On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Transition Delay in Hypervelocity Boundary Layers by Means of CO₂/Acoustic Instability Interactions

A novel method to delay transition in hypervelocity flows over slender bodies by injecting CO₂ into the boundary layer of interest is investigated. The results presented here consist of both experimental and computational data. The experimental data was obtained at Caltech's T5 reflected shock tunnel, while the computational data was obtained at the University of Minnesota. The experimental model was a 5 degree sharp cone, chosen because of its relevance to axisymmetric hypersonic vehicle designs and the wealth of experimental and numerical data available for this geometry. The model was instrumented with thermocouples, providing heat transfer measurements from which transition locations were determined and the efficacy of adding CO₂ in delaying transition was gauged. For CO₂/N₂ freestream blends without injection, the transition Reynolds number more than doubled for mixtures with 40% CO₂ mole fraction compared to the case of 100% N₂. For the cases with injection, shadowgraph visualizations were obtained, allowing verification of the injection timing. The computations provide encouraging results that for the injection schemes proposed CO₂ is reaching high enough temperatures to excite vibrational modes and thus delay transition