# Allen Tesdall Associate Professor

I am interested in numerical solution methods for partial differential equations (PDEs) which arise in problems in applied mathematics. Recently I and my co-authors have investigated a paradox, discovered by von Neumann in the 1940s, that involves the reflection of weak waves in a gas. Experiments show that when a weak shock wave reflects off a thin wedge, a reflection pattern consisting of three shock waves that meet at a ``triple point'' apparently occurs. Von Neumann showed, however, that such a point is impossible - it cannot conserve mass, momentum, and energy. Therefore, the apparent triple point must have an unknown local structure of small but finite size. To study this phenomenon, problems for several systems of conservation laws, including the Euler equations of gasdynamics, were formulated. Numerical solutions of these problems have led to a determination of the local structure near the apparent triple point, and theoretical analysis shows that this structure provides a resolution of the paradox. Recent experimental evidence appears to confirm this resolution.

I received my PhD from the University of California, Davis in 2001. Prior to coming to CSI, I was a visiting member of the Fields Institute, Toronto, ON, and held visiting positions at the University of Houston and Southern Methodist University.