Modeling the Pollution of Pristine Gas in the Early Universe

We conduct a comprehensive theoretical and numerical investigation of the pollution of pristine gas in turbulent flows, designed to provide new tools for modeling the evolution of the first generation of stars. The properties of such Population III (Pop III) stars are thought to be very different than later generations, because cooling is dramatically different in gas with a metallicity below a critical value Z_c, which lies between ~10^-6 and 10^-3 solar value. Z_c is much smaller than the typical average metallicity, , and thus the mixing efficiency of the pristine gas in the interstellar medium plays a crucial role in the transition from Pop III to normal star formation. The small critical value, Z_c, corresponds to the far left tail of the probability distribution function (PDF) of the metallicity. Based on closure models for the PDF formulation of turbulent mixing, we derive equations for the fraction of gas, P, lying below Z_c, in compressible turbulence. Our simulation data shows that the evolution of the fraction P can be well approximated by a generalized self-convolution model, which predicts dP/dt = -n/tau_con P (1-P^(1/n)), where n is a measure of the locality of the PDF convolution and the timescale tau_con is determined by the rate at which turbulence stretches the pollutants. Using a suite of simulations with Mach numbers ranging from M = 0.9 to 6.2, we provide accurate fits to n and tau_con as a function of M, Z_c/, and the scale, L_p, at which pollutants are added to the flow. For P>0.9, mixing occurs only in the regions surrounding the pollutants, such that n=1. For smaller P, n is larger as mixing becomes more global. We show how the results can be used to construct one-zone models for the evolution of Pop III stars in a single high-redshift galaxy, as well as subgrid models for tracking the evolution of the first stars in large cosmological simulations.Comment: 37 pages, accepted by Ap

Insights from the Field: Forests for Water

This issue brief describes analyses by the World Resources Institute (WRI) in support of emerging payments for watershed services (PWS) programs in two major watersheds in Maine and North Carolina and insights gleaned from work in progress. The three pilot initiatives discussed represent different approaches to establishing PWS programs that protect forests and other green infrastructure elements. In the Neuse River Basin in North Carolina, WRI is working with partners to identify beneficiaries and their water-related dependencies. We learned that clear documentation of the risks that beneficiaries face from water pollution, drought, and watershed degradation will help jump-start their participation in emerging PWS programs. In the Sebago Lake Watershed in Maine, WRI is finalizing a methodology for "green-gray" analysis that will provide beneficiaries a way to identify cost-effective green infrastructure solutions to water infrastructure demands of the 21 st century. Green infrastructure comprises all natural, seminatural and artificial networks of multifunctional ecological systems within, around, and between urban areas at all spatial scales. We learned that, to convince public investment managers to invest in green rather than gray, it is important to make the financial and business case using the same basic methodologies that are used for calculating the costs and benefits of conventional gray approaches. WRI is also working to develop PWS programs that help the city of Raleigh meet streetscape, conservation development, tree conservation, storm water management, and water quality goals contained in its Unified Development Ordinance in a least cost manner. We learned that market-based solutions like PWS can play a large role in land-use planning processes and that these processes may represent a large untapped demand driver for PWS programs throughout the Sout

Efficient Relocation of Spectrum Incumbents

Changes in technologies and in consumer demands have made prior radio spectrum allocations far from efficient. To address this problem the FCC has recently reallocated spectrum for more flexible use in bands that are partially occupied by incumbent license holders. Often, it is necessary for the new license holder to relocate incumbents to make efficient use of the spectrum. Regulations structuring the negotiation between incumbent and new entrant can promote efficiency. In particular, giving the new entrant the right to move the incumbent with compensation can reduce negotiation costs and promote efficiency when there is private information about spectrum values but good public information about the cost of relocating the incumbent. We examine the experience of broadband PCS entrants in relocating microwave incumbents. We conclude with some remarks on how these ideas might be applied to digital television spectrum.Bargaining; Auctions; Spectrum Auctions; Telecommunications Policy

van der Waals dispersion power laws for cleavage, exfoliation and stretching in multi-scale, layered systems

Layered and nanotubular systems that are metallic or graphitic are known to exhibit unusual dispersive van der Waals (vdW) power laws under some circumstances. In this letter we investigate the vdW power laws of bulk and finite layered systems and their interactions with other layered systems and atoms in the electromagnetically non-retarded case. The investigation reveals substantial difference between `cleavage' and `exfoliation' of graphite and metals where cleavage obeys a $C_2 D^{-2}$ vdW power law while exfoliation obeys a $C_3 \log(D/D_0) D^{-3}$ law for graphitics and a $C_{5/2} D^{-5/2}$ law for layered metals. This leads to questions of relevance in the interpretation of experimental results for these systems which have previously assumed more trival differences. Furthermore we gather further insight into the effect of scale on the vdW power laws of systems that simultaneously exhibit macroscopic and nanoscopic dimensions. We show that, for metallic and graphitic layered systems, the known "unusual" power laws can be reduced to standard or near standard power laws when the effective scale of one or more dimension is changed. This allows better identification of the systems for which the commonly employed `sum of $C_6 D^{-6}$' type vdW methods might be valid such as layered bulk to layered bulk and layered bulk to atom