On the harmonic-mean property of model dispersive systems emerging under mononuclear, mixed and polynuclear path conditions

The goal of our study is to make use of the (fractally-defined) harmonic-mean criterion (HMC) as an indicator of proper/improper matter nucleation-transportation and matter-(non) densification tasks realized over certain thermodynamickinetic pathways in d-dimensional environments. We investigate three dynamic processes: self-avoiding random walk (SAW), cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA). They are all considered as dispersive systems characteristic of excluded-volume effect (EVE). From our mean-field investigation it turns out that the HMC shows that SAW and CCA belong to the same kinetic (or, dispersive chemical kinetics) class, whereas DLA does not since it is realized over a mixed (non-homogeneous) thermodynamic-kinetic pathway. Our findings clearly reveal that the dimension two appears to be kinetically optimal for SAW and CCA but cast again some serious doubts on whether the so-called DLA 2D "paradigm" is here a well-posed problem.