Spectral C*-categories and Fell bundles with path-lifting

Following Crane's suggestion that categorification should be of fundamental importance in quantising gravity, we show that finite dimensional even $S^o$-real spectral triples over \bbc are already nothing more than full C*-categories together with a self-adjoint section of their domain and range maps, while the latter are equivalent to unital saturated Fell bundles over pair groupoids equipped with a path-lifting operator given by a normaliser. Interpretations can be made in the direction of quantum Higgs gravity. These geometries are automatically quantum geometries and we reconstruct the classical limit, that is, general relativity on a Riemannian spin manifold.Comment: 20 pages, 1 figur

Nonlinear elastic polymers in random flow

Polymer stretching in random smooth flows is investigated within the framework of the FENE dumbbell model. The advecting flow is Gaussian and short-correlated in time. The stationary probability density function of polymer extension is derived exactly. The characteristic time needed for the system to attain the stationary regime is computed as a function of the Weissenberg number and the maximum length of polymers. The transient relaxation to the stationary regime is predicted to be exceptionally slow in the proximity of the coil-stretch transition.Comment: 10 pages, to be published in J. Fluid Mec

Justification of Sexual Reproduction by Modified Penna Model of Ageing

We generalize the standard Penna bit-string model of biological ageing by assuming that each deleterious mutation diminishes the survival probability in every time interval by a small percentage. This effect is added to the usual lethal but age-dependent effect of the same mutation. We then find strong advantages or disadvantages of sexual reproduction (with males and females) compared to asexual cloning, depending on parameters.Comment: 4 pages, 2 figures, submitted to Physica