Energy spectra and photoluminescence of fractional quantum Hall systems containing a valence-band hole

The energy spectrum of a two-dimensional electron gas (2DEG) interacting with a valence-band hole is studied in the high magnetic field limit as a function of the filling factor nu and the separation d between the electron and hole layers. For d smaller than the magnetic length lambda, the hole binds one or more electrons to form neutral (X) or charged (X-) excitons. The low-lying states can be understood in terms of Laughlin-like correlations among the constituent charged fermions (electrons and X-). For d comparable to lambda, the electron-hole interaction is not strong enough to bind a full electron, and fractionally charged excitons hQEn (bound states of a hole and one or more Laughlin quasielectrons, QE) are formed. The effect of these excitonic complexes on the photoluminescence spectrum is studied numerically for a wide range of values of nu and d.Comment: 15 pages, 5 figures, submitted to Phil.Mag.

Design sensitivity analysis and optimization of built-up structures

Developments during the course of the research in design sensitivity analysis and optimization of built-up structures, with both sizing and shape design variables, show clearly that a unified variational approach to design sensitivity analysis can yield derivatives of structural response with respect to design. Rigorous and practically computable results for structural components and built-up structures have been demonstrated and used to solve design optimization problems

On the chain length dependence of local correlations in polymer melts and a perturbation theory of symmetric polymer blends

The self-consistent field (SCF) theory of dense polymer liquids assumes that short-range correlations are almost independent of how monomers are connected into polymers. Some limits of this idea are explored in the context of a perturbation theory for mixtures of structurally identical polymer species, A and B, in which the AB pair interaction differs slightly from the AA and BB interaction, and the difference is controlled by a parameter alpha Expanding the free energy to O(\alpha) yields an excess free energy of the form alpha $z(N)\phi_{A}\phi_{B}$, in both lattice and continuum models, where z(N) is a measure of the number of inter-molecular near neighbors of each monomer in a one-component liquid. This quantity decreases slightly with increasing N because the self-concentration of monomers from the same chain is slightly higher for longer chains, creating a deeper correlation hole for longer chains. We analyze the resulting $N$-dependence, and predict that $z(N) = z^{\infty}[1 + \beta \bar{N}^{-1/2}]$, where $\bar{N}$ is an invariant degree of polymerization, and $\beta=(6/\pi)^{3/2}$. This and other predictions are confirmed by comparison to simulations. We also propose a way to estimate the effective interaction parameter appropriate for comparisons of simulation data to SCF theory and to coarse-grained theories of corrections to SCF theory, which is based on an extrapolation of coefficients in this perturbation theory to the limit $N \to \infty$. We show that a renormalized one-loop theory contains a quantitatively correct description of the $N$-dependence of local structure studied here.Comment: submitted to J. Chem. Phy

Design sensitivity analysis using EAL. Part 1: Conventional design parameters

A numerical implementation of design sensitivity analysis of builtup structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its database management system. The finite element code used in the implemenatation presented is the Engineering Analysis Language (EAL), which is based on a hybrid method of analysis. It was shown that design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate database. Conventional (sizing) design parameters such as cross-sectional area of beams or thickness of plates and plane elastic solid components are considered. Compliance, displacement, and stress functionals are considered as performance criteria. The method presented is being extended to implement shape design sensitivity analysis using a domain method and a design component method