Universal Bounds in Even-Spin CFTs

We prove using invariance under the modular $S$- and $ST$-transformations that every unitary two-dimensional conformal field theory (CFT) of only even-spin operators (with no extended chiral algebra and with central charges $c,\tilde{c}>1$) contains a primary operator with dimension $\Delta_1$ satisfying $0 < \Delta_1 < (c+\tilde{c})/24 + 0.09280...$ After deriving both analytical and numerical bounds, we discuss how to extend our methods to bound higher conformal dimensions before deriving lower and upper bounds on the number of primary operators in a given energy range. Using the AdS$_3$/CFT$_2$ dictionary, the bound on $\Delta_1$ proves the lightest massive excitation in appropriate theories of 3D matter and gravity with cosmological constant $\Lambda < 0$ can be no heavier than $1/(8G_N)+O(\sqrt{-\Lambda})$; the bounds on the number operators are related via AdS/CFT to the entropy of states in the dual gravitational theory. In the flat-space approximation, the limiting mass is exactly that of the lightest BTZ black hole.Comment: arXiv admin note: text overlap with arXiv:0902.2790 by other authors; author note: this work is an extension of arXiv:0902.2790, please refer to it for additional details..new version has corrected typos and reference

Bounds on Operator Dimensions in 2D Conformal Field Theories

We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $\Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $\Delta_1$: $\Delta_2 \leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $\Delta_3$, and present a method for deriving bounds on $\Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $\Delta_n \leq \frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the gravitational implications of these results.Comment: Corrected typos; revised arguments (adding detail) for clarity, results unchange

UNIVERSAL CONSTRAINTS ON 2D CFTS AND 3D GRAVITY

We study constraints imposed on a general unitary two-dimensional conformal field theory by modular invariance. We begin with a review of previous bounds on the conformal dimension Delta1 of the lowest primary operator assuming unitarity, a discrete spectrum, modular invariance, cL, cR \u3e 1, and no extended chiral algebra. We then obtain bounds on the conformal dimensions Delta2, Delta3 using no additional assumptions. We also show that in order to find a bound for Delta4 or higher Deltan, we need to assume a larger minimum value for ctot that grows logarithmically with n. We next extend the previous results to remove the requirement that our two-dimensional conformal field theories have no extended chiral algebra. We then show that modular invariance also implies an upper bound on the total number of states of positive energy less than ctot=24 (or equivalently, states of conformal dimension between ctot=24 and ctot=12), in terms of the number of negative energy states. Finally, we consider the case where the CFT has a gravitational dual and investigate the gravitational interpretation of our results. Using the AdS3/CFT2 correspondence, we obtain an upper bound on the lightest few massive excitations (both with and without the constraint of no chiral primary operators) in a theory of 3D matter and gravity with Lambda \u3c 0. We show our results are consistent with facts and expectations about the spectrum of BTZ black holes in 2+1 gravity. We then discuss the upper and lower bounds on number of states and primary operators in the dual gravitational theory, focusing on the case of AdS3 pure gravity

Stardust Entry Reconstruction

An overview of the reconstruction analyses performed for the Stardust capsule entry is described. The results indicate that the actual entry was very close to the pre-entry predictions. The capsule landed 8.1 km north-northwest of the desired target at Utah Test and Training Range. Analyses of infrared video footage and radar range data (obtained from tracking stations) during the descent show that drogue parachute deployment was 4.8 s later than the pre-entry prediction, while main parachute deployment was 19.3 s earlier than the pre-set timer indicating that main deployment was actually triggered by the backup baroswitch. Reconstruction of a best estimated trajectory revealed that the aerodynamic drag experienced by the capsule during hypersonic flight was within 1% of pre-entry predications. Observations of the heatshield support the pre-entry estimates of small hypersonic angles of attack, since there was very little, if any, charring of the shoulder region or the aftbody. Through this investigation, an overall assertion can be made that all the data gathered from the Stardust capsule entry were consistent with flight performance close to nominal pre-entry predictions. Consequently, the design principles and methodologies utilized for the flight dynamics, aerodynamics, and aerothermodynamics analyses have been corroborated

Analysis of Factors Affecting Farmers’ Willingness to Adopt Switchgrass Production

In the United States, biomass is the largest source of renewable energy accounting for over 3 percent of the energy consumed domestically and is currently the only source for liquid, renewable, transportation fuels. Continued development of biomass as a renewable energy source is being driven in large part by the Energy Independence and Security Act of 2007, which mandates that by 2022 at least 36 billion gallons of fuel ethanol be produced, with at least 16 billion gallons being derived from cellulose, hemi-cellulose, or lignin. However, the market for cellulosic biofuels is still under development. As such, little is known about producer response to feedstock prices paid for dedicated energy crops. While there have been some studies done on factors that determine farmers’ willingness to produce switchgrass, these have been very regional in nature. This study will provide information regarding potential switchgrass adoption by agricultural producers in twelve southeastern states. The objectives of this research are 1) to determine the likelihood of farmers growing switchgrass as a biomass feedstock and the acres they would be willing to devote to switchgrass production and 2) to evaluate some of the factors that are likely to influence these decisions, including the price of switchgrass.Switchgrass, Farmer Adoption, Crop Production/Industries, Research and Development/Tech Change/Emerging Technologies, Resource /Energy Economics and Policy, Q12, Q16,

What is the Priestley–Taylor wet-surface evaporation parameter? Testing four hypotheses

This study compares four different hypotheses regarding the nature of the Priestley–Taylor parameter α. They are as follows: α is a universal constant. The Bowen ratio (H/LE, where H is the sensible heat flux, and LE is the latent heat flux) for equilibrium (i.e., saturated air column near the surface) evaporation is a constant times the Bowen ratio at minimal advection (Andreas et al., 2013). Minimal advection over a wet surface corresponds to a particular relative humidity value. α is a constant fraction of the difference from the minimum value of 1 to the maximum value of α proposed by Priestley and Taylor (1972). Formulas for α are developed for the last three hypotheses. Weather, radiation, and surface energy flux data from 171 FLUXNET eddy covariance stations were used. The condition LEref=LEp \u3e0.90 was taken as the criterion for nearly saturated conditions (where LEref is the reference, and LEp is the apparent potential evaporation rate from the equation by Penman, 1948). Daily and monthly average data from the sites were obtained. All formulations for α include one model parameter which is optimized such that the root mean square error of the target variable was minimized. For each model, separate optimizations were done for predictions of the target variables α, wet-surface evaporation (α multiplied by equilibrium evaporation rate) and actual evaporation (the latter using a highly successful version of the complementary relationship of evaporation). Overall, the second and fourth hypotheses received the best support from the data

Reconstruction of the Genesis Entry

An overview of the reconstruction analyses performed for the Genesis capsule entry is described. The results indicate that the actual entry prior to the drogue deployment failure was very close to the pre-entry predictions. The capsule landed 8.3 km south of the desired target at Utah Test and Training Range. Analysis on infrared video footage (obtained from the tracking stations) during the descent estimated the onset of the capsule tumble at Mach 0.9. Frequency analysis on the infrared video data indicates that the aerodynamics generated for the Genesis capsule reasonably predicted the drag and static stability. Observations of the heatshield support the pre-entry simulation estimates of a small hypersonic angles-of-attack, since there is very little, if any, charring of the shoulder region or the aftbody. Through this investigation, an overall assertion can be made that all the data gathered from the Genesis entry is consistent with flight performance that was close to the nominal preentry prediction. Consequently, the design principles and methodologies utilized for the flight dynamics, aerodynamics, and aerothermodynamics analyses have been corroborated