池田 晴國

Significance The jamming transition is a key property of granular materials, including sand and dense suspensions. In the generic situation of nonspherical particles, its scaling properties are not completely understood. Previous empirical and theoretical work in ellipsoids and spherocylinders indicates that both structural and vibrational properties are fundamentally affected by shape. Here we explain these observations using a combination of marginal stability arguments and the replica method. We unravel a universality class for particles with internal degrees of freedom and derive how the structure of packings and their vibrations scale as the particles evolve toward spheres.

The swap Monte Carlo algorithm combines the translational motion with the exchange of particle species and is unprecedentedly efficient for some models of glass former. In order to clarify the physics underlying this acceleration, we study the problem within the mean field replica liquid theory. We extend the Gaussian Ansatz so as to take into account the exchange of particles of different species, and we calculate analytically the dynamical glass transition points corresponding to the swap and standard Monte Carlo algorithms. We show that the system evolved with the standard Monte Carlo algorithm exhibits the dynamical transition before that of the swap Monte Carlo algorithm. We also test the result by performing computer simulations of a binary mixture of the Mari-Kurchan model, both with standard and swap Monte Carlo. This scenario provides a possible explanation for the efficiency of the swap Monte Carlo algorithm. Finally, we discuss how the thermodynamic theory of the glass transition should be modified based on our results.