The researchers observed other excitations (rotons and maxons) having a classical origin, even though these excitations were previously thought to be intrinsically quantum mechanical when observed in helium superfluids. These domain wall “kinks” can convert a potential energy difference into rotational kinetic energy, moving as solitons, which are pulses with unusually rich properties. For instance, the domain walls that separate regions of different dynamics can move axially while rotating. The researchers observed unusual excitations in the cactus’ energy landscape. The team found that the dynamics of the magnetic cactus reveal interesting physical processes. “Cristiano's simulations of the dynamical system, coupled to Nathan and Jay's experiments with the physical magnet system, then revealed fascinating new physics in the dynamical regime.” “Having approached the system from the physics end, we were naturally equipped and disposed to study dynamics,” he said. As Crespi explained, biological systems are highly damped and so don't have well-defined phonons or soliton modes. Dynamic phyllotaxis had not previously been explored since historically people had been thinking in terms of biological systems. Once the researchers realized that they had rediscovered static phyllotaxis, they decided to investigate the dynamics. We had made an independent re-discovery - several centuries later!” Only after that did we realize that our system had strong connections to biological phyllotaxis as well. Then Cristiano found Levitov's paper explaining similar static physics, but in a layered geometry. “We were quite excited by the beautiful mathematics and physics of the static ground-state energy plots, with the commensurate peaks and valleys in between.
“Initially, we rediscovered all of static phyllotaxis, not realizing that it had already been discovered and investigated by figures such as Kepler, da Vinci, Bravais, and even the ancient Romans/Greeks,” coauthor Vincent Crespi, a physics professor at PSU, told.
They found that the statics of phyllotaxis had been intriguing historical figures for the past several centuries and more. The mathematical regularity of these static patterns of phyllotaxis surprised the researchers, until they made an even more surprising discovery. The spines on the magnetic cactus, like those on a plant, form a helix around the cylindrical stem by growing around these particular angles. The unfavorable angles are fractional multiples of 2π (i.e. Then the scientists observed as the magnets (spines) arranged to form phyllotactic spirals, generating a so-called Farey tree of unfavorable angles. In their experiment, the researchers put the system in a low-energy state by mechanical agitation.
With this setup, the researchers, from Los Alamos National Laboratory in New Mexico Cornell University in Ithaca, New York and The Pennsylvania State University (PSU), have verified Levitov’s model, and their study has been published in a recent issue of Physical Review Letters.
FIBONACCI SPIRAL CACTUS FREE
Now, researchers have constructed a “magnetic cactus” with 50 outward-pointing magnets acting as spines, which are mounted on bearings and free to rotate on a vertical axis acting as the plant stem. Levitov proposed a model of phyllotaxis suggesting that the appearance of the Fibonacci sequence and golden mean in the pattern of spines on a cactus can be replicated for cylindrically constrained, repulsive objects. In a recent study, researchers have experimentally demonstrated for the first time a celebrated model of “phyllotaxis,” the study of mathematical regularities in plants.
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