A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Unoccupied electronic states of epitaxial iron layers on Cu(100)

Inverse photoemission spectra were taken for thin epitaxial iron films on Cu(100). For a film thickness of eight monolayers the observed electronic states are characteristic for a fcc(100) surface. Thed-bands of iron show a ferromagnetic exchange splitting of 1.1 eV, considerably smaller than the bulk value of 1.8 eV, which we observe for film thicknesses above 18 monolayers.     

Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum

We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a real eigenvalue crosses the imaginary axis. For a model we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a pitchfork bifurcation of equilibria and the nonlinear stability of the bifurcating equilibria, again with respect to spatially localized perturbations.     

Possible application of X-ray optical elements for reducing the spectral bandwidth of an X-ray SASE FEL

A new design for a single pass X-ray Self-Amplified Spontaneous Emission (SASE) FEL is proposed. The scheme consists of two undulators and an X-ray monochromator located between them. The first stage of the FEL amplifier operates in the SASE linear regime. After the exit of the first undulator the electron bunch is guided through a non-isochronous bypass and the X-ray beam enters the monochromator. The main function of the bypass is to suppress the modulation of the electron beam induced in the first undulator. This is possible because of the finite value of the natural energy spread in the beam. At the entrance to the second undulator the radiation power from the monochromator dominates significantly over the shot noise and the residual electron bunching. As a result the second stage of the FEL amplifier operates in the steady-state regime when the input signal bandwidth is small with respect to that of the FEL amplifier. Integral losses of the radiation power in the monochromator are relatively small because grazing incidence optics can be used. The proposed scheme is illustrated for the example of the 6 nm option SASE FEL at the TESLA Test Facility under construction at DESY. As shown in this paper the spectral bandwidth of such a two-stage SASE FEL (Δλ/λ 5 × 10⁻⁵) is close to the limit defined by the finite duration of the radiation pulse. The average brilliance is equal to 7 × 10²⁴ photons/(s × mrad² × mm² × 0.1% bandw.) which is by two orders of magnitude higher than the value which could be reached by the conventional SASE FEL. The monochromatization of the radiation is performed at a low level of radiation power (about 500 times less than the saturation level) which allows one to use conventional X-ray optical elements (grazing incidence grating and mirrors) for the monochromator design.     

Wavelength independence of Eu quantum yields

A quantitative comparison between the excitation and absorption spectra of Eu³⁺ in aqueous solution is given which leads to the conclusion that fluorescence quantum yields are independent of the excitation wavelength. Use is made therefore of the series of homologous lines ⁵D₃, ⁵D₂, ⁵D₁, ⁵D₀ → ⁷F₁.     

Analysis of the 3-dimensional electron distribution in silicon using directional Compton profile measurements

A method of reconstructing the electron momentum density (p), and its Fourier transform,B(t), from a series of directional Compton profiles is described. It is based on a double Fourier inversion technique and an expansion in lattice harmonic functions. The effect of random errors has been analysed, and the implications for the data collection discussed. We have used the reconstruction technique to obtain (p) andB(t) for silicon from six directional Compton profiles measured with 412 KeV gamma-radiation. The experimental result is in good agreement with earlier measurements and with available solid state theories. A recent Wannier function calculation for silicon using orthogonalised bond orbitals provides a useful tool for identifying the physical origins of the observed anisotropies. A comparison between the information presented in position and momentum space shows that the ease of interpretation depends upon the degree to which the various interactions give rise to localised features in each representation.