Ultrathin Fe film on Cu(0 0 1): Exchange splitting of image states from first principles

The theoretical investigation of the image states in front of an ultrathin iron film grown on copper has been performed by means of the embedding method and a recently developed procedure for the inclusion of the image potential tail in a first principle calculation. From the electronic response to an applied electric field, the image plane position has been evaluated. This also allows one to obtain useful information about the spin dependent screening properties of the system. Exchange splitting, effective mass, and lifetime of such surface states result in good agreement with recently performed two-photon photoemission experiments [see A.B. Schmidt, M. Pickel, M. Wiemhöfer, M. Donath, M. Weinelt, Phys. Rev. Lett. 95 (2005) 107402].     

Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Itô calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.     

在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.