We present the first direct experimental test of the complex ion structure in liquid carbon at pressures around 100 GPa, using spectrally resolved x-ray scattering from shock-compressed graphite samples. Our results confirm the structure predicted by ab initio quantum simulations and demonstrate the importance of chemical bonds at extreme conditions similar to those found in the interiors of giant planets. The evidence presented here thus provides a firmer ground for modeling the evolution and current structure of carbon-bearing icy giants like Neptune, Uranus, and a number of extrasolar planets.

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We have carried out X-ray scattering experiments on iron foil samples that have been compressed and heated using laser-driven shocks created with the VULCAN laser system at the Rutherford-Appleton Laboratory. This is the highest Z element studied in such experiments so far and the first time scattering from warm dense iron has been reported. Because of the importance of iron in telluric planets, the work is relevant to studies of warm dense matter in planetary interiors. We report scattering results as well as shock breakout results that, in conjunction with hydrodynamic simulations, suggest the target has been compressed to a molten state at several 100 GPa pressure.Initial comparison with modelling suggests more work is needed to understand the structure factor of warm dense iron.

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The difficulty of inspiring spring-semester senior science and engineering students to take another elective advanced mathematics course is well known. Mathematical Physics taught from a text such as Mathematical Methods for Physicists by George B. Arfken and Hans J. Weber has a particularly bad reputation among undergraduates. But any graduate science or engineering student, who realizes the value of advanced mathematics courses, eventually will include this great mathematics book on their shelf as one of their most used reference books. The trick is to make the course interesting and "enjoyable" enough that students look forward to class, without sacrificing the proper challenges for the student to achieve a proper level of mathematical expertise as preparation for graduate school courses. This paper discusses how to use a combination of: 1.) Textbooks, 2.) Special projects, 3.) Personal interest in the students, and 4.) Relating the material in the course to real world situations, to reach that goal. These techniques have resulted in positive student critiques, including one evaluation which the author has framed and is on his wall to be reread when he has a bad day.