Transport phenomena in nanostructures and non-differentiable space–time

Considering that the motion of the micro-particles takes place on continuous but non-differentiable curves, in the topological dimension DT = 1, a theoretical approach of the transport mechanisms in nanostructures is established: generalized Euler’s type equations, Schrödinger’s type equation as an irrotational motion of the Euler’s fluid, Josephson type effect, and hydrodynamic model with the current expressions and conductance quantization. The correspondence with El Naschie’s ε(∞) space–time is given by means of some examples (the heat transfer in nanofluids, the compatibility of the acoustic regime of the phononic spectrum with the optical one, etc.).