We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations. Short title: RSB in the Random Replicant Model

Despite the fact that quantitative experimental data have been available for more than forty years now, nematoacoustics still poses intriguing theoretical and experimental problems. In this paper, we prove that the main observed features of acoustic wave propagation through a nematic liquid crystal cell - namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation - can be explained by properly accounting for two fundamental features of the nematic response: anisotropy and relaxation. The latter concept - new in liquid crystal modelling - provides the first theoretical explanation of the structural relaxation process hypothesised long ago by Mullen and co-workers [Mullen et al., Phys. Rev. Lett., 1972, 28, 799]. We compare and contrast our proposal with an alternative theory where the liquid crystal is modelled as an anisotropic second-gradient fluid.

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We consider the coupling between the local curvature tensor of a membrane and the local two-dimensional nematic order parameter, deriving it from a quasi-microscopic argument. This coupling makes the nematic director aligned along the lowest curvature eigenvector in a local metric. Local bending of a membrane may then generate nematic ordering. Alternatively, emerging nematic order leads to shape instabilities of closed vesicles. The theory is applied to a spherical isotropic vesicle, which turns into a prolate shape with two +1 disclinations on its poles as the nematic order sets in the membrane, described within the Landau-de Gennes continuum model.