New simple properties of a few irregular systems

This paper presents seven results on irregular systems that are both new and can be described simply. The first three results are related to dynamical and static properties of gradient percolation. Firstly, it is shown that the transient regimes which lead to self-organized gradient percolation due to corrosion do not scale like gradient percolation itself. Secondly, it is shown that there is no diffusion front in 1-D but there exists a zone of fluctuations with a size of the order of the system size. Thirdly, the geometry of realistic intermetallic contacts in 3-D is shown to be closely related to that of diffusion fronts, but different. The two next results are related to reactive irregular surfaces. Firstly, molecular dynamics results indicates that, in 2-D, the size of the active zone of purely absorptive surfaces in the Knudsen diffusion regime is larger than that found in the molecular diffusion regime. Secondly, it is then shown that, in this last regime, the particles that really interacts with the surface, remains near the surface within a distance equal to the unscreened perimeter length. The following topic is related to the vibrations of deterministic surface fractals: with very good approximation, the extended disordered modes can be described as a superposition of regular (non-localized) trivial modes of the initiator of the fractal morphology. Finally, it is shown that the diffusion reorganized aggregation mechanism may display transitory fractal states with a life time increasing so rapidly with the system mass that dynamical equilibrium may never been reached, even for systems of relatively small size. This could be a simple example of the so-called “inherent states”.