Index to Library Trends Volume 38

published or submitted for publicatio

Capturing Hiproofs in HOL Light

Hierarchical proof trees (hiproofs for short) add structure to ordinary proof trees, by allowing portions of trees to be hierarchically nested. The additional structure can be used to abstract away from details, or to label particular portions to explain their purpose. In this paper we present two complementary methods for capturing hiproofs in HOL Light, along with a tool to produce web-based visualisations. The first method uses tactic recording, by modifying tactics to record their arguments and construct a hierarchical tree; this allows a tactic proof script to be modified. The second method uses proof recording, which extends the HOL Light kernel to record hierachical proof trees alongside theorems. This method is less invasive, but requires care to manage the size of the recorded objects. We have implemented both methods, resulting in two systems: Tactician and HipCam

An invariant second-order closure model of the compressible turbulent boundary layer on a flat plate

The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant

Melting of tantalum at high pressure determined by angle dispersive x-ray diffraction in a double-sided laser-heated diamond-anvil cell

The high pressure and high temperature phase diagram of Ta has been studied in a laser-heated diamond-anvil cell (DAC) using x-ray diffraction measurements up to 52 GPa and 3800 K. The melting was observed at nine different pressures, being the melting temperature in good agreement with previous laser-heated DAC experiments, but in contradiction with several theoretical calculations and previous piston-cylinder apparatus experiments. A small slope for the melting curve of Ta is estimated (dTm/dP = 24 K/GPa at 1 bar) and a possible explanation for this behaviour is given. Finally, a P-V-T equation of states is obtained, being the temperature dependence of the thermal expansion coefficient and the bulk modulus estimated.Comment: 31 pages, 8 figures, to appear in J.Phys.:Cond.Matte