Surface structures formed by individual adsorption and coadsorption of Mn and Bi on Cu(0 0 1), studied by LEED

We have studied the individual adsorption of Mn and Bi, and their coadsorption on Cu(0 0 1) by low-energy electron diffraction (LEED). For Mn, we have determined the c(2 × 2) structure formed at 300 K, whose structure had been determined by several methods. We reconfirmed by a tensor LEED analysis that it is a substitutional structure and that a previously reported large corrugation (0.30 Å) between substitutional Mn and remaining surface Cu atoms coincides perfectly with the present value. In the individual adsorption of Bi, we have found a c(4 × 2) structure, which is formed by cooling below ∼250 K a surface prepared by Bi deposition of ∼0.25 ML coverage at 300 K where streaky half-order LEED spots appear. The c(4 × 2) structure has been determined by the tensor LEED analysis at 130 K and it is a substitutional structure. In the coadsorption, we found a c(6 × 4) structure, which has been determined by the tensor LEED analysis. It is very similar to the previously determined structure of the c(6 × 4) formed by coadsorption of Mg and Bi, and embedded MnBi₄ clusters are arranged in the top Cu layer instead of MgBi₄. Large lateral displacements of Bi atoms in the c(6 × 4)-(Mn + Bi) suggest that the Mn atoms undergo the size-enhancement caused by their large magnetic moment.     

Germanium growth on Br-terminated Si(1 0 0)

The consequences of Ge deposition on Br-terminated Si(1 0 0) were studied with scanning tunneling microscopy at ambient temperature after annealing at 650 K. One monolayer of Br was sufficient to prevent the formation of Ge huts beyond the critical thickness of 3 ML. This is possible because Br acts as a surfactant whose presence lowered the diffusivity of Ge adatoms. Hindered mobility was manifest at low coverage through the formation of short Ge chains. Further deposition resulted in the extension and connection of the Ge chains and gave rise to the buildup of incomplete layers. The deposition of 7 ML of Ge resulted in a rough surface characterized by irregularly shaped clusters. A short 800 K anneal desorbed the Br and allowed Ge atoms to reorganize into the more energetically favorable “hut” structures produced by conventional Ge overlayer growth on Si(1 0 0).     

Method of lines with boundary elements for 1‐D transient diffusion‐reaction problems

Time‐dependent differential equations can be solved using the concept of method of lines (MOL) together with the boundary element (BE) representation for the spatial linear part of the equation. The BE method alleviates the need for spatial discretization and casts the problem in an integral format. Hence errors associated with the numerical approximation of the spatial derivatives are totally eliminated. An element level local cubic approximation is used for the variable at each time step to facilitate the time marching and the nonlinear terms are represented in a semi‐implicit manner by a local linearization at each time step. The accuracy of the method has been illustrated on a number of test problems of engineering significance. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

A nilpotent Roth theorem

Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L ²-norm for any u, v∈L ^∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T _-n A∩S ^{- n} A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L ²(X) for all u, v∈L ^∞(X) if and only if T×S is ergodic on X×X and the group generated by T ^-1 S, T ^-2 S ²,..., T ^-c S ^c acts ergodically on X. Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001     

On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Tagging of the Magnetization with the Transition Zones of 360° Rotations Generated by a Tandem of Two Adiabatic DANTE Inversion Sequences

A new technique is presented for generating myocardial tagging using the signal intensity minima of the transition zones between the bands of 0° and 360° rotations, induced by a tandem of two adiabatic delays alternating with nutations for tailored excitation (DANTE) inversion sequences. With this approach, the underlying matrix corresponds to magnetization that has experienced 0° or 360° rotations. The DANTE sequences were implemented from adiabatic parent pulses for insensitivity of the underlying matrix to B₁ inhomogeneity. The performance of the proposed tagging technique is demonstrated theoretically with computer simulations and experimentally on phantom and on the canine heart, using a surface coil for both RF transmission and signal reception. The simulations and the experimental data demonstrated uniform grid contrast and sharp tagging profiles over a twofold variation of the B₁ field magnitude.     

A novel and efficient synthesis of porphine

meso-Tetra(n-hexyloxycarbonyl)porphyrin was found to be converted into porphine, the mother compound of porphyrins, in a 77% yield when heated in aqueous sulfuric acid at 180 °C over 30 min under an inert atmosphere. The observation demonstrates that the substituted porphyrin serves as a novel and useful precursor for porphine.     

A modified predictor–corrector scheme for the two-dimensional sine-Gordon equation

A three-time level finite-difference scheme based on a fourth order in time and second order in space approximation has been proposed for the numerical solution of the nonlinear two-dimensional sine-Gordon equation. The method, which is analysed for local truncation error and stability, leads to the solution of a nonlinear system. To avoid solving it, a predictor–corrector scheme using as predictor a second-order explicit scheme is proposed. The procedure of the corrector has been modified by considering as known the already evaluated corrected values instead of the predictor ones. This modified scheme has been tested on the line and circular ring soliton and the numerical experiments have proved that there is an improvement in the accuracy over the standard predictor–corrector implementation. This research was co-funded by E.U. (75%) and by the Greek Government (25%).