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A generalized magnetically controlled ballistic rain-like deposition (MBD) model of granular piles has been numerically investigated in 2D. The grains are taken to be elongated disks whence characterized by a two-state scalar degree of freedom, called "nip", their interaction being described through a Hamiltonian. The results are discussed in order to search for the effect of nip flip (or grain rotation from vertical to horizontal and conversely) probability in building a granular pile. The characteristics of creation of + (or -) nip's clusters and clusters of holes (missing nips) are analyzed. Two different cluster-mass regimes have been identified, through the cluster-mass distribution function which can be exponential or have a power law form depending on whether the nip flip (or grain rotation) probability is large or small. Analytical forms of the exponent are empirically found in terms of the Hamiltonian parameters.

This work is a systematic computational study of random and ballistic deposition (BD) in 1+1 dimension for deposition of two differently shaped particles. The effect of particle shape and size on different growth parameters has been reported. It has been observed that when the shape of the particle gets changed, the surface that evolves following the mechanism of random deposition (RD) model shows acute correlation effect. The growth appeared with two regions along with saturation with two acutely different slopes, one of which is around 0.5 and, other is nearly 0.33. This shows that initially, the deposition obeys the RD model, while when particle shape changes correlation gets introduced, the deposition mechanism obeys the law of BD. Same when applied in the case of BD, it had been observed that introduction of this artificial correlation introduces another region in the growth regime separating the entire regime into three parts along with saturation. In each case, different critical exponents were calculated along with the other associated parameters like porosity, growth velocity, etc. Also, it has been shown that porosity has profound effect on size and shape of the particle deposited and it varies between 0 and 0.5 for the surfaces evolved by RD model whereas the same has value between 0.75 and 0.6 in the case of BD.

We illustrate a technique of analysis of time series, aiming at revealing crucial events, as a theoretical tool for the physical foundation of the subordination approach.