Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

Crafting analytical tools to study institutional change

Most powerful analytical tools used in the social sciences are well suited for studying static situations. Static and mechanistic analysis, however, is not adequate to understand the changing world in which we live. In order to adequately address the most pressing social and environmental challenges looming ahead, we need to develop analytical tools for analyzing dynamic situations -particularly institutional change. In this paper, we develop an analytical tool to study institutional change, more specifically, the evolution of rules and norms. We believe that in order for such an analytical tool to be useful to develop a general theory of institutional change, it needs to enable the analyst to concisely record the processes of change in multiple specific settings so that lessons from such settings can eventually be integrated into a more general predictive theory of change. Copyright © The JOIE Foundation 2010.