An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $\Theta(n)$ such tilings exist.Comment: In proceedings of ISAAC 201

Experimental application of sum rules for electron energy loss magnetic chiral dichroism

We present a derivation of the orbital and spin sum rules for magnetic circular dichroic spectra measured by electron energy loss spectroscopy in a transmission electron microscope. These sum rules are obtained from the differential cross section calculated for symmetric positions in the diffraction pattern. Orbital and spin magnetic moments are expressed explicitly in terms of experimental spectra and dynamical diffraction coefficients. We estimate the ratio of spin to orbital magnetic moments and discuss first experimental results for the Fe L_{2,3} edge.Comment: 11 pages, 2 figure

Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation

A nonlinear description of the interaction of charged particles penetrating a solid has become of basic importance in the interpretation of a variety of physical phenomena. Here we develop a many-body theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in an interacting free electron gas. Explicit expressions for these quantities are obtained either within the random-phase approximation (RPA) or with full inclusion of short-range exchange and correlation effects. The Z^3 correction to the energy loss of ions is evaluated beyond RPA, in the limit of low velocities.Comment: 5 pages, 2 figures To appear in Phys. Rev.

Energy-loss magnetic chiral dichroism (EMCD): Magnetic chiral dichroism in the electron microscope

A new technique called energy-loss magnetic chiral dichroism (EMCD) has recently been developed [P. Schattschneider, et al. Nature 441, 486 (2006)] to measure magnetic circular dichroism in the transmission electron microscope (TEM) with a spatial resolution of 10 nm. This novel technique is the TEM counterpart of x-ray magnetic circular dichroism, which is widely used for the characterization of magnetic materials with synchrotron radiation. In this paper we describe several experimental methods that can be used to measure the EMCD signal [P. Schattschneider, et al. Nature 441, 486 (2006); C. Hébert, et al. Ultramicroscopy 108(3), 277 (2008); B. Warot-Fonrose, et al. Ultramicroscopy 108(5), 393 (2008); L. Calmels, et al. Phys. Rev. B 76, 060409 (2007); P. van Aken, et al. Microsc. Microanal. 13(3), 426 (2007)] and give a review of the recent improvements of this new investigation tool. The dependence of the EMCD on several experimental conditions (such as thickness, relative orientation of beam and sample, collection and convergence angle) is investigated in the transition metals iron, cobalt, and nickel. Different scattering geometries are illustrated; their advantages and disadvantages are detailed, together with current limitations. The next realistic perspectives of this technique consist of measuring atomic specific magnetic moments, using suitable spin and orbital sum rules, [L. Calmels, et al. Phys. Rev. B 76, 060409 (2007); J. Rusz, et al. Phys. Rev. B 76, 060408 (2007)] with a resolution down to 2 to 3 n

Oxygen K-edge in vanadium oxides: simulations and experiments

Band-structure (BS) calculations of the density of states (DOS) using the full potential augmented plane waves code WIEN97 were performed on the four single-valence vanadium oxides VO, V2O3, VO2 and V2O5. The DOS are discussed with respect to the distortions of the VO6 octahedra, the oxidation states of vanadium and the orbital hybridisations of oxygen atoms. The simulated oxygen K-edge fine structures (ELNES) calculated with the TELNES program were compared with experimental results obtained by electron energy-loss spectrometry (EELS), showing good agreement. We show that changes in the fine structures of the investigated vanadium oxides mainly result from changes in the O-p DOS and not from the shift of the DOS according to a rigid band model