Quantitative Methods for the Characterization of Complex Surface Structures

Attempting to model the processes resulting in complex pattern formation and small-scale roughness of surfaces and to compare with experimental measurements calls for numerical methods which allow a quantitative characterization being as complete as possible. New methods incorporating wavelets and stochastic approaches based on the theory of Markov processes allow a stepwise characterization of increasing completeness and unambiguousness. In this paper we demonstrate the underlying numerical approaches taking electropolished and laser-jet etched surfaces for demonstration.     

On Polyhedral Projection and Parametric Programming

This paper brings together two fundamental topics: polyhedral projection and parametric linear programming. First, it is shown that, given a parametric linear program (PLP), a polyhedron exists whose projection provides the solution to the PLP. Second, the converse is tackled and it is shown how to formulate a PLP whose solution is the projection of an appropriately defined polyhedron described as the intersection of a finite number of halfspaces. The input to one operation can be converted to an input of the other operation and the resulting output can be converted back to the desired form in polynomial time—this implies that algorithms for computing projections or methods for solving parametric linear programs can be applied to either problem class. E.C. Kerrigan’s research was supported in part by the Royal Academy of Engineering, UK.     

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.     

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.     

Analysis of the transition from normal modes to local modes in a system of two harmonically coupled Morse oscillators

Summary The system consisting of two Morse oscillators coupled via either a potential or a kinetic quadratic term is considered. The corresponding classical equations of motion have been numerically integrated and the initial conditions have been systematically analyzed in the regime of low total excitation energy of the system. Particular attention was paid to the full characterization of an intermediate type of motion, herein called transition mode, which appears at total energy values in between those typical of normal modes and those where local and normal modes coexist. A previously proposed perturbative approach (Jaffé C, Brumer P (1980) J Chem Phys 73:5646) is reanalyzed and compared with the results of numerical experiments, with the purpose of lending further support to the existence of transition modes.     

Some Remarks about the FM-partners of <Emphasis Type="Italic">K</Emphasis>3 Surfaces with Picard Numbers 1 and 2

In this paper we describe some results about K3 surfaces with Picard number 1 and 2. In particular, we give a new simple proof of a theorem due to Oguiso which shows that, given an integer N, there is a K3 surface with Picard number 2 and at least N non-isomorphic FM-partners. We describe also the Mukai vectors of the moduli spaces associated to the FM-partners of K3 surfaces with Picard number 1.     

A method for solving problems on the limit equilibrium of reinforced shells of revolution

Rigid-plastic reinforced shells of revolution with a piecewise linear condition of plasticity are considered. It is shown that, in solving problems on their limit equilibrium, the application of linearized yield surfaces or the approximation of derivatives by finite differences restricts the set of possible solutions. In this paper, an asymptotic method for solving the problems by constructing a convergent sequence of solutions is offered. Each of these solutions is constructed numerically, and to approximate the derivatives, special finite differences coordinated with suppositions of the theory of thin shells are used. A feature of this method is that, with piecewise smooth yield surfaces, it is not necessary to determine a sequence of various plastic states, because the approximating yield surfaces are constructed during solution of the problem. Shells of revolution with positive and negative Gaussian curvatures and compound constructions of shells with various structures of reinforcement are examined. It is shown that the junction boundaries of rigid and plastic regions and the sequence of realization of plastic hinges greatly depend on the accuracy of approximation of the surfaces. With these approximations tending to the true yield surface, the sizes of the rigid regions decrease, and the range of structural and geometrical parameters of the shells grows when the yield state is reached through out their span. It is noted that, for closed constructions of shells reinforced only with spiral fibers at placement angles less that 55°, all possible mechanisms of plastic flow correspond to the direction of operating forces, whereas for other reinforcement structures, mechanisms of plastic flow with the opposite direction of velocities are possible. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 613–632, September–October, 2008.