Non-rigidity of spherical inversive distance circle packings

We give a counterexample of Bowers-Stephenson's conjecture in the spherical case: spherical inversive distance circle packings are not determined by their inversive distances.Comment: 6 pages, one pictur

Hyperbolic ends with particles and grafting on singular surfaces

We prove that any 3-dimensional hyperbolic end with particles (cone singularities along infinite curves of anglesless than \pi) admits a unique foliation by constant Gauss curvature surfaces. Using a form of duality between hyperbolic ends with particles and convex globally hyperbolic maximal (GHM) de Sitter spacetime with particles, it follows that any convex GHM de Sitter spacetime with particles also admits a unique foliation by constant Gauss curvature surfaces. We prove that the grafting map from the product of Teichmüller space with the space of measured laminations to the space of complex projective structures is a homeomorphism for surfaces with cone singularities of angles less than \pi, as well as an analogue when grafting is replaced by “smooth grafting”

VPI-7: The First Zincosilicate Molecular Sieve Containing Three-membered T-Atom Rings

VPI-7: the first microporous zincosilicate to contain 3-membered rings (3MR) is reported

Minimal surfaces and particles in 3-manifolds

We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichm\"uller theory. In the hyperbolic settings both questions have positive answers for a certain subset of the quasi-Fuchsian manifolds: those containing a closed surface with principal curvatures at most 1. We show that this subset is parameterized by an open domain of the cotangent bundle of Teichm\"uller space. These results are extended to ``quasi-Fuchsian'' manifolds with conical singularities along infinite lines, known in the physics literature as ``massive, spin-less particles''. Things work better for globally hyperbolic anti-de Sitter manifolds: the parameterization by the cotangent of Teichm\"uller space works for all manifolds. There is another description of this moduli space as the product two copies of Teichm\"uller space due to Mess. Using the maximal surface description, we propose a new parameterization by two copies of Teichm\"uller space, alternative to that of Mess, and extend all the results to manifolds with conical singularities along time-like lines. Similar results are obtained for de Sitter or Minkowski manifolds. Finally, for all four settings, we show that the symplectic form on the moduli space of 3-manifolds that comes from parameterization by the cotangent bundle of Teichm\"uller space is the same as the 3-dimensional gravity one.Comment: 53 pages, no figure. v2: typos corrected and refs adde

Estimating the impact of climate change on crop yields: The importance of non-linear temperature effects

There has been an active debate whether global warming will result in a net gain or net loss for United States agriculture. With mounting evidence that climate is warming, we show that such warming will have substantial impacts on agricultural yields by the end of the century: yields of three major crops in the United States are predicted to decrease by 60 to 79% under the most rapid warming scenario. We use a 55-year panel of crop yields in the United States and pair it with a unique fine-scale weather data set that incorporates the whole distribution of temperatures between the minimum and maximum within each day and across all days in the growing season. The key contribution of our study is in identifying a highly non-linear and asymmetric relationship between temperature and yields. Yields increase in temperature until about 29° C for corn and soybeans and 33° C for cotton, but temperatures above these thresholds quickly become very harmful, and the slope of the decline above the optimum is significantly steeper than the incline below it. Previous studies average temperatures over a season, month, or day and thereby dilute this highly non-linear relationship. We use encompassing tests to compare our model with others in the literature and find its out-of-sample forecasts are significantly better. The stability of the estimated relationship across regions, crops, and time suggests it may be transferable to other crops and countries

Identifying Supply and Demand Elasticities of Agricultural Commodities: Implications for the US Ethanol Mandate

We present a new framework to identify demand and supply elasticities of agricultural commodities using yield shocks - deviations from a time trend of output per area, which are predominantly caused by weather fluctuations. Demand is identified using current-period shocks that give rise to exogenous shifts in supply. Supply is identified using past shocks, which affect expected future prices through inventory accretion or depletion. We use our estimated elasticities to evaluate the impact of ethanol subsidies and mandates on world food commodity prices, quantities, and food consumers' surplus. The current US ethanol mandate requires that about 5 percent of world caloric production from corn, wheat, rice, and soybeans be used for ethanol generation. As a result, world food prices are predicted to increase by about 30 percent and global consumer surplus from food consumption is predicted to decrease by 155 billion dollars annually. If a third of the biofuel calories are recycled as feed stock for livestock, the predicted price increase scales back to 20 percent. While commodity demand is extremely inelastic, price response is muted by a significant supply response that is obscured if futures prices are not instrumented. The resulting expansion of agricultural growing area potentially offsets the CO2 emission benefits from biofuels.

