No matter whether theyre big, little, long, short, skinny or fat -- classic stalactites have the same singular shape.
Almost everyone knows that stalactites, formations that hang from the roof of caves, are generally long, slender and pointy. But the uniqueness of their form had gone unrecognized. "Theres only one shape that all stalactites tend to be. The difference is one of magnification -- its either big or its small, but its still the same shape," said researcher Martin Short of the University of Arizona in Tucson.
Short and his colleagues have developed a mathematical theory that explains how stalactites get their shape. "Its an ideal shape in nature and in mathematics that had not been known before," said Raymond Goldstein, a UA physics professor and senior author on the research report. "The Greek philosopher Plato had the concept that there are ideal forms underlying what we see in nature. Although any particular stalactite may have some bumps and ridges that deform it, one might say that within all stalactites is a idealized form trying to get out."
The universality of stalactites had probably been overlooked because the cave formations vary so much in size, said Short, a doctoral candidate in physics at UA. "The result was a surprise," he said. "We had no idea going into this that wed find this basic shape."
An article detailing the findings of Short, Goldstein and their colleagues will be published in an upcoming issue of Physical Review Letters. The Research Corporation and the National Science Foundation funded the research. Other authors on the article are James C. Baygents, a UA associate professor of chemical and environmental engineering; J. Warren Beck, a research scientist in UAs department of physics; David A. Stone, a doctoral candidate in UAs department of soil, water and environmental science; and Rickard S. Toomey, III, science and research manager for Arizona State Parks.
Although people have investigated how cave formations grow, few scientists examined why stalactites have their characteristic shape. After someone suggested that the tubules David Stone was growing in the laboratory resembled some cave formations, Goldstein became intrigued by caves.
He and his colleagues took a field trip to the famed Kartchner Caverns State Park in Benson, Ariz. and were floored by the variety of forms, especially the ripples many structures possess. So Goldstein suggested that his student Martin Short investigate the formation of ripples on stalactites. That task turned out to be extremely difficult, Short said. First he had to learn about the underlying dynamics of stalactite growth.
Stalactites grow when water laden with carbon dioxide and calcium carbonate drips from cracks or holes in the caves ceiling. As a water droplet hangs from the crack, the carbon dioxide escapes, much as a bottle of sparkling water fizzes when opened. As a result, the calcium carbonate comes out of solution and is left behind as a tiny bit of solid calcium carbonate. As each successive drip flows over the minute mineral deposit, the sequence repeats, ultimately forming a stalactite. Because the shape stems from the flow of water over the surface of the growing stalactite, the team turned to the field of fluid dynamics. The researchers developed an equation to describe how a stalactites shape evolves. "Its a general equation of motion for the growth of stalactites," Goldstein said. "Its a geometric law of motion."
Then the researchers plugged the equation into a computer and asked it to "grow" some shapes. To the teams surprise, no matter what shape was used as a starting point, the computers formations lengthened and thickened in a universal manner. The results looked strikingly like classic stalactites. "The computer told us there was something unique to look for, this ideal form," Goldstein said. The researchers then solved their equation of motion and obtained a specific mathematical expression that describes the carrot-like shape of stalactites.
The next step was to test their model against the real thing, so the researchers returned to Kartchner Caverns. "We spent four hours in the cave with cameras and strobe lights and laptops. We took dozens of pictures," said Goldstein.
Because cave formations are delicate, the researchers could not stomp around measuring the stalactites by hand. Instead, the scientists used lasers to project a pair of green dots onto the stalactites from afar and then took pictures of the stalactites. The researchers knew how far apart the green dots were, so the dots served as a scale bar for the pictures. Then the researchers could garner the stalactites dimensions from the pictures. Back in the lab, the researchers analyzed the actual stalactites and compared their shapes to the ideal form predicted by the mathematics. The real and the ideal differed by less than 5 percent. "We calculated the shape mathematically and said, well, we have to go see if this is right," Goldstein said. "And we did. And it was."
Kartchners Toomey said, "Its cool because the research contributes to learning new things about this cave that apply as well to other caves throughout the world," adding, "Missions of state parks include preservation, understanding and education. To have Kartchner and other state parks available for these types of studies helps further these missions." Now, Short and Goldstein say, they finally know enough to figure out what gives stalactites their ripples.
Mari N. Jensen | University of Arizona
New Study Will Help Find the Best Locations for Thermal Power Stations in Iceland
19.01.2017 | University of Gothenburg
Water - as the underlying driver of the Earth’s carbon cycle
17.01.2017 | Max-Planck-Institut für Biogeochemie
An important step towards a completely new experimental access to quantum physics has been made at University of Konstanz. The team of scientists headed by...
Yersiniae cause severe intestinal infections. Studies using Yersinia pseudotuberculosis as a model organism aim to elucidate the infection mechanisms of these...
Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.
While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...
Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales
Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...
Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.
As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...
19.01.2017 | Event News
10.01.2017 | Event News
09.01.2017 | Event News
20.01.2017 | Awards Funding
20.01.2017 | Materials Sciences
20.01.2017 | Life Sciences