The interior of a cell is very crowded (up to 35% protein by weight), with significant consequences for diffusive transport. The possible trajectories of a given tracer particle are constrained by the labyrinth of obstacles. For a static obstacle configuration, a percolation transition takes place at a certain critical obstacle density, so that above this density no long-range transport is poss...

Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, n. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We use a recently developed algorithm, based on transfer matrix methods, to enumerate plane meanders. This allows us to calculate the number of closed meander...

We show that all Lie point symmetries of various classes of nonlinear differential equations involving critical nonlinearities are variational/divergence symmetries.