Computing Mountain Passes

Mountain Passes and Saddle Points

Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points. Criteria for the existence of minima or maxima are well-known, ...

Level set methods for finding critical points of mountain pass type

Computing mountain passes is a standard way of finding critical points. We describe a numerical method for finding critical points that is convergent in the nonsmooth case and locally superlinearly convergent in the smooth finite dimensional case. We apply these techniques to describe a strategy for addressing the Wilkinson problem of calculating the distance from a matrix to a closest matrix w...

Are mountain passes higher in the tropics? Janzen's hypothesis revisited.

Synopsis In 1967 Daniel Janzen published an influential paper titled "Why Mountain Passes Are Higher in the Tropics." Janzen derived a simple climatic-physiological model predicting that tropical mountain passes would be more effective barriers to organismal dispersal than would temperate-zone passes of equivalent altitude. This prediction derived from a recognition that the annual variation in...

Finding transition pathways : throwing ropes over rough mountain passes , in the dark

Data on morphotectonic indices of Dashtekhak district, Iran

Morphotectonic indices by representing the longer period of time than recorded earthquake data, are useful in evaluating the tectonic activity of a region. Dashtkhak area is located in Kerman province of Iran, where one of the most active faults, Kouhbanan strike slip fault, passes through. This data article provides a precise level data on mountain fronts and valleys of Dashtkhak region that i...