Binomial multiplicative model of critical fragmentation

We report the binomial multiplicative model for low impact energy fragmentation. Impact fragmentation experiments were performed for low impact energy region, and it was found that the weighted mean mass is scaled by the pseudo control parameter multiplicity. We revealed that the power of this scaling is a non-integer (fractal) value and has a multi-scaling property. This multi-scaling can be interpreted by a binomial multiplicative (simple biased cascade) model. Although the model cannot explain the power-law of fragment-mass cumulative distribution in fully fragmented states, it can produce the multi-scaling exponents that agree with experimental results well.Comment: 10 pages, 6 figures, A typo in Eq.(6b) was improved in Ver.

Explosive fragmentation of thin ceramic tube using pulsed power

This study experimentally examined the explosive fragmentation of thin ceramic tubes using pulsed power. A thin ceramic tube was threaded on a thin copper wire, and high voltage was applied to the wire using a pulsed power generator. This melted the wire and the resulting vapor put pressure on the ceramic tube, causing it to fragment. We examined the statistical properties of the fragment mass distribution. The cumulative fragment mass distribution obeyed the double exponential or power-law with exponential decay. Both distributions agreed well with the experimental data. We also found that the weighted mean fragment mass was scaled by the multiplicity. This result was similar to impact fragmentation, except for the crossover point. Finally, we obtained universal scaling for fragmentation, which is applicable to both impact and explosive fragmentation.Comment: 5 pages, 6 figure

Force Chain Evolution in a Two-Dimensional Granular Packing Compacted by Vertical Tappings

We experimentally study the statistics of force-chain evolution in a vertically-tapped two-dimensional granular packing by using photoelastic disks. In this experiment, the tapped granular packing is gradually compacted. During the compaction, the isotropy of grain configurations is quantified by measuring the deviator anisotropy derived from fabric tensor, and then the evolution of force-chain structure is quantified by measuring the interparticle forces and force-chain orientational order parameter. As packing fraction increases, the interparticle force increases and finally saturates to an asymptotic value. Moreover, the grain configurations and force-chain structures become isotropically random as the tapping-induced compaction proceeds. In contrast, the total length of force chains remains unchanged. From the correlations of those parameters, we find two relations: (i) a positive correlation between the isotropy of grain configurations and the disordering of force-chain orientations, and (ii) a negative correlation between the increasing of interparticle forces and the disordering of force-chain orientations. These relations are universally held regardless of the mode of particle motions with/without convection

Crossover of the weighted mean fragment mass scaling in 2D brittle fragmentation

We performed vertical and horizontal sandwich 2D brittle fragmentation experiments. The weighted mean fragment mass was scaled using the multiplicity $\mu$. The scaling exponent crossed over at $\log \mu_c \simeq -1.4$. In the small $\mu (\ll\mu_c)$ regime, the binomial multiplicative (BM) model was suitable and the fragment mass distribution obeyed log-normal form. However, in the large $\mu (\gg\mu_c)$ regime, in which a clear power-law cumulative fragment mass distribution was observed, it was impossible to describe the scaling exponent using the BM model. We also found that the scaling exponent of the cumulative fragment mass distribution depended on the manner of impact (loading conditions): it was 0.5 in the vertical sandwich experiment, and approximately 1.0 in the horizontal sandwich experiment.Comment: 5 pages, 3 figure