<< a certain geometrical structure of knots, which scientists call a Hopfion, manifests itself in unexpected corners of the universe, ranging from particle physics, to biology, to cosmology. >>
<< In a recent theoretical study, (..) (AA) discovered the presence of the Hopfion structure in nano-sized particles of ferroelectrics. >>
<< The Hopfion is a very abstract mathematical concept, (..) but the structure shows up in hydrodynamics, electrodynamics and even in the packing of DNA and RNA molecules in biological systems and viruses. >> Valerii Vinokur
<< When we visualized the polarization, we saw the Hopfion structure emerge, (..) We thought, wow, there is a whole world inside of these nanoparticles. >> Igor Luk'yanchuck.
Savannah Mitchem. Novel insight reveals topological tangle in unexpected corner of the universe. Argonne National Laboratory. May 26, 2020.
Luk’yanchuk I., Tikhonov Y., et al. Hopfions emerge in ferroelectrics.
Nat Commun 11, 2433. doi: 10.1038/ s41467-020-16258-w. May 15, 2020.
