We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong shock solution. Elling-Liu’s theorem (2008) indicates that the steady supersonic weak shock solution can be regarded as a long-time asymptotics of an unstead...

In developing the next generation supersonic transport airplane, two major challenges must be resolved. The fuel efficiency must be significantly improved, and the sonic boom propagating to the ground must be dramatically reduced. Both of these objectives can be achieved by reducing the shockwaves formed in supersonic flight. The Busemann biplane is famous for using favorable shockwave interact...

[1] Plasma, electric, and magnetic field data on the Polar spacecraft have been analyzed for the 29 May 1996 magnetopause traversal searching for evidence of in situ reconnection and traversal of the separator. In this paper we confine our analysis to model-free observations and intrasensor coherence of detection of the environs of the separator. (1) We illustrate the first documented penetrati...

We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k · ( 1 + log nk ) , thus refining the previously known bounds, as stated by Robertson and Seymour (1986) and by Bodlaender et al. (1995). Fu...

Dried and ground leaves of Crithmum maritimum were used as a matrix for supercritical extraction of volatile oil with CO2. Operative conditions were: extractor, 90 bar and 50 °C for 240 min; first separator, 90 bar and –10°C; second separator, 15 bar and 15 °C. GC/MS analysis of the leaves volatile oil revealed that it mainly consisted of: para-cymene, βphellandrene, γ-terpinene, thymol methyl ...

Short lived Ra isotopes have been produced at the TRIμP facility in inverse kinematics via the fusion-evaporation reaction Pb+C at 8 MeV/u. Isotopes are separated from other reaction products online using the TRIμP magnetic separator. The energetic radium (Ra) isotopes at the exit of the separator were converted into low energy ions with a thermal ionizer. Ra isotopes have been identified by ob...

In this note we develop some of the properties of separators of points in a multiprojective space. In particular, we prove multigraded analogs of results of Geramita, Maroscia, and Roberts relating the Hilbert function of X and X \ {P} via the degree of a separator, and Abrescia, Bazzotti, and Marino relating the degree of a separator to shifts in the minimal multigraded free resolution of the ...

We have conducted experiments and numerical simulations to investigate supersonic cracks. The experiments are performed at 85 ◦C to suppress strain-induced crystallites that complicate experiments at lower temperature. Calibration experiments were performed to obtain the parameters needed to compare with a theory including viscous dissipation. We find that both experiments and numerical simulat...

We relate the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting (7. Towards this end, we introduce node-searching, a slight variant of searching, in which an edge is cleared by placing searchers on both of its endpoints. We also show that the minimum number of searchers necessary to node-sea...