New theory of the gamma-alpha phase transition in Ce: quadrupolar ordering

We present a theoretical model of the "isostructural" \gamma-\alpha phase transition in Ce which is based on quadrupolar interactions due to coupled charge density fluctuations of 4f electrons and of conduction electrons. Conduction electrons are treated in tight-binding approximation. The \gamma-\alpha transition is described as an orientational ordering of quadrupolar electronic densities in a Pa3 structure. The quadrupolar order of the conduction electron densities is complementary to the quadrupolar order of 4f electron densities. The inclusion of conduction electrons leads to an increase of the lattice contraction at the \gamma-\alpha transition in comparison to the sole effect of 4f electrons. We calculate the Bragg scattering law and suggest synchrotron radiation experiments in order to check the Pa3 structure. The theory is capable of accounting for transitions to phases of non-cubic symmetry, but it is not sufficient to describe the magnetic phenomena which we ascribe to the Kondo mechanism. We also present a microscopic derivation of multipolar interactions and discuss the crystal field of \gamma-Ce.Comment: 19 pages, 4 figures, full version to be published in Eur. Phys. J.

Parallelization of implicit finite difference schemes in computational fluid dynamics

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed

Crystal Structures of Polymerized Fullerides AC60, A=K, Rb, Cs and Alkali-mediated Interactions

Starting from a model of rigid interacting C60 polymer chains on an orthorhombic lattice, we study the mutual orientation of the chains and the stability of the crystalline structures Pmnn and I2/m. We take into account i) van der Waals interactions and electric quadrupole interactions between C60 monomers on different chains as well as ii) interactions of the monomers with the surrounding alkali atoms. The direct interactions i) always lead to an antiferrorotational structure Pmnn with alternate orientation of the C60 chains in planes (001). The interactions ii) with the alkalis consist of two parts: translation-rotation (TR) coupling where the orientations of the chains interact with displacements of the alkalis, and quadrupolar electronic polarizability (ep) coupling, where the electric quadrupoles on the C60 monomers interact with induced quadrupoles due to excited electronic d states of the alkalis. Both interactions ii) lead to an effective orientation-orientation interaction between the C60 chains and always favor the ferrorotational structure I2/m where C60 chains have a same orientation. The structures Pmnn for KC60 and I2/m for Rb- and CsC60 are the result of a competition between the direct interaction i) and the alkali-mediated interactions ii). In Rb- and CsC60 the latter are found to be dominant, the preponderant role being played by the quadrupolar electronic polarizability of the alkali ions.Comment: J.Chem.Phys., in press, 14 pages, 3 figures, 8 table

Inert states of spin-S systems

We present a simple but efficient geometrical method for determining the inert states of spin-S systems. It can be used if the system is described by a spin vector of a spin-S particle and its energy is invariant in spin rotations and phase changes. Our method is applicable to an arbitrary S and it is based on the representation of a pure spin state of a spin-S particle in terms of 2S points on the surface of a sphere. We use this method to find candidates for some of the ground states of spinor Bose-Einstein condensates.Comment: 4 pages, 2 figures, minor changes, references added, typos correcte

Induced polarization and electronic properties of carbon doped boron-nitride nanoribbons

The electronic properties of boron-nitride nanoribbons (BNNRs) doped with a line of carbon atoms are investigated by using density functional calculations. Three different configurations are possible: the carbon atoms may replace a line of boron or nitrogen atoms or a line of alternating B and N atoms which results in very different electronic properties. We found that: i) the NCB arrangement is strongly polarized with a large dipole moment having an unexpected direction, ii) the BCB and NCN arrangement are non-polar with zero dipole moment, iii) the doping by a carbon line reduces the band gap independent of the local arrangement of boron and nitrogen around the carbon line, iv) an electric field parallel to the carbon line polarizes the BN sheet and is found to be sensitive to the presence of carbon dopants, and v) the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital decreases linearly with increasing applied electric field directed parallel to the carbon line. We show that the polarization and energy gap of carbon doped BNNRs can be tuned by an electric field applied parallel along the carbon line.Comment: 11 pages, 6 figure