The Skyrme model is a low energy, effective field theory for QCD which when coupled to a gravitational field provides an ideal semi-classical model to describe neutron stars. We use the Skyrme crystal solution composed of a lattice of $alpha$-like pa
rticles as a building block to construct minimum energy neutron star configurations, allowing the crystal to be strained anisotropically. We find that below 1.49 solar masses the stars crystal deforms isotropically and that above this critical mass, it undergoes anisotropic strain. We then find that the maximum mass allowed for a neutron star is 1.90 solar masses, in close agreement with a recent observation of the most massive neutron star yet found. The radii of the computed solutions also match the experimentally estimated values of approximately 10km.
Polarons, introduced by Davydov to explain energy transport in $alpha$-helices, correspond to electrons localised on a few lattice sites because of their interaction with phonons. While the static polaron field configurations have been extensively st
udied, their displacement is more difficult to explain. In this paper we show that, when the next to nearest neighbour interactions are included, for physical values of the parameters, polarons can spontaneously move, at T=0, on bent chains that exhibit a positive gradient in their curvature. At room temperature polarons perform a random walk but a curvature gradient can induce a non-zero average speed similar to the one observed at zero temperature. We also show that at zero temperature a polaron bounces on sharply kinked junctions. We interpret these results in light of the energy transport by transmembrane proteins.