Collisions of particles in locally AdS spacetimes I. Local description and global examples

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities along a graph $\Gamma$. We impose physically relevant conditions on the cone singularities, e.g. positivity of mass (angle less than $2\pi$ on time-like singular segments). We construct examples of such manifolds, describe the cone singularities that can arise and the way they can interact (the local geometry near the vertices of $\Gamma$). We then adapt to this setting some notions like global hyperbolicity which are natural for Lorentz manifolds, and construct some examples of globally hyperbolic AdS manifolds with interacting particles.Comment: This is a rewritten version of the first part of arxiv:0905.1823. That preprint was too long and contained two types of results, so we sliced it in two. This is the first part. Some sections have been completely rewritten so as to be more readable, at the cost of slightly less general statements. Others parts have been notably improved to increase readabilit

New Luttinger liquid physics from photoemission on Li0.9_{0.9}Mo6_6O17_{17}

Temperature dependent high resolution photoemission spectra of quasi-1 dimensional Li$_{0.9}$Mo$_6$O$_{17}$ evince a strong renormalization of its Luttinger liquid density-of-states anomalous exponent. We trace this new effect to interacting charge neutral critical modes that emerge naturally from the two-band nature of the material. Li$_{0.9}$Mo$_6$O$_{17}$ is shown thereby to be a paradigm material that is capable of revealing new Luttinger physics.Comment: 4 pages, 3 figures. Accepted for publication by Phys. Rev. Let

The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry

Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider convex regions of hyperbolic three-space bounded by two properly embedded disks which meet at infinity along a Jordan curve in the ideal boundary. In this setting, it is natural to augment the notion of induced metric on the boundary of the convex set to include a gluing map at infinity which records how the asymptotic geometry of the two surfaces compares near points of the limiting Jordan curve. Restricting further to the case in which the induced metrics on the two bounding surfaces have constant curvature K 2 Π1; 0/ and the Jordan curve at infinity is a quasicircle, the gluing map is naturally a quasisymmetric homeomorphism of the circle. The main result is that for each value of K, every quasisymmetric map is achieved as the gluing map at infinity along some quasicircle. We also prove analogous results in the setting of three-dimensional anti-de Sitter geometry. Our results may be viewed as universal versions of the conjectures of Thurston and Mess about prescribing the induced metric on the boundary of the convex core of quasifuchsian hyperbolic manifolds and globally hyperbolic anti-de Sitter spacetimes

Estimating the Impact of Climate Change on Crop Yields: The Importance of Nonlinear Temperature Effects

The United States produces 41% of the world's corn and 38% of the world's soybeans, so any impact on US crop yields will have implications for world food supply. We pair a panel of county-level crop yields in the US with a fine-scale weather data set that incorporates the whole distribution of temperatures between the minimum and maximum within each day and across all days in the growing season. Yields increase in temperature until about 29C for corn, 30C for soybeans, and 32C for cotton, but temperatures above these thresholds become very harmful. The slope of the decline above the optimum is significantly steeper than the incline below it. The same nonlinear and asymmetric relationship is found whether we consider time series or cross-sectional variation in weather and yields. This suggests limited potential for adaptation within crop species because the latter includes farmers' adaptations to warmer climates and the former does not. Area-weighted average yields given current growing regions are predicted to decrease by 31-43% under the slowest warming scenario and 67-79% under the most rapid warming scenario by the end of the century.