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The evolution of energy in subaerial and subaqueous granular column collapses is studied. Employing the refractive index matching method and planar laser-induced fluorescence technique, we obtain granular and liquid images simultaneously in a single experiment of subaqueous flow. Particle image velocimetry and particle tracking velocimetry are used to process the data for the fluid and granular phase. We find stepwise decreases in the total kinetic energy of the granular material. The stage of rapidly falling energy corresponds to large transverse changes in the direction of the massive granular particles. Moreover, in this stage, a major fraction of the granular kinetic energy transferred from the granular potential energy is lost or transferred. Interestingly, compared with dry granular flow, the existence of an ambient liquid seems to reduce the total dissipated energy, which may be the reason why previous studies observed similar granular runout distances in subaqueous and dry granular collapses. [ABSTRACT FROM AUTHOR]

We investigate the area distribution of clusters (loops) in the honeycomb O(n) loop model by means of the worm algorithm with n = 0:5, 1; 1:5, and 2. At the critical point, the number of clusters, whose enclosed area is greater than A, is proportional to A-1 with a proportionality constant C. We confirm numerically that C is universal, and its value agrees well with the predictions based on the Coulomb gas method. [ABSTRACT FROM AUTHOR]