Sound speed measurements in liquid oxygen-liquid nitrogen mixtures

The sound speed in liquid oxygen (LOX), liquid nitrogen (LN2), and five LOX-LN2 mixtures was measured by an ultrasonic pulse-echo technique at temperatures in the vicinity of -195.8C, the boiling point of N2 at a pressure of I atm. Under these conditions, the measurements yield the following relationship between sound speed in meters per second and LN2 content M in mole percent: c = 1009.05-1.8275M+0.0026507 M squared. The second speeds of 1009.05 m/sec plus or minus 0.25 percent for pure LOX and 852.8 m/sec plus or minus 0.32 percent for pure LN2 are compared with those reported by past investigators. Measurement of sound speed should prove an effective means for monitoring the contamination of LOX by Ln2

Invariant measures for Burgers equation with stochastic forcing

In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts all other solutions with the same forcing. This is done by studying the so-called one-sided minimizers. We also give a detailed description of the structure and regularity properties for the stationary solutions. In particular, we prove, under some non-degeneracy conditions on the forcing, that almost surely there is a unique main shock and a unique global minimizer for the stationary solutions. Furthermore the global minimizer is a hyperbolic trajectory of the underlying system of characteristics.Comment: 84 pages, published version, abstract added in migratio

On the uniqueness of Gibbs states in the Pirogov-Sinai theory

We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume state is exponentially fast.Comment: 12 pages, Plain TeX, to appear in Communications in Mathematical Physic

Breaking the silence of the 500-year-old smiling garden of everlasting flowers: The En Tibi book herbarium

We reveal the enigmatic origin of one of the earliest surviving botanical collections. The 16th-century Italian En Tibi herbarium is a large, luxurious book with c. 500 dried plants, made in the Renaissance scholarly circles that developed botany as a distinct discipline. Its Latin inscription, translated as “Here for you a smiling garden of everlasting flowers”, suggests that this herbarium was a gift for a patron of the emerging botanical science. We follow an integrative approach that includes a botanical similarity estimation of the En Tibi with contemporary herbaria (Aldrovandi, Cesalpino, “Cibo”, Merini, Estense) and analysis of the book’s watermark, paper, binding, handwriting, Latin inscription and the morphology and DNA of hairs mounted under specimens. Rejecting the previous origin hypothesis (Ferrara, 1542–1544), we show that the En Tibi was made in Bologna around 1558. We attribute the En Tibi herbarium to Francesco Petrollini, a neglected 16th-century botanist, to whom also belongs, as clarified herein, the controversial “Erbario Cibo” kept in Rome. The En Tibi was probably a work on commission for Petrollini, who provided the plant material for the book. Other people were apparently involved in the compilation and offering of this precious gift to a yet unknown person, possibly the Habsburg Emperor Ferdinand I. The En Tibi herbarium is a Renaissance masterpiece of art and science, representing the quest for truth in herbal medicine and botany. Our multidisciplinary approach can serve as a guideline for deciphering other anonymous herbaria, kept safely “hidden” in treasure rooms of universities, libraries and museums

The relative importance of ecological drivers of arbuscularmycorrhizal fungal distribution varies with taxon phylogeneticresolution

The phylogenetic depth at which arbuscular mycorrhizal (AM) fungi harbor a coherent eco-logical niche is unknown, which has consequences for operational taxonomic unit (OTU)delineation from sequence data and the study of their biogeography. We tested how changes in AM fungi community composition across habitats (beta diver-sity) vary with OTU phylogenetic resolution. We inferred exact sequence variants (ESVs) toresolve phylotypes at resolutions finer than provided by traditional sequence clustering andanalyzed beta diversity profiles up to order-level sequence clusters. At the ESV level, we detected the environmental predictors revealed with traditional OTUsor at higher genetic distances. However, the correlation between environmental predictorsand community turnover steeply increased at a genetic distance ofc. 0.03 substitutions persite. Furthermore, we observed a turnover of either closely or distantly related taxa (respec-tively at or above 0.03 substitutions per site) along different environmental gradients. This study suggests that different axes of AM fungal ecological niche are conserved at dif-ferent phylogenetic depths. Delineating AM fungal phylotypes using DNA sequences shouldscreen different phylogenetic resolutions to better elucidate the factors that shape communi-ties and predict the fate of AM symbioses in a changing environment

A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page