Osmosis describes the flow of water across semipermeable membranes powered by the chemical free energy extracted from salinity gradients. While osmosis can be expressed in simple terms via the van 't Hoff ideal gas formula for the osmotic pressure, it is a complex phenomenon taking its roots in the subtle interactions occurring at the scale of the membrane nanopores. Here we use new opportunities offered by nanofluidic systems to create an osmotic diode exhibiting asymmetric water flow under reversal of osmotic driving. We show that a surface charge asymmetry built on a nanochannel surface leads to nonlinear couplings between water flow and the ion dynamics, which are capable of water flow rectification. This phenomenon opens new opportunities for water purification and complex flow control in nanochannels.

We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility, also present in how much plastic deformation is accumulated prior to fracture. The dynamics of yielding exhibits avalanches with a power-law distribution.