From Liquid Structure to Configurational Entropy: Introducing Structural Covariance

We connect the configurational entropy of a liquid to the geometrical properties of its local energy landscape, using a high-temperature expansion. It is proposed that correlations between local structures arises from their overlap and, being geometrical in nature, can be usefully determined using the inherent structures of high temperature liquids. We show quantitatively how the high-temperature covariance of these local structural fluctuations arising from their geometrical overlap, combined with their energetic stability, control the decrease of entropy with decreasing energy. We apply this formalism to a family of Favoured Local Structure (FLS) lattice models with two low symmetry FLS's which are found to either crystallize or form a glass on cooling. The covariance, crystal energy and estimated freezing temperature are tested as possible predictors of glass-forming ability in the model system

Convergence of HX Preconditioner for Maxwell's Equations with Jump Coefficients (ii): The Main Results

This paper is the second one of two serial articles, whose goal is to prove convergence of HX Preconditioner (proposed by Hiptmair and Xu, 2007) for Maxwell's equations with jump coefficients. In this paper, based on the auxiliary results developed in the first paper (Hu, 2017), we establish a new regular Helmholtz decomposition for edge finite element functions in three dimensions, which is nearly stable with respect to a weight function. By using this Helmholtz decomposition, we give an analysis of the convergence of the HX preconditioner for the case with strongly discontinuous coefficients. We show that the HX preconditioner possesses fast convergence, which not only is nearly optimal with respect to the finite element mesh size but also is independent of the jumps in the coefficients across the interface between two neighboring subdomains.Comment: with 25 pages, 2 figure