Flow through randomly curved manifolds
  We have found that the relation between the flow through campylotic
(generically curved) media, consisting of randomly located curvature
perturbations, and the average Ricci scalar of the system exhibits two distinct
functional expressions (hysteresis), depending on whether the typical spatial
extent of the curvature perturbation lies above or below the critical value
maximizing the overall Ricci curvature. Furthermore, the flow through such
systems as a function of the number of curvature perturbations presents a
sublinear behavior for large concentrations due to the interference between
curvature perturbations that, consequently, produces a less curved space. For
the purpose of this study, we have developed and validated a lattice kinetic
model capable of describing fluid flow in arbitrarily curved manifolds, which
allows to deal with highly complex spaces in a very compact and efficient way.
