The surface energy of strained foam clusters

We derive general equations relating the surface energy of strained bubble clusters to the volumes and pressures in the bubbles. These equations generalize a similar equation for free bubble clusters. We apply the equations to periodic clusters, clusters between two parallel walls and clusters enclosed by a wall.     

Surface energy of free clusters of bubbles: An estimation

We propose an approximate equation for the surface energy of two-dimensional free bubble clusters which we compare with exact calculations of the surface energy of symmetrical clusters consisting of a central bubble surrounded by one or two shells of bubbles of two different areas. The accuracy of the equation is good for relatively narrow distributions of the areas and of the number of sides of the bubbles but underestimates the energy for large widths of those distributions. We propose a similar approximate equation for the surface energy of three-dimensional clusters.     

Comparative and categorical spatial judgments in the monkey: “high” and “low”

Adult human subjects can classify the height of an object as belonging to either of the high or low categories by utilizing an abstract concept of midline that divides the vertical dimension into two halves. Children lack this abstract concept of midline, do not have a sense that these categories are directional opposites, and their categorical and comparative usages of high(er) or low(er) are restricted to the corresponding poles. We investigated the abilities of a rhesus monkey to perform categorical judgments in space. We were also interested in the presence of the congruity effect (a decrease in response time when the objects compared are closer to the category pole) in the monkey. The presence of this phenomenon in the monkey would allow us to relate the behavior of the animal to the two major competing hypotheses that have been suggested to explain the congruity effect in humans: the analog and semantic models. The monkey was trained in delayed match-to-sample tasks in which it had to categorize objects as belonging to either a high or low category. The monkey was able to generate an abstract notion of midline in a fashion similar to that of adult human subjects. The congruity effect was also present in the monkey. These findings, taken together with the notion that monkeys are not considered to think in propositional terms, may favor an analog comparison model in the monkey.