A cusp catastrophe model is developed for slip-buckling slope by catastrophe theory, and the formulations of the necessary and su1⁄2cient conditions for instability of the slope are presented. It is found that di ̈erent regions (II, III and IV in Fig. 4) in the control space divided by the bifurcation set correspond well to the primary, secondary and tertiary creep phases. The corresponding disc...

Dynamic instability, in which abrupt transitions occur between growing and shrinking states, is an intrinsic property of microtubules that is regulated by both mechanics and specialized proteins. We discuss a model of dynamic instability based on the popular idea that growth is maintained by a cap at the tip of the fiber. The loss of this cap is thought to trigger the transition from growth to ...

Most studies that compare price and quantity controls for greenhouse gas emissions under uncertainty find that price mechanisms perform substantially better. In these studies, the benefits from reducing emissions are proportional to the level of reductions, and such linear benefits strongly favor price policies (Weitzman 1974). Catastrophic damages, however, challenge that intuition as conseque...