On Kähler manifolds with positive orthogonal bisectional curvature

For any irreducible Kähler manifold which admits positive orthogonal bisectional curvature and C₁>0, if this positivity condition is preserved under the flow, then the underlying manifold is biholomorphic to CPn.     

Suitable-portfolio investors,nondominated frontier sensitivity,and the effect of multiple objectives on standard portfolio selection

In standard portfolio theory, an investor is typically taken as having one stochastic objective, to maximize the random variable of portfolio return. But in this paper, we focus on investors whose purpose is to build, more broadly, a “suitable portfolio” taking additional concerns into account. Such investors would have additional stochastic and deterministic objectives that might include liquidity, dividends, number of securities in a portfolio, social responsibility, and so forth. To accommodate such investors, we develop a multiple criteria portfolio selection formulation, corroborate its appropriateness by examining the sensitivity of the nondominated frontier to various factors, and observe the conversion of the nondominated frontier to a nondominated surface. Furthermore, multiple criteria enable us to provide an explanation as to why the “market portfolio,” so often found deep below the nondominated frontier, is roughly where one would expect it to be with multiple criteria. After commenting on solvability issues, the paper concludes with the idea that what is the “modern portfolio theory” of today might well be interpreted as a projection onto two-space of a real multiple criteria portfolio selection problem from higher dimensional space. M. Hirschberger: Research conducted while a Visiting Scholar at the Department of Banking and Finance, Terry College of Business, University of Georgia, October 2003–March 2004.     

Shape cycle of Ga clusters on GaAs during coalescence growth

GaAs(1 0 0) was heated above its decomposition temperature of 585 °C bringing it into a phase separation regime where the thermodynamic favoured state is liquid Ga clusters on the surface. Varying the annealing times and temperatures provided an overview of the clustering at all stages from transitioning ripening at lower temperatures to coalescence at higher temperatures. We observed a shape cycle between round and rectangular shaped clusters during the growth. This cycle is driven by subcluster etching where pits are formed under clusters during the growth due to preferential loss of As through the liquid Ga cluster. The newly observed shape cycle is compared to a shape cycle observed previously in In on InP illustrating that shape cycles are a common feature of the decomposition of Group III-V semiconductors.     

The magnetic map of NiMn alloy thin films on Co(0 0 1) and Co(1 1 1)

Following the experimental work of Groudeva-Zotova et al. [S. Groudeva-Zotova, D. Elefant, R. Kaltofen, D. Tietjen, J. Thomas, V. Hoffmann, C.M. Schneider, J. Magn. Magn. Mater. 263 (2003) 57] where the magnetic and structural characteristics of a bi-layer NiMn-Co exchange biasing systems was investigated, density functional calculations with generalized gradient corrections were performed on (Mn_0.5Ni_0.5)_n ordered alloy on Co(0 0 1) and one Mn_1−xNi_x monolayer on Co(1 1 1). For the Mn_0.5Ni_0.5 monolayer on Co(0 0 1), magnetic moments per surface atom of 0.65 μ_B and 3.76 μ_B were obtained for Ni and Mn, respectively. Those magnetic moments are aligned parallel to the total moment of Co(0 0 1). A complex behavior of the Mn moment in dependence of the thickness “n” is obtained for (Mn_0.5Ni_0.5)_n on Co(0 0 1). Investigations on Mn_1−xNi_x monolayer on Co(1 1 1) have shown that the crystallographic orientation does not modify significantly neither the magnetic moments of Mn and Ni atoms nor their ferromagnetic coupling with the Co(1 1 1) substrate, except for x = 0.66. For x = 0.66 the Mn sub-lattice presents an antiferromagnetic coupling leading to a quenching of the Ni magnetic moment.     

The calculation of the surface energy of high-index surfaces in metals at zero temperature

We used the molecular dynamics simulation with interatomic potentials of the embedded atom method to calculate the high-index surface energies of the surfaces containing the 〈0 0 1〉 axis or 〈−1 1 0〉 axis in f.c.c. metal Al, Cu and Ni at zero temperature. We generalized an empirical formula based on structural unit model for high-index surfaces and present some new formulas that can be used to estimate the surface energy and structural feature of high-index surfaces very well. The results show that the closest surfaces have the lowest surface energy and the surface energies of the closest (1 1 1) surface and the next closest (1 1 0), (1 0 0) surfaces are the extremum on the curve of surface energy versus orientation angle. We also calculated the b.c.c. metal Fe and obtained a similar result. The difference is that in the b.c.c. metal the surface energies of the closest (1 1 0) surface and the next closest (1 0 0), (1 1 2) surfaces are the extremum on the curve of surface energy versus orientation angle. The results of theoretical simulation and the empirical formula consist well with the experiment data.     

Structure and mobility on amorphous silicon surfaces

The structure and dynamics of amorphous surfaces are poorly understood. The present work develops methods employing classical molecular dynamics (MD) simulations to elucidate these phenomena on amorphous silicon. Careful relaxation of the initial ensemble and taking account of exchange with the bulk yield surface diffusion coefficients in good agreement with experiment. Randomly oriented dimer pairs dominate the surface structure. Diffusion proceeds by several pathways, which all differ in basic character from those typically observed on crystalline silicon. The primary pathways involve single atoms and dimer pairs, which typically move only one or two atomic diameters before reincorporating into the surface. Frequent vertical migration takes place between the first two atomic layers.     

Computational study of low energy ion surface hyperchanneling

Classical ion trajectory simulations using the scattering and recoiling imaging code (SARIC) have been applied to study the low energy ion surface hyperchanneling phenomenon. It was found that the ion-surface interaction geometry, projectile type, surface chemisorbed hydrogen, and phonon amplitudes had a profound effect on the scattered ion trajectories. It is possible to determine the surface Debye temperature through analysis of the scattering yields and angular distributions. The simulations will find application in delineation of classical ion trajectories for specific as well as generic ion surface interactions.