Physics of free climbing

Abstract

Theory of stochastic processes provides theoretical tools which can be efficiently used to explore properties of noise induced escape kinetics. Since noise facilitated escape over the potential barrier resembles free climbing, one can use the first passage time theory in analysis of rock climbing. We perform the analysis of the mean first passage time in order to answer the question regarding the optimal, i.e., resulting in the fastest climbing, rope length. It is demonstrated that there is a discrete set of favorable rope lengths assuring shortest climbing times, as they correspond to local minima of mean first passage time. Within the set of favorable rope lengths there is the optimal rope giving rise to the shortest climbing time. In particular, more experienced climbers can decrease their climbing time by using longer ropes.

7 pages, 6 figures

References in corpus (7)

• Diffusion with Stochastic Resetting
• Stochastic Resetting and Applications
• Diffusion with Optimal Resetting
• Kinematic reconstructions of extended theories of gravity at small and intermediate redshifts
• First passage under stochastic resetting in an interval
• Optimizing Brownian escape rates by potential shaping
• Prediction and Quantification of Individual Athletic Performance