1. Keeping Track of Shock Waves ● Shock waves arise when a projectile hurtles into a medium at speeds faster than sound. They are common in applications involving explosives, and in new experiments with very powerful lasers. ● The speed of shock waves can be calculated if one knows a curve called the Hugoniot that involves pressure, temperature, and density in the material before and after passage of the shock. ● We found a new way to calculate shock speeds in solids at the atomic scale. The method allows a parallel supercomputer to focus on the region right near the shock front without wasting time on atoms far ahead or far behind. See J. M. D. Lane and M. Marder, in Shock Compression of Condensed Matter, M D Furnish et. al. eds, pp. 331-334, (AIP, 2006) Michael Marder (PI), The University of Texas at Austin MT/DMR/MPS 0401766 Illustration of method employed to allow molecular dynamics simulation to focus on shock front. Computation of shock speed in tin as a function of speed of impacting piston, including speeds of two independent shock fronts at lower impact velocities.

2. Keeping Track of Shock Waves Introduction Previous dynamic fracture studies have often been concerned with the speed of crack propagation through a material, the branching that occurs when the crack speed approaches the sound speed in the material, and the path that a crack will take in a material under varying strains. The existing theory cannot predict these quantities for crack paths, but we believe that our studies of oscillating crack paths will provide a fresh perspective, perhaps providing details to complete the theory. Summary of results We have studied crack paths in latex rubber sheets stretched in two orthogonal directions, and observed that originally straight cracks undergo a transition to oscillating paths as the amount of biaxial strain is increased. We mapped a phase diagram of these states, and from measurements of the amplitude and wavelength of the oscillation near the onset of the instability, find that this transition can be characterized as a Hopf bifurcation. Finally, we ruled out several possible mechanisms that could drive this instability.

3. UTeach in Gathering Storm Report –PI Marder directs UTeach, Texas' largest program to prepare secondary mathematics, science, and computer science teachers. –UTeach is featured in Rising Above the Gathering Storm (National Academy Press, 2006) as the first model program accompanying recommendation A-1: TEN THOUSAND TEACHERS FOR TEN MILLION MINDS. Annually recruit 10,000 science and mathematics teachers... Students enrolled in student teaching for science and mathematics from 1997 to 2006 at UT Austin, showing growth due to UTeach. Postbaccs are degree holders getting certification. Michael Marder (PI), The University of Texas at Austin MT/DMR/MPS 0401766