Sequential Posted Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a take-it-or-leave-it offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i's, we prove that a constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be extracted.Comment: 29 pages, To appear in WINE 201

Analysis of the characteristics of DC nozzle arcs in air and guidance for the search of SF6 replacement gas

It is shown that the arc model based on laminar flow cannot predict satisfactorily the voltage of an air arc burning in a supersonic nozzle. The Prandtl mixing length model (PML) and a modified k-epsilon turbulence model (MKE) are used to introduce turbulence enhanced momentum and energy transport. Arc voltages predicted by these two turbulence models are in good agreement with experiments at the stagnation pressure (P 0) of 10 bar. The predicted arc voltages by MKE for P 0  =  13 bar and 7 bar are in better agreement with experiments than those predicted by PML. MKE is therefore a preferred turbulence model for an air nozzle arc. There are two peaks in ρC P of air at 4000 K and 7000 K due, respectively, to the dissociation of oxygen and that of nitrogen. These peaks produce corresponding peaks in turbulent thermal conductivity, which results in very broad radial temperature profile and a large arc radius. Thus, turbulence indirectly enhances axial enthalpy transport, which becomes the dominant energy transport process for the overall energy balance of the arc column at high currents. When the current reduces, turbulent thermal conduction gradually becomes dominant. The temperature dependence of ρC P has a decisive influence on the radial temperature profile of a turbulent arc, thus the thermal interruption capability of a gas. Comparison between ρC P for air and SF6 shows that ρC P for SF6 has peaks below 4000 K. This renders a distinctive arc core and a small arc radius for turbulent SF6, thus superior arc quenching capability. It is suggested, for the first time, that ρC P provides guidance for the search of a replacement switching gas for SF6

Modelling of turbulent sf6 switching arcs

The present work aims at a comparative study of the performance of relevant turbulence models in predicting the behaviour of SF6 switching arcs during the current zero period. Turbulence models studied include the Prandtl mixing length model, the standard k-ϵ model and its two variants, i.e.The Chen-Kim model and the RNG model. In order to demonstrate the effects of turbulence, a laminar flow case is also modelled. Based on the computational results, a detailed analysis of the physical mechanisms encompassed in each flow model is given to show the adequacy of each model in describing the rapidly varying arcing process during the current zero period. The computed values of the critical rate of rise of recovery voltage (RRRV) are subject to verification by experimental results covering a wide range of discharge conditions. The relative merits of the flow models are discussed

Z-transform-based FDTD analysis of perfectly conducting cylinder covered with unmagnetized plasma

In this paper, a novel and normalized Z-transform-based finite-difference time-domain (ZTFDTD) method is presented for simulating the interaction of the electromagnetic (EM) wave with unmagnetized plasma. The 2-D ZTFDTD formulations for unmagnetized plasma are derived. Using a simplified 2-D model for a perfectly conducting cylinder covered with unmagnetized plasma, the stealth effect of unmagnetized plasma is studied in different thicknesses of plasma, electron densities of plasma, EM wave frequencies, and plasma collision frequencies. Numerical results indicate that plasma stealth is effective in theory and reasonable selection for the plasma parameters can greatly enhance its effectiveness. © 2007 IEEE