The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Public–private interaction in pharmaceutical research

We empirically examine interaction between the public and private sectors in pharmaceutical research using qualitative data on the drug discovery process and quantitative data on the incidence of coauthorship between public and private institutions. We find evidence of significant reciprocal interaction, and reject a simple “linear” dichotomous model in which the public sector performs basic research and the private sector exploits it. Linkages to the public sector differ across firms, reflecting variation in internal incentives and policy choices, and the nature of these linkages correlates with their research performance.