also be discussed. Students are required to develop the computer code by using Matlab or other tools and to obtain the solutions to a few simple geometries of pacing/sensing leads. On the last day of the workshop, students need to give a presentation on their findings and submit a written report.

[+] Team 4: Modeling Crystal Growth

**Mentor** David Misemer, 3M- David Ambrose, Duke University
- Connie Fournelle, University of Kentucky
- Katharine Gurski, University of Maryland
- Danping Peng, University of California, Los Angeles
- Vivek Shekhar, University of Cincinnati
- Valsa Varghese, University of Cincinnati

Growing a population of small crystals from solution is an important process for several industries, particularly those engaged in the production of photographic, agricultural and pharmaceutical chemicals. The properties that need to be controlled range from the shape and type of individual crystals to the distribution of sizes in the final population. All of the properties are determined, at least in part, by the availability of the crystal constituents in the surrounding solution.

In this activity, we will concentrate on the distribution of crystal sizes in the population. Two processes are important in determining the distribution: nucleation, the creation of new crystals, and growth, the addition of material to existing crystals.

We will developing numerical simulations that predict the evolution of the crystal population.

[+] Team 5: Mathematics in GPS

**Mentor** Craig Poling, Lockheed Martin- Aleksei Beltukov, Tufts University
- Jongho Choi, University of Wisconsin, Madison
- Leonard Hoffnung, University of Kentucky
- Nilima Nigam, University of Delaware
- David Sterling, University of Colorado
- Paul Tupper, Stanford University

On day 1, 7/22/98, we will briefly survey the wide range of commercial, defense and scientific applications where the Global Satellite Positioning System GPS has had a major impact. Following the introduction we will develop the mathematical notation, definitions and framework necessary to describe: 1) conventional, 2) differential and 3) interferometric, or real time kinematic, positioning and attitude determination. Following the development of the mathematical framework necessary to understand GPS we will pose selected challenging mathematical problems which arise from attempts to determine ultra high precision interferometic position and attitude. GPS workshop participants will then be given selected reading material to aid in the mathematical modeling and solution of the problems that are posed.

During the course of the workshop GPS antenna and receivers will be used to collect pseudorange and integrated carrier phase data. This data can be used by the workshop participants to evaluate their mathematics models and approaches to achieving high precision position and attitude estimates. Some exposure to classical mechanics, numerical analysis, and stochastic processes would be helpful, although the workshop is designed to be self-contained.

By the end of the GPS workshop, participants will have learned how to resolve positions anywhere on the earth to subcentimeter accuracy and to determine orientation in space with accuracy comparable to that achieved byVLBI methods using quasars (e.g. 1.4 x 10-8 degrees). In addition, workshop participants will have been exposed to some of the principal research questions which arise in high precision GPS position and attitude applications.

**Recommended GPS reference:**

Global Positioning System: Theory and Applications; Volumes 1 and 2, edited by Bradford W. Parkenson, James J. Spilker Jr., Associate Editors, Penina Axelrod and Per Enge, Volume 164; Progress in Astronautics and Aeronautics, Paul Zarchan Editor-in-chief, published by AIAA 1996.

[+] Team 6: A Pricing Problem in the Energy Industry

**Mentor** Samer Takriti, IBM- Kashi Abhyankar, University of California, Berkeley
- Tiernan Fogarty, University of Washington
- Jennifer Kimber, Kent State University
- Anhua Lin, Johns Hopkins University
- Seung Seo, University of Minnesota, Twin Cities

The electric power industry is going through deregulation. The current picture of a single utility controlling the market in a specific region will soon disappear. Instead, there will be power producers who sell their production to a power pool; and power suppliers who will buy power from the pool and sell it to their customers. As a result, generating companies are faced with increasing demand uncertainty and must consider volatile electricity prices in their operations. We study scheduling the generating units in the presence of uncertainty. The resulting models are large-scale mixed-integer programs. We investigate solving these models using branch-and-bound (CPLEX) and using Lagrangian relaxation.