A Posteriori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain

We present a posteriori error estimates for a recently developed atomistic/continuum coupling method, the Consistent Energy-Based QC Coupling method. The error estimate of the deformation gradient combines a residual estimate and an a posteriori stability analysis. The residual is decomposed into the residual due to the approximation of the stored energy and that due to the approximation of the external force, and are bounded in negative Sobolev norms. In addition, the error estimate of the total energy using the error estimate of the deformation gradient is also presented. Finally, numerical experiments are provided to illustrate our analysis

Plasmonic Light Trapping in an Ultrathin Photovoltaic Layer with Film-Coupled Metamaterial Structures

A film-coupled metamaterial structure is numerically investigated for enhancing the light absorption in an ultrathin photovoltaic layer of crystalline gallium arsenide (GaAs). The top subwavelength concave grating and the bottom metallic film could not only effectively trap light with the help of wave interference and magnetic resonance effects excited above the bandgap, but also practically serve as electrical contacts for photon-generated charge collection. The energy absorbed by the active layer is greatly enhanced in the film-coupled metamaterial structure, resulting in significant enhancement on the short-circuit current density by three times over a free-standing GaAs layer at the same thickness. The results would facilitate the development of next-generation ultrathin solar cells with lower cost and higher efficiency

Curvilinear Base Points, Local Complete Intersection and Kozsul Syzygies in Biprojective Spaces

We prove analogs of results of Cox/Schenck on the structure of certain ideals in the bigraded polynomial ring k[s,u;t,v].Comment: 12 page

Castelnuovo-Mumford Regularity in Biprojective Spaces

We define the concept of regularity for bigraded modules and bigraded polynomial ring. In this setting we prove analogs of some of the classical results on $m$-regularity for graded modules over polynomial algebras.Comment: 17 Pages, 2 figure

Shelf Space Fees and Inter-Brand Competition

When in-store display influences consumer choices, shelf space allocation can be strategically used by retailers to extract payments from manufacturers. The paper finds that manufacturers with more popular brands have higher willingness-to-pay for the premium shelf spaces of supermarkets. Shelf space fees soften inter-brand competition and result in higher sale-weighted average retail price as well as inter-brand price differences. The fees increase the industry profit but lower the upstream profit. Both the aggregate consumer surplus and social welfare are negatively affected. This paper suggests that even when the fees do not drive small manufacturers out of retail stores, they might still be anti-competitive.Antitrust, In-store display, Shelf space fee, Retail market, Slotting allowance

Slotting Allowances and Retailer Market Power

This paper uses a bilateral oligopoly model to study the slotting allowances in retailing industries. There are two symmetric manufacturers competing in the upstream market. In the downstream, there are a large retailer with considerable market share, and many small retailers with insignificant market shares. Suppose that only the large retailer is able to require slotting allowances. The retailers engage in price competition with spatial differentiation. The model suggests that the large retailer uses slotting allowances to capitalize its market power. By requiring slotting fees, the large retailer can raise the wholesale prices faced by the competing small retailers, and therefore lower their profit margins and market shares. The large retailer, on the contrary, achieves greater profit margins and market share. The lump sum part of the slotting fees is wholly bore by the manufacturers. But the slotting fees that are linear to the sales are actually bore by the competing small retailers and their customers. In this sense, requiring slotting allowance is an exclusionary strategy of the large retailer.Exclusionary strategy, Market power, Slotting allowance