Should Optimal Designers Worry About Consideration?

Consideration set formation using non-compensatory screening rules is a vital component of real purchasing decisions with decades of experimental validation. Marketers have recently developed statistical methods that can estimate quantitative choice models that include consideration set formation via non-compensatory screening rules. But is capturing consideration within models of choice important for design? This paper reports on a simulation study of a vehicle portfolio design when households screen over vehicle body style built to explore the importance of capturing consideration rules for optimal designers. We generate synthetic market share data, fit a variety of discrete choice models to the data, and then optimize design decisions using the estimated models. Model predictive power, design "error", and profitability relative to ideal profits are compared as the amount of market data available increases. We find that even when estimated compensatory models provide relatively good predictive accuracy, they can lead to sub-optimal design decisions when the population uses consideration behavior; convergence of compensatory models to non-compensatory behavior is likely to require unrealistic amounts of data; and modeling heterogeneity in non-compensatory screening is more valuable than heterogeneity in compensatory trade-offs. This supports the claim that designers should carefully identify consideration behaviors before optimizing product portfolios. We also find that higher model predictive power does not necessarily imply better design decisions; that is, different model forms can provide "descriptive" rather than "predictive" information that is useful for design.Comment: 5 figures, 26 pages. In Press at ASME Journal of Mechanical Design (as of 3/17/15

Development of fine diameter mullite fiber

Results are presented of a program to develop and evaluate mullite fiber with a mean diameter under two microns. The two micron fiber is produced by a blowing process at room temperature from a low viscosity (10-25 poise) solution. The blown fiber was evaluated for dimensional stability in thermal cycling to 1371 C, and was equivalent to the 5 micron spun B and W mullite fiber. An additive study was conducted to evaluate substitutes for the boron. Three levels of chromium, lithium fluoride, and magnesium were added to the standard composition in place of boron and the fiber produced was evaluated for chemical and dimensional stability in thermal cycling to 1371 C. The magnesium was the most chemically stable, but the chrome additive imparted the best dimensional stability

Single and Many Particle Correlation Functions and Uniform Phase Bases for Strongly Correlated Systems

The need for suitable many or infinite fermion correlation functions to describe some low dimensional strongly correlated systems is discussed. This is linked to the need for a correlated basis, in which the ground state may be postive definite, and in which single particle correlations may suffice. A particular trial basis is proposed, and applied to a certain quasi-1D model. The model is a strip of the 2D square lattice wrapped around a cylinder, and is related to the ladder geometries, but with periodic instead of open boundary conditions along the edges. Analysis involves a novel mean-field approach and exact diagonalisation. The model has a paramagnetic region and a Nagaoka ferromagnetic region. The proposed basis is well suited to the model, and single particle correlations in it have power law decay for the paramagnet, where the charge motion is qualitatively hard core bosonic. The mean field also leads to a BCS-type model with single particle long range order.Comment: 23 pages, in plain tex, 12 Postscript figures included. Accepted for publication in J.Physics : Condensed Matte

Spin density wave in oxypnictide superconductors in a three-band model

The spin density wave and its temperature dependence in oxypnictide are studied in a three-band model. The spin susceptibilities with various interactions are calculated in the random phase approximation(PPA). It is found that the spin susceptibility peaks around the M point show a spin density wave(SDW) with momentum (0, $\pi$) and a clear stripe-like spin configuration. The intra-band Coulomb repulsion enhances remarkably the SDW but the Hund's coupling weakens it. It is shown that a new resonance appears at higher temperatures at the $\Gamma$ point indicating the formation of a paramagnetic phase. There is a clear transition from the SDW phase to the paramagnetic phase.Comment: 4 pages,8 figure

PAMELA: An Open-Source Software Package for Calculating Nonlocal Exact Exchange Effects on Electron Gases in Core-Shell Nanowires

We present a new pseudospectral approach for incorporating many-body, nonlocal exact exchange interactions to understand the formation of electron gases in core-shell nanowires. Our approach is efficiently implemented in the open-source software package PAMELA (Pseudospectral Analysis Method with Exchange & Local Approximations) that can calculate electronic energies, densities, wavefunctions, and band-bending diagrams within a self-consistent Schrodinger-Poisson formalism. The implementation of both local and nonlocal electronic effects using pseudospectral methods is key to PAMELA's efficiency, resulting in significantly reduced computational effort compared to finite-element methods. In contrast to the new nonlocal exchange formalism implemented in this work, we find that the simple, conventional Schrodinger-Poisson approaches commonly used in the literature (1) considerably overestimate the number of occupied electron levels, (2) overdelocalize electrons in nanowires, and (3) significantly underestimate the relative energy separation between electronic subbands. In addition, we perform several calculations in the high-doping regime that show a critical tunneling depth exists in these nanosystems where tunneling from the core-shell interface to the nanowire edge becomes the dominant mechanism of electron gas formation. Finally, in order to present a general-purpose set of tools that both experimentalists and theorists can easily use to predict electron gas formation in core-shell nanowires, we document and provide our efficient and user-friendly PAMELA source code that is freely available at http://alum.mit.edu/www/usagiComment: Accepted by AIP Advance

On l-adic representations for a space of noncongruence cuspforms

This paper is concerned with a compatible family of 4-dimensional \ell-adic representations \rho_{\ell} of G_\Q:=\Gal(\bar \Q/\Q) attached to the space of weight 3 cuspforms S_3 (\Gamma) on a noncongruence subgroup \Gamma \subset \SL. For this representation we prove that: 1.)It is automorphic: the L-function L(s, \rho_{\ell}^{\vee}) agrees with the L-function for an automorphic form for \text{GL}_4(\mathbb A_{\Q}), where \rho_{\ell}^{\vee} is the dual of \rho_{\ell}. 2.) For each prime p \ge 5 there is a basis h_p = \{h_p ^+, h_p ^- \} of S_3 (\Gamma) whose expansion coefficients satisfy 3-term Atkin and Swinnerton-Dyer (ASD) relations, relative to the q-expansion coefficients of a newform f of level 432. The structure of this basis depends on the class of p modulo 12. The key point is that the representation $\rho_{\ell}$ admits a quaternion multiplication structure in the sense of a recent work of Atkin, Li, Liu and Long.Comment: Second revised version. To appear: Proceedings of the American Mathematical Societ

Studies of molecular properties of polymeric materials

Aerospace environment effects (high energy electrons, thermal cycling, atomic oxygen, and aircraft fluids) on polymeric and composite materials considered for structural use in spacecraft and advanced aircraft are examined. These materials include Mylar, Ultem, and Kapton. In addition to providing information on the behavior of the materials, attempts are made to relate the measurements to the molecular processes occurring in the material. A summary and overview of the technical aspects are given along with a list of the papers that resulted from the studies. The actual papers are included in the appendices and a glossary of technical terms and definitions is included in the front matter

Solving the Dirac equation with nonlocal potential by Imaginary Time Step method

The Imaginary Time Step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schr\"odinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schr\"odinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus $^{16}$O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained