## 2004 Outstanding Paper Prizes: A Good Reflection of the Breadth of SIAM

**October 26, 2004**

Paolo Zunino (with co-authors Alfio Quarteroni and Alessandro Veneziani, not shown) received one of three 2004 SIAM Outstanding Paper Prizes presented by SIAM president Mac Hyman at the SIAM Annual Meeting in Portland. The paper, published in SIAM Journal on Scientific Computing, elegantly integrates physical modeling (of blood dynamics), numerical analysis, and computational implementation, according to the (hard-working) prize committee.

Each year, the SIAM president appoints a three-member committee whose charge is to select the three SIAM journal papers whose authors will receive that year's Outstanding Paper Prizes. For 2004, the committee members, appointed by SIAM president Mac Hyman, were Walter Strauss of Brown University (chair), editor-in-chief of *SIAM Journal on Mathematical Analysis*; Thomas Hou of Caltech, editor-in-chief of *Multiscale Modeling and Simulation*; and Jerrold Griggs of the University of South Carolina, editor-in-chief of *SIAM Journal on Discrete Mathematics*.

Eligible papers must have been published in any SIAM journal within the three years (based on date of electronic publication) preceding the award date. Originality is the main criterion: Good choices, according to the prize specifications, are "papers that bring a fresh look at an existing field or that open up new areas of applied mathematics." Young people are to be given some preference.

"It was really hard to choose only three among so many great papers," Strauss says. "We ended up with three papers that nicely exemplify the breadth of SIAM: discrete and continuous, analytical and computational, physical and biological."

The authors of the papers selected by Strauss, Griggs, and Hou were honored at the awards luncheon during the SIAM Annual Meeting in Portland. For SIAM News, the committee provided the following brief statements of the significance of the winning papers.

Ideal Binary Clutters, Connectivity, and a Conjecture of Seymour." By Gérard Cornuéjols and Bertrand Guenin, *SIAM Journal on DiscreteMathematics*, Vol. 15, 2002, pages 329-352.

This paper proves that certain binary clutters are ideal if and only if they do not contain certain minors. This is a deep result, in that it partially solves Seymour's problem, generalizes Guenin's characterization of weakly bipartite graphs, and generalizes a classic theorem of Edmonds and Johnson in mathematical programming.

Seymour's problem is applicable to certain covering problems. "Covering problems" in general are defined as finding a minimum-size set that intersects all sets in a given collection of sets. The proof relates combinatorial properties (excluded minor characterization) to programming properties (integrality of polytopes of certain combinatorial optimization problems). It thus represents essential progress in an important area of combinatorial optimization in which the goal is to find conditions under which a given polyhedron has integer vertices, so that integer optimization problems can be solved as linear programs.

*****

"Convergence of Viscosity Solutions for Isothermal Gas Dynamics." By F. Huang and Z. Wang, *SIAM Journal on Mathematical Analysis*, Vol. 34, 2002, pages 595-610.

The authors of this very original work consider the classic equations for an isothermal gas, the compressible Euler equations in one dimension with the pressure proportional to the density. Because there are shock waves, smooth solutions are not possible.

Huang and Wang have found a novel way to use the method of compensated compactness to construct global weak entropy solutions. In particular, by using the analytic extension theorem, they establish the commutation relations not only for the weak entropies but also for the strong ones. Prior to this work, no one was able to use the compensated compactness theorem in this situation because of the inability to show that strong entropies satisfy sufficient compactness conditions. The authors of this paper permit the initial data to have large amplitude, to have discontinuities, and to include regions of vanishing density.

*****

"A Domain Decomposition Method for Advection-Diffusion Processes with Application to Blood Solutes." By Alfio Quarteroni, Alessandro Veneziani, and Paolo Zunino, *SIAM Journal on Scientific Computing*, Vol. 23, 2002, pages 1959-1980.

The authors derive a model of blood dynamics, demonstrate its utility for analyzing a useful problem (atherosclerosis), establish the analytic properties of the model, and develop an efficient iterative algorithm for solving the discrete system of equations. The paper thus combines physical modeling, numerical analysis, and computational implementation in an integrated fashion. Each of these issues is elegantly addressed.

The model describes the dynamics of a blood solute both in the vascular lumen and inside the arterial wall. The governing equations are the incompressible Navier-Stokes equations for the blood dynamics, coupled with a mixed-type advection-diffusion system. The solute concentration is discontinuous across the membrane. A specific domain decomposition algorithm and resulting subdomain iterative method are developed, analyzed, and numerically tested.