Using the fractional interaction law to model the impact dynamics of multiparticle collisions in arbitrary form

Abstract

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual particle within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.

The dynamical nature of a backlash system with and without fluid friction

“…Inhomogeneous time or space scales or, equivalently, coexistence of many different scales are indeed at the origin of the fractional derivatives modeling of systems in viscoelasticity and other fields [19][20][21][22]. The emphasis on the inhomogeneity of the integration scale also provides a nice geometrical interpretation of fractional integration [23], similar to Bullock's interpretation of the Riemann-Stieltjes integral [24].…”

“…Fractional calculus, a well developed mathematical field, has recently found a growing range of applications in physics and engineering [13][14][15][16][17][18][19][20][21][22].…”

Modeling the transition between stable and unstable operation while emptying a silo

“…However, to carry out such a series of experiments is technically complicated and requires the involvement of advanced research equipment. Therefore, using DEM [25] we decided to carry out simulations of intermediate states of the outflow of granular material from the silo. Simulations were performed for the same set of parameters describing the granular material as in the experiment.…”

“…In order to predict the empirical constant Hc i, j we performed preliminary simulations for a stack of particles which contact with the bottom plate due to gravity action. In these simulations we used the fractional interaction law [25] as a model of repulsive force which gives proper results in the energy dissipation and contact time for multiparticle collisions. For above data we estimated the empirical constant as Hc i, j = 0.1.…”

Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields

“…We shall in the near future investigate (12) in much greater detail, and also delve into what are perhaps more realistic fractional analogues in which the actual interaction forces in the particle fields are fundamentally fractional in nature as for example in [15].…”