Fractal Transport Phenomena through the Scale Relativity Model

A correspondence between Nottale's scale relativity model and Cresson's mathematical procedures is analyzed. It results that the "synchronization" of the movements at different scales (fractal scale, differential scale etc.) gives conductive type properties to the fractal fluid, while the absence of "synchronization" is inducing properties of convective type. The behavior of a conductive fractal fluid is illustrated through the numerical simulation of plasma diffusion that is generated by laser ablation. Rotational and irrotational convective behaviors of a fractal fluid are established. Particularly, at Compton spatial and temporal scales, the irrotational behavior implies the standard Schrödinger equation.