Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

Abstract

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1<d<2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t−1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model.

Modelling Fractional Behaviours Without Fractional Models

“…This class of model is particularly interesting to make interpretation of fractional behaviours produced by adsorption phenomena (Tartaglione et al, 2020), (Tartaglione et al, 2021) as it will be shown soon by the author. The Laplace transform of relation ( 24) is given by sx(s) A 0 x(s) + A 1 The transfer function linking the system input u(t) to the system output x(t) is thus defined by:…”

Competitive random sequential adsorption of binary mixtures of disks and discorectangles

“…In the multistep models the substrates are covered by the particles of different sort sequentially. The deposition of mixtures of disks have been intensively discussed for the competitive [23][24][25][26] and the multi-step [27][28][29][30][31][32] RSA models. Particularly the multi-step depositions on heterogeneous, partially pre-covered, pre-patterned of fractal surfaces (multistep RSA models) were studied.…”