Absence of stable atomic structure in fluorinated graphene

Based on the results of first-principles calculations we demonstrate that significant distortion of graphene sheets caused by adsorption of fluorine atoms leads to the formation of metastable patterns for which the next step of fluorination is considerably less energetically favorable. Existence of these stable patterns oriented along the armchair direction makes possible the synthesis of various CFx structures. The combination of strong distortion of the nonfluorinated graphene sheet with the doping caused by the polar nature of C-F bonds reduces the energy cost of migration and the energy of migration barriers, making possible the migration of fluorine atoms on the graphene surface as well as transformation of the shapes of fluorinated areas. The decreasing energy cost of migration with increasing fluorine content also leads to increasing numbers of single fluorine adatoms, which could be the source of magnetic moments.Comment: 16 pages, 6 figures (one figure added), accepted in PCC

Atomic and electronic structure of nitrogen- and boron-doped phosphorene

First principle modeling of nitrogen- and boron-doped phosphorene demonstrates the tendency toward formation of highly ordered structures. Nitrogen doping leads to the formation of -N-P-P-P-N- lines. Further transformation to -P-N-P-N- lines across the chains of phosphorene occurs with increasing band gap and increasing nitrogen concentration, which coincides with the decreasing chemical activity of N-doped phosphorene. In contrast to the case of nitrogen, boron atoms prefer to form -B-B- pairs with the further formation of -P-P-B-B-P-P- patterns along the phosphorene chains. The low concentration of boron dopants converts the phosphorene from a semiconductor into a semimetal with the simultaneous enhancement of its chemical activity. Co-doping of phosphorene by both boron and nitrogen starts from the formation of -B-N- pairs, which provide flat bands and the further transformation of these pairs to hexagonal BN lines and ribbons across the phosphorene chains.Comment: 21 pages, 8 figures, 2 tables, to appear at PCC

A narrow-band unfitted finite element method for elliptic PDEs posed on surfaces

The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method allows a surface to be given implicitly as a zero level of a level set function. A surface equation is extended to a narrow-band neighborhood of the surface. The resulting extended equation is a non-degenerate PDE and it is solved on a bulk mesh that is unaligned to the surface. An unfitted finite element method is used to discretize extended equations. Error estimates are proved for finite element solutions in the bulk domain and restricted to the surface. The analysis admits finite elements of a higher order and gives sufficient conditions for archiving the optimal convergence order in the energy norm. Several numerical examples illustrate the properties of the method.Comment: arXiv admin note: text overlap with arXiv:1301.470

Structured Sparse Modelling with Hierarchical GP

In this paper a new Bayesian model for sparse linear regression with a spatio-temporal structure is proposed. It incorporates the structural assumptions based on a hierarchical Gaussian process prior for spike and slab coefficients. We design an inference algorithm based on Expectation Propagation and evaluate the model over the real data.Comment: SPARS 201