Caustic graphene plasmons with Kelvin angle

A century-long argument made by Lord Kelvin that all swimming objects have an effective Mach number of 3, corresponding to the Kelvin angle of 19.5 degree for ship waves, has been recently challenged with the conclusion that the Kelvin angle should gradually transit to the Mach angle as the ship velocity increases. Here we show that a similar phenomenon can happen for graphene plasmons. By analyzing the caustic wave pattern of graphene plasmons stimulated by a swift charged particle moving uniformly above graphene, we show that at low velocities of the charged particle, the caustics of graphene plasmons form the Kelvin angle. At large velocities of the particle, the caustics disappear and the effective semi-angle of the wave pattern approaches the Mach angle. Our study introduces caustic wave theory to the field of graphene plasmonics, and reveals a novel physical picture of graphene plasmon excitation during electron energy-loss spectroscopy measurement.Comment: 15 pages, 4 figure

Strategic Remanufacturing Decision in a Supply Chain with an External Local Remanufacturer

This paper develops a model for remanufacturing decisions in a two-stage supply chain with one manufacturer, one retailer and one external local remanufacturer, who collects used products and then reproduces them into a new one if the manufacturer does not join in remanufacturing process. This paper is different from most of the extant studies about remanufacturing because they consider decisions of firms rather than supply chains. We mainly focus on the remanufacturing strategy of the manufacturer when there is a local remanufacturer. We derive the equilibrium results for all players and do some comparative studies under different cases. We find that product substitutability can invert the effect of manufacturer’s extension decision on the retailer’s profit. We also consider the effect of channel structure by comparing the decentralized channel with the centralized channel. We find that the manufacturer has a higher incentive to extend its product line in the centralized channel than the decentralized channel; and the competition can strengthen its motivation to extend the line