Structure and dynamics of the missing-row reconstruction on O/Cu(0 0 1) and O/Ag(0 0 1)

The geometry and the vibrational properties of missing row reconstructed O/Cu(0 0 1) and O/Ag(0 0 1) surfaces are investigated by means of density functional theory and density functional perturbation theory, using the local density and the generalized-gradient approximations. Our results predict very similar structural and vibrational properties for the two reconstructed surfaces. In the case of copper our calculations reproduce quite accurately the experimental results, while for the missing row reconstructed O/Ag(0 0 1) surface the agreement between theory and experiment is less satisfactory.     

On a singular minimizing problem

We investigate the non-homogeneous modular Dirichlet problem Δ _p (·)u(x) = f (x) (where Δ _p (·)u(x) = div(|?u|^p(x-2)?u(x)) from the functional analytic point of view and we prove the stability of the solutions \({\left( {{u_{{p_i}}}} \right)_i}\) of the equation \({\Delta _{{p_i}\left( \cdot \right)}}{u_{{p_i}\left( \cdot \right)}} = f\) as p _i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals.     

Adaptive pseudospectral solution of a diffuse interface model

A diffuse interface type model, using an energy-based variational formulation with a free energy that is a function of the density and its gradients is presented. All of the boundary terms are retained and related to external surface forces, which can be of particular interest when considering the fluid–fluid–solid region. The numerical solution of these types of problems can be troublesome if a thin transition layer is desired. Here, Chebyshev pseudospectral methods with mesh adaptation for the solution of diffuse interface type problems are studied. A mesh adaptation algorithm based in the equidistribution principle following a continuation process is derived. In order to achieve high precision for problems exhibiting thin transition layers, a modified version of the arc-length monitor function is proposed which yields a sufficiently smooth coordinate transformation. At every step of the continuation process, a fixed number of iterations is implemented, so that the equidistribution equations are not solved completely at each step, which saves a considerable amount of computational effort. Numerical results for the static phase field model exhibiting thin transition layers are presented.     

Streaminglike diffusion in the low-dimensional stochastic pump model

In this paper we analyze a diffusion phenomenon in a few-dimensional Hamiltonian system of coupled mappings in which the principal component of diffusion occurs along resonances. The result is that the diffusion can have power-law dependence in coupling parameter mu and be independent of the stochastic parameter K. For the same range of parameters, the usual analytical Arnold diffusion across resonances is dependent on K and can be much smaller than resonance streaming diffusion. The results are used to qualitatively explain recent results in multidimensional coupled standard maps.     

Synthesis and reactivity of (C6F5)3B-N-heterocycle complexes. 1. Generation of highly acidic sp3 carbons in pyrroles and indoles

The reaction of pyrroles and indoles with B(C(6)F(5))(3) and BCl(3) produces 1:1 B-N complexes containing highly acidic sp(3) carbons, for example, N-[tris(pentafluorophenyl)borane]-5H-pyrrole (1) and N-[tris(pentafluorophenyl)borane]-3H-indole (2), that are formed by a new formal N-to-C hydrogen shift, the mechanism of which is discussed. With some derivatives, restricted rotation around the B-N bond and/or the B-C bonds was observed by NMR techniques, and some rotational barriers were calculated from experimental data. The acidity of the sp(3) carbons in these complexes is shown by their ability to protonate NEt(3), with formation of pyrrolyl- and indolyl-borate ammonium salts. The driving force for this reaction is given by the restoration of the aromaticity of the heterocycle.     

A simple model for damage in the elastic range

A brittle material presents significant loss of strength after being subjected to a process of repeated loading and unloading. This effect is usually described in a generic way as the body being damaged. A very simple method for treating this damage is to assume that, aside from the main cracks which characterize the limit strength of the material, other cracks also exist which modify its fundamental stress state and which therefore influence the stress intensity factor of the main cracks.     

Short synthesis of tryptophane and β-carboline derivatives by reaction of indoles with N-(diphenylmethylene)-α,β-didehydroamino acid esters

The ethylaluminum dichloride catalyzed Michael-type addition of indoles 1a-h to the N-(diphenylmethylene)-α,β-didehydroamino acid esters 2a-c allows a new synthesis of β-methyltryptophanes 41,m and a new route for 1,1-diphenyl-3-carbalkoxy-1,2,3,4-tetrahydro-β-carbolines 5a-m.