Coarse-graining the Dynamics of a Driven Interface in the Presence of Mobile Impurities: Effective Description via Diffusion Maps

Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an effective description of a driven interface in the presence of mobile impurities, based on an Ising variant model and a single empirical coarse variable, was partially successful; yet it underlined the necessity of selecting additional coarse variables in certain parameter regimes. In this paper we use a data mining approach to help identify the coarse variables required. We discuss the implementation of this diffusion map approach, the selection of a similarity measure between system snapshots required in the approach, and the correspondence between empirically selected and automatically detected coarse variables. We conclude by illustrating the use of the diffusion map variables in assisting the atomistic simulations, and we discuss the translation of information between fine and coarse descriptions using lifting and restriction operators.Comment: 28 pages, 10 figure

Solving headswitching translation cases in LFG-DOT

It has been shown that LFG-MT (Kaplan et al., 1989) has difficulties with Headswitching data (Sadler et al., 1989, 1990; Sadler & Thompson, 1991). We revisit these arguments in this paper. Despite attempts at solving these problematic constructions using approaches based on linear logic (Van Genabith et al., 1998) and restriction (Kaplan & Wedekind, 1993), we point out further problems which are introduced. We then show how LFG-DOP (Bod & Kaplan, 1998) can be extended to serve as a novel hybrid model for MT, LFG-DOT (Way, 1999, 2001), which promises to improve upon the DOT model of translation (Poutsma 1998, 2000) as well as LFG-MT. LFG-DOT improves the robustness of LFG-MT through the use of the LFG-DOP Discard operator, which produces generalized fragments by discarding certain f-structure features. LFG-DOT can, therefore, deal with ill-formed or previously unseen input where LFG-MT cannot. Finally, we demonstrate that LFG-DOT can cope with such translational phenomena which prove problematic for other LFG-based models of translation

T-duality simplifies bulk-boundary correspondence: some higher dimensional cases

Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.Comment: 25 pages. To appear in Ann. Henri Poincar