Ikeda and Miyazaki Reply to Rolf Schilling and Bernhard Schmid [arXiv:1101.5577]
Reply to the preceding comment by Rolf Schilling and Bernhard Schmid [arXiv:1101.5577, Phys. Rev. Lett. 106, 049601 (2011)].
cond-mat.soft↗
arXiv subjects
Atsushi Ikeda
Publications and source records attributed to Atsushi Ikeda.
Glass Transition of the Monodisperse Gaussian Core Model
We numerically study dynamical properties of the one-component Gaussian Core Model in the supercooled states. We find that nucleation is suppressed as density increases. Concomitantly the system exhibits glassy slow dynamics characterized by the two-step and stretched exponential relaxation of the density correlation as well as drastic increase of the relaxation time. It is found that violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than typical model glass formers, implying weaker dynamic heterogeneities. Besides, agreement of simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of slow dynamics of this ultra-soft particle fluid is mean-field-like. This fact may be understood as the consequences of multiple overlaps of the constituent particles at high densities.
cond-mat.soft↗
The double cover of cubic surfaces branched along their Hessian
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of the ambient projective space branched along the cubic surface. And we introduce a method to study the infinitesimal variations of Hodge structure of the double cover of the cubic surface. Using these results, we compute the Néron-Severi lattices for the double cover of a generic cubic surface and the Fermat cubic surface.
math.AG↗
The varieties of tangent lines to hypersurfaces in projective spaces
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs forms a smooth variety for a general hypersurface.
math.AG↗
Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
Mode-coupling theory (MCT) is conjectured to be a mean-field description of dynamics of the structural glass transition and the replica theory to be its thermodynamic counterpart. However, the relationship between the two theories remains controversial and quantitative comparison is lacking. In this Letter, we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions above three and compare the results with replica theory. We find grave discrepancies between the predictions of two theories. While MCT describes the nonergodic parameter quantitatively better than the replica theory in three dimension, it predicts a completely different dimension dependence of the dynamical transition point. We find it to be due to the pathological behavior of the nonergodic parameters derived from MCT, which exhibit negative tails in real space at high dimensions.
cond-mat.soft↗
On the Hodge structure of degenerating hypersurfaces in toric varieties
We introduce an algebraic method for describing the Hodge filtration of degenerating hypersurfaces in projective toric varieties. For this purpose, we show some fundamental properties of logarithmic differential forms on proper equivariant morphisms of toric varieties.
math.AG↗