Isospectral but physically distinct: Modular symmetries and their implications for carbon nanotori

Oscillating carbon nanotori along carbon nanotubes

The discovery of carbon nanostructures, such as nanotubes and C60 fullerenes, has given rise to a number of potential nanoscale devices. One such device is the gigahertz oscillator, comprising an inner shell sliding inside an outer shell of a multiwalled carbon nanotube, and which, at least theoretically, generates oscillatory frequencies in the gigahertz range. Following the concept of these g...

Colossal paramagnetic moments in metallic carbon nanotori.

Carbon nanostructures with unusually large paramagnetic moments have been discovered in a theoretical study of the electronic and magnetic properties of carbon nanotubes bent into toroids. Specifically, nanotori formed from metallic nanotubes with lambda(F) = 3T, where lambda(F) is the Fermi wavelength and T the translation vector of the nanotube, exhibit giant paramagnetic moments at selected ...

Orbiting atoms and C 60 fullerenes inside carbon nanotori

Essentially Isospectral Transformations and Their Applications

We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of e...

Detecting Modular ACU Structural Symmetries

We present an efficient encoding of order-sorted modular ACU terms into colored directed graphs. Then, by computing the automorphism groups of the encoded graphs, we are able to extract modular ACU structural symmetries both inside a term and across a set of terms. Finally, we show how the computed symmetries can be applied to the optimization of the equational generalization algorithms for mod...