Deciphering patterns in nature is a specialty of UA researchers Martin B. Short, James C. Baygents and Raymond E. Goldstein. In 2005, the team figured out that stalactites, the formations that hang from the ceilings of caves, have a unique underlying shape described by a strikingly simple mathematical equation.
However, stalactites aren't the only natural formations that look like elongated carrots. Once the researchers had found a mathematical representation of the stalactite's shape, they began to wonder if the solution applied to other similarly shaped natural formations caused by dripping water.
So the team decided to investigate icicles. Although other scientists have studied how icicles grow, they had not found a formula to describe their shape.
Surprisingly, the team found that the same mathematical formula that describes the shape of stalactites also describes the shape of icicles.
"Everyone knows what an icicle is and what it looks like, so this research is very accessible. I think it is amazing that science and math can explain something like this so well. It really highlights the beauty of nature," Short said.
The finding is surprising because the physical processes that form icicles are very different from those that form stalactites. Whereas heat diffusion and a rising air column are keys to an icicle's growth, the diffusion of carbon dioxide gas fuels a stalactite's growth.
Short, a doctoral candidate in UA's physics department, Baygents, a UA associate professor of chemical and environmental engineering, and Goldstein, a UA professor of physics and the Schlumberger Professor of Complex Physical Systems at the University of Cambridge in England, published their article, "A Free-Boundary Theory for the Shape of the Ideal Dripping Icicle," in the August 2006 issue of Physics of Fluids. The National Science Foundation funded the research.
As residents of cold climates know, icicles form when melting snow begins dripping down from a surface such as the edge of a roof. For an icicle to grow, there must be a constant layer of water flowing over it.
The growth of an icicle is caused by the diffusion of heat away from the icicle by a thin fluid layer of water and the resulting updraft of air traveling over the surface. The updraft of air occurs because the icicle is generally warmer than its surrounding environment, and thus convective heating causes the air surrounding the icicle to rise. As the rising air removes heat from the liquid layer, some of the water freezes, and the icicle grows thicker and elongates.
"At first, we focused only on the thin water layer covering the icicle, just like we did with stalactites," said Short. "It was only later that we examined the layer of rising air, which is technically more correct. Strangely though, both methods lead to the same mathematical shape for icicles."
The resulting shape turns out to be described by the same mathematical equation that describes stalactites. One could call it the Platonic form.
The team wanted to compare the predicted shape to real icicles. Because icicles are scarce in Tucson, the scientists naturally turned to the Internet. They were able to compare pictures of actual icicles with their predicted shape.
The team found that it doesn't matter how big or small the actual icicles were, they could all fit to the shape generated by the mathematical equation.
"Fundamentally, just like in the early stalactite work, it's a result that implies that the shape of an icicle, at least in its ideal, pristine form, ought to be described by this mathematical equation. And we found, examining images of icicles, that it is a very good fit," senior author Goldstein said.
The team's next step will be to solve the problem of how ripples are formed on the surfaces of both stalactites and icicles.
Mari N. Jensen | EurekAlert!
Study offers new theoretical approach to describing non-equilibrium phase transitions
27.04.2017 | DOE/Argonne National Laboratory
SwRI-led team discovers lull in Mars' giant impact history
26.04.2017 | Southwest Research Institute
More and more automobile companies are focusing on body parts made of carbon fiber reinforced plastics (CFRP). However, manufacturing and repair costs must be further reduced in order to make CFRP more economical in use. Together with the Volkswagen AG and five other partners in the project HolQueSt 3D, the Laser Zentrum Hannover e.V. (LZH) has developed laser processes for the automatic trimming, drilling and repair of three-dimensional components.
Automated manufacturing processes are the basis for ultimately establishing the series production of CFRP components. In the project HolQueSt 3D, the LZH has...
Reflecting the structure of composites found in nature and the ancient world, researchers at the University of Illinois at Urbana-Champaign have synthesized thin carbon nanotube (CNT) textiles that exhibit both high electrical conductivity and a level of toughness that is about fifty times higher than copper films, currently used in electronics.
"The structural robustness of thin metal films has significant importance for the reliable operation of smart skin and flexible electronics including...
The nearby, giant radio galaxy M87 hosts a supermassive black hole (BH) and is well-known for its bright jet dominating the spectrum over ten orders of magnitude in frequency. Due to its proximity, jet prominence, and the large black hole mass, M87 is the best laboratory for investigating the formation, acceleration, and collimation of relativistic jets. A research team led by Silke Britzen from the Max Planck Institute for Radio Astronomy in Bonn, Germany, has found strong indication for turbulent processes connecting the accretion disk and the jet of that galaxy providing insights into the longstanding problem of the origin of astrophysical jets.
Supermassive black holes form some of the most enigmatic phenomena in astrophysics. Their enormous energy output is supposed to be generated by the...
The probability to find a certain number of photons inside a laser pulse usually corresponds to a classical distribution of independent events, the so-called...
Microprocessors based on atomically thin materials hold the promise of the evolution of traditional processors as well as new applications in the field of flexible electronics. Now, a TU Wien research team led by Thomas Müller has made a breakthrough in this field as part of an ongoing research project.
Two-dimensional materials, or 2D materials for short, are extremely versatile, although – or often more precisely because – they are made up of just one or a...
20.04.2017 | Event News
18.04.2017 | Event News
03.04.2017 | Event News
27.04.2017 | Life Sciences
27.04.2017 | Physics and Astronomy
27.04.2017 | Earth Sciences