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

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

Asymptotic function for multi-growth surfaces using power-law noise

Numerical simulations are used to investigate the multiaffine exponent $\alpha_q$ and multi-growth exponent $\beta_q$ of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of $\beta_q$ are compared with the asymptotic function $\beta_q = \frac{1}{q}$ that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agreement for large $q$. The simulated $\alpha_q$ is found in the range $\frac{1}{q} \leq \alpha_q \leq \frac{2}{q+1}$. This implies that large rare events tend to break the KPZ universality scaling-law at higher order $q$.Comment: 5 pages, 4 figures, to be published in Phys. Rev.