Magnetically controlled ballistic deposition. A model of polydisperse granular packing

Abstract

The ow and deposition of polydisperse granular materials is simulated through the magnetic di usion limited aggregation (MDLA) model. The random walk undergone by an entity in the MDLA model is modiÿed such that the trajectories are ballistic in nature, leading to a magnetically controlled ballistic deposition (MBD) model. This allows to obtain important ingredients about a di cult problem that of the nonequilibrium segregation of polydisperse sandpiles and heterogeneous adsorption of a binary distribution of particles which can interact with each other and with an external ÿeld. Our detailed results from many simulations of MBD clusters on a two-dimensional triangular lattice above a at surface in a vertical ÿnite size box for binary systems indicates intriguing variations of the density, "magnetization", types of clusters and fractal dimensions. We derive the ÿeld and grain interaction-dependent susceptibility and compressibility. We deduce a completely new phase diagram for binary granular piles and discuss its complexity inherent to di erent grain competition and cluster growth probabilities.

Effects of relaxation processes during deposition of anisotropic grains on a flat substrate

“…Notice that the relaxation processes make the departures from linearity still smaller; the smallest departures exist in the case II, total gravitational relaxation (Fig.3b). As it was mentioned in [6] this has to be expected if one recalls that q, in a first approximation, is the fraction of deposited up-spins.…”

“…A few changes to the experimental procedure presented in [6] are hereby introduced. We propose an algorithm for creating a pile with a fixed probability q ∈ [0; 1] for spin flip.…”

“…In [6] a non linear-like dependence on q was found for the magnetization though with small departure from linearity due to the changes in the interaction strength. Notice that the relaxation processes make the departures from linearity still smaller; the smallest departures exist in the case II, total gravitational relaxation (Fig.3b).…”

“…We have studied such a model [6,7], within a (magnetic) ballistic deposition process; it is similar to the Tetris model [8], but more simplified. Basically the (2-dimensional) grains are anisotropic and are deposited vertically as in a gravity controlled rain.…”

“…We have previously examined clustering effects as in [6,7], through the cluster fractal dimension, the pile overall density, the distribution of grain orientations, ... and have found through percolation arguments [10,11] the existence of different cluster growth "mechanisms".…”