We study wrappings of smooth (convex) surfaces by a flat piece of paper or foil. Such wrappings differ from standard mathematical origami because they require infinitely many infinitesimally small folds (“crumpling”) in order to transform the flat sheet into a surface of nonzero curvature. Our goal is to find shapes that wrap a given surface, have small area and small perimeter (for efficient m...

Evaluating and improving snow models and outflow predictions for hydrological applications is hindered by the lack of continuous data on bulk volumetric liquid water content (θw) and storage capacity of the melting snowpack. The combination of upward looking ground-penetrating radar and conventional snow height sensors enable continuous, nondestructive determinations of θw in natural snow cover...

This paper summarizes our theoretical understanding of supernova events in a “back of the envelope” way. It is intended to aid in the recognition and understanding of those events which are not “standard”, and which may provide the most insight.