Fredrickson-Andersen model on Bethe lattice with random pinning

We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A3 singularity point for the glass transition.Comment: 6 pages, 7 figure

One-dimensional Kac model of dense amorphous hard spheres

We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, $-1/4$ for the dynamical transition and $-1$ for the ideal glass transition, which are consistent with those of the $p$-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.Comment: 6 pages, 4 figure

The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions

We investigate the dynamics of the randomly pinned Fredrickson-Andersen model on the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamical critical properties are in the same universality class of the $A_2$ and $A_3$ transitions of Mode Coupling Theory. The $A_3$ behavior appears at the terminal point, where the relaxation becomes logarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and Random Field Ising Model.Comment: 8 pages, 7 figure

Effect of particle exchange on the glass transition of binary hard spheres

We investigate the replica theory of the liquid-glass transition for a binary mixture of large and small additive hard spheres. We consider two different ans\"atze for this problem: the frozen glass ansatz (FGA) in whichs the exchange of large and small particles in a glass state is prohibited, and the exchange glass ansatz (EGA), in which it is allowed. We calculate the dynamical and thermodynamical glass transition points with the two ans\"atze. We show that the dynamical transition density of the FGA is lower than that of the EGA, while the thermodynamical transition density of the FGA is higher than that of the EGA. We discuss the algorithmic implications of these results for the density-dependence of the relaxation time of supercooled liquids. We particularly emphasize the difference between the standard Monte Carlo and swap Monte Carlo algorithms. Furthermore, we discuss the importance of particle exchange for estimating the configurational entropy.Comment: 16 pages, 5 figure

HYDROLOGICAL SURVEY OF THE HUONG RIVER IN 2005

Joint Research on Environmental Science and Technology for the Eart