Stalactite: Geometry as Destiny

Scientists at the University of Arizona, bringing together ideas and observational techniques from the physics and geophysics disciplines, have derived a mathematical theory to explain the morphology of cave formations such as stalactites (the carrot-like shapes hanging down from the roof) and stalagmites (growing up from the floor). The precipitative growth of speleotherms (the collective name for cave shapes) is important since features of weather from thousands of years ago can be unfolded from the layering in these underground repositories, much as tree rings or ice core samples render up clues to ancient climate.

Stalactites are composed of calcium carbonate precipitated from water entering the cave after percolating through CO2-rich soil and rock Treating stalactite growth as a "free boundary problem" (meaning that no a prior assumptions were made as to the evolving shape of the speleothem), the researchers linked the fluid dynamics and precipitative growth to obtain a law for surface growth which produces a unique “attractor” in the space of shapes (that is, a recurrent favored shape or trajectory in the abstract space of possible morphologies), one which closely matches observed shapes. Raymond Goldstein (520-621-1065, gold@physics.arizona.edu) suggests that the new theory should be applicable to other speleothem formations, and highlights interesting related problems such as the growth of hydrothermal vents, chemical gardens, and mollusk shells. (Short et al., Physical Review Letters, 14 January 2005)