Some upwinding techniques for finite element approximations of convection-diffusion equations

Summary A uniform framework for the study of upwinding schemes is developed. The standard finite element Galerkin discretization is chosen as the reference discretization, and differences between other discretization schemes and the reference are written as artificial diffusion terms. These artificial diffusion terms are spanned by a four dimensional space of element diffusion matrices. Three basis matrices are symmetric, rank one diffusion operators associated with the edges of the triangle; the fourth basis matrix is skew symmetric and is associated with a rotation by /2. While finite volume discretizations may be written as upwinded Galerkin methods, the converse does not appear to be true. Our approach is used to examine several upwinding schemes, including the streamline diffusion method, the box method, the Scharfetter-Gummel discretization, and a divergence-free scheme.The work of this author was supported by the Office of Naval Research under contract N00014-89J-1440The work of this author was supported through KWF-Landis/Gyr Grant 1496, AT & T Bell Laboratories, and Cray Research     

Cyclophane with eclipsed pyrene units enables construction of spin interfaces with chemical accuracy

Advanced functionality in molecular electronics and spintronics is orchestrated by exact molecular arrangements at metal surfaces, but the strategies for constructing such arrangements remain limited. Here, we report the synthesis and surface hybridization of a cyclophane that comprises two pyrene groups fastened together by two ferrocene pillars. Crystallographic structure analysis revealed pyrene planes separated by ∼352 pm and stacked in an eclipsed geometry that approximates the rare configuration of AA-stacked bilayer graphene. We deposited this cyclophane onto surfaces of Cu(111) and Co(111) at submonolayer coverage and studied the resulting hybrid entities with scanning tunnelling microscopy (STM). We found distinct characteristics of this cyclophane on each metal surface: on non-magnetic Cu(111), physisorption occurred and the two pyrene groups remained electronically coupled to each other; on ferromagnetic Co(111) nanoislands, chemisorption occurred and the two pyrene groups became electronically decoupled. Spin-polarized STM measurements revealed that the ferrocene groups had spin polarization opposite to that of the surrounding Co metal, while the pyrene stack had no spin polarization. Comparisons to the non-stacked analogue comprising only one pyrene group bolster our interpretation of the cyclophane''s STM features. The design strategy presented herein can be extended to realize versatile, three-dimensional platforms in single-molecule electronics and spintronics.

A chemical strategy for the bottom-up construction of 3D spin interfaces is presented. Scanning tunnelling microscopy reveals distinct electronic features of a cyclophane with precisely designed pi-stacking on ferromagnetic Co(111) nanoislands.     

Origin of the planar Hall effect in nanocrystalline Co60Fe20B20

An angle dependent analysis of the planar Hall effect (PHE) in nanocrystalline single-domain Co(60)Fe(20)B(20) thin films is reported. In a combined experimental and theoretical study we show that the transverse resistivity of the PHE is entirely driven by anisotropic magnetoresistance (AMR). Our results for Co(60)Fe(20)B(20) obtained from first principles theory in conjunction with a Boltzmann transport model take into account the nanocrystallinity and the presence of 20 at.?% boron. The ab initio AMR ratio of 0.12% agrees well with the experimental value of 0.22%. Furthermore, we experimentally demonstrate that the anomalous Hall effect contributes negligibly in the present case.     

Investigation of the icosahedral quasicrystal Al68Pd23Mn9 by LEED and STM

The surface of icosahedral Al₆₈Pd₂₃Mn₉ was investigated by Low Energy Electron Diffraction (LEED) and Scanning Tunneling Microscopy (STM). Fivefold symmetric LEED patterns of this three dimensional (3D) quasicrystal were analysed in terms of the Fourier transform of a Fibonacci pentagrid. High resolution STM images of this surface prove the quasicrystalline nature ofi-Al₆₈Pd₂₃Mn₉ both laterally and vertically. Atomically flat terraces with nm-sized fivefold symmetric objects like fivefold stars and pentagonal holes were observed in real space. A Fibonacci pentagrid connecting the pentagonal holes was found to have line separations, which are within experimental errors identical to those derived from LEED data. The terraces are separated by steps of two incommensurable heights, whose succession forms part of the Fibonacci sequence. Cutting a 6D lattice yields lateral separations and step heights in 3D space, which agree with the experimentally determined values.     

Metallic-type oscillatory interlayer exchange coupling across an epitaxial FeSi spacer

We study interlayer exchange coupling in epitaxial Fe/Fe(0.56)Si(0.44)/Fe trilayers. Iron-silicide spacers with high structural and compositional homogeneity for thicknesses up to 34 A are grown by coevaporation from two electron-beam sources. The coupling strength oscillates with spacer thickness for temperatures from 20 to 300 K with two antiferromagnetic maxima at 12 and 26 A, and it clearly increases with decreasing temperature down to 80 K. We conclude that the coupling across ordered Fe(1-x)Si(x) ( x approximately 0.5) is described by the conventional theory of interlayer coupling across metallic spacers.     

Eine Bemerkung über R-orientierte Kohomologietheorien

Ohne Zusammenfassung     

A note on the algebra P(n)*(P(n)) for the prime 2

Let P(n) denote the Brown-Peterson spectrum with coefficients in the invariant prime ideal I_n. In this note we compute the algebra P(n)*(P(n)) for the prime p=2 and observe that several results connected with the theories P(n)*(–) previously known for p>2 carry over to the case p=2.     

Realisierung formaler Gruppen durch Kohomologiefunktoren

To any multiplicative cohomology theory h with the property that complex line bundles are h-oriented corresponds a formal group law F(X,Y) over the ring h(pt) which describes the Euler class of a tensor product of line bundles by means of the Euler classes of its factors. We consider this formal group as an invariant of h and give sufficient conditions under which a morphism between formal groups of cohomology theories h,k can be extended in one and only one way to a transformation of theories hk. Some typical applications will be discussed.