Statistical Mechanics of Discrete Multicomponent Fragmentation

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity, and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation, and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.

Fragility and an extremely low shear modulus of high porosity silicic magma

<p>The rheology and strength of bubbly magma govern eruption dynamics by determining the possibility of fragmentation of ascending magmas. The rheology of magma also regulates the propagation velocity and attenuation of seismic waves, and are required parameters for understanding seismic monitoring. We measured the rheology and strength of high porosity (>0.86) rhyolitic magma at 500-950 degrees C. The measured shear modulus and strength are several orders of magnitude lower than bubble-free rhyolite melt, implying that high porosity magma cannot avoid fracturing during magma ascent. The occurrence of fractures is observed in the low-temperature magma (<800 degrees C). In this temperature range, the measured attenuation is low (Q>1). That is, the elastic energy originated by deformations avoids attenuation and is stored in the bubbly magma to cause fracturing. The newly found porosity-dependent strength based on our measurements comprehensively explains three different fragmentation criteria that have been previously proposed independently. Our measurements also show that the shear modulus becomes lower by increasing porosity, which can slow the shear wave velocity. These results suggest that knowing the attenuation of the seismic wave is useful to evaluate magma temperature and the possibility of a fragmentation event that may determine subsequent volcanic activities.</p><p>Reference: Namiki et al. Journal of Volcanology and Geothermal Research (2020).</p>