The effect of shape on the adhesion of fibrillar surfaces.

Experimental data have demonstrated that mushroom-shaped fibrils adhere much better to smooth substrates than punch-shaped fibrils. We present a model that suggests that detachment processes for such fibrils are controlled by defects in the contact area that are confined to its outer edge. Stress analysis of the adhered fibril, carried out for both punch and mushroom shapes with and without friction, suggests that defects near the edge of the adhesion area are much more damaging to the pull-off strength in the case of the punch than for the mushroom. The simulations show that the punch has a higher driving force for extension of small edge defects compared with the mushroom adhesion. The ratio of the pull-off force for the mushroom to that of the punch can be predicted from these simulations to be much greater than 20 in the friction-free case, similar to the experimental value. In the case of sticking friction, a ratio of 14 can be deduced. Our analysis also offers a possible explanation for the evolution of asymmetric mushroom shapes (spatulae) in the adhesion organ of geckos.

Deriving acceptable biological catch from the overfishing limit: implications for assessment models

The recently revised Magnuson–Stevens Fishery Conservation and Management Act requires that U.S. fishery management councils avoid overfishing by setting annual catch limits (ACLs) not exceeding recommendations of the councils’ scientific advisers. To meet that requirement, the scientific advisers will need to know the overfishing limit (OFL) estimated in each stock assessment, with OFL being the catch available from applying the limit fishing mortality rate to current or projected stock biomass. The advisers then will derive ‘‘acceptable biological catch’’ (ABC) from OFL by reducing OFL to allow for scientific uncertainty, and ABC becomes their recommendation to the council. We suggest methodology based on simple probability theory by which scientific advisers can compute ABC from OFL and the statistical distribution of OFL as estimated by a stock assessment. Our method includes approximations to the distribution of OFL if it is not known from the assessment; however, we find it preferable to have the assessment model estimate the distribution of OFL directly. Probability-based methods such as this one provide well-defined approaches to setting ABC and may be helpful to scientific advisers as they translate the new legal requirement into concrete advice.