Shape of an elastica under growth restricted by friction

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure-8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions

Shape of an elastica under growth restricted by friction

We investigate the quasi-static growth of elastic fibers in the presence of isotropic dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of stability against infinitesimal perturbations over finite time intervals is proposed and a semi-analytical method for the determination of the critical length is developed. The post-critical behavior of the system is studied by using an appropriate numerical scheme based on variational methods. We find post-critical shapes for uniformly distributed as well as for concentrated growth and demonstrate convergence to a figure 8 shape for large lengths when self-crossing is allowed. Comparison with simple physical experiments yields reasonable accuracy of the theoretical predictions

The database of the PREDICTS (Projecting Responses of Ecological Diversity In Changing Terrestrial Systems) project

The PREDICTS project—Projecting Responses of Ecological Diversity In Changing Terrestrial Systems (www.predicts.org.uk)—has collated from published studies a large, reasonably representative database of comparable samples of biodiversity from multiple sites that differ in the nature or intensity of human impacts relating to land use. We have used this evidence base to develop global and regional statistical models of how local biodiversity responds to these measures. We describe and make freely available this 2016 release of the database, containing more than 3.2 million records sampled at over 26,000 locations and representing over 47,000 species. We outline how the database can help in answering a range of questions in ecology and conservation biology. To our knowledge, this is the largest and most geographically and taxonomically representative database of spatial comparisons of biodiversity that has been collated to date; it will be useful to researchers and international efforts wishing to model and understand the global status of biodiversity