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

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

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

Soil protist function varies with elevation in the Swiss Alps

Protists are abundant and play key trophic functions in soil. Documenting how their trophic contributions vary across large environmental gradients is essential to understand and predict how biogeochemical cycles will be impacted by global changes. Here, using amplicon sequencing of environmental DNA in open habitat soil from 161 locations spanning 2600 m of elevation in the Swiss Alps (from 400 to 3000 m), we found that, over the whole study area, soils are dominated by consumers, followed by parasites and phototrophs. In contrast, the proportion of these groups in local communities shows large variations in relation to elevation. While there is, on average, three times more consumers than parasites at low elevation (400–1000 m), this ratio increases to 12 at high elevation (2000–3000 m). This suggests that the decrease in protist host biomass and diversity toward mountains tops impact protist functional composition. Furthermore, the taxonomic composition of protists that infect animals was related to elevation while that of protists that infect plants or of protist consumers was related to soil pH. This study provides a first step to document and understand how soil protist functions vary along the elevational gradient

Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected], [email protected], [email protected]

PP/PP-HI/silica nanocomposites for HVDC cable insulation: Are silica clusters beneficial for space charge accumulation?

New potential High Voltage Direct Current (HVDC) cable insulation materials based on nanocomposites are developed in this study. The nanocomposites are produced by blending of polypropylene (PP), propylene-ethylene copolymer (PP–HI) and a modified fumed silica (A-silica) in a concentration of 1 and 2 wt %. The A-silica is successfully modified with (3-aminopropyl)triethoxysilane (APTES) via a solvent-free method, as proven by infrared spectroscopy, thermogravimetry and transmission electron microscope mapping. A-silica in the polymer matrix acts as a nucleating agent resulting in an increase of the crystallization temperature of the polymers and a smaller crystal size. Moreover, the silica addition modified the crystals morphology of the unfilled PP/PP-HI blend. The composite containing A-silica with 2 wt% contains bigger-size silica clusters than the composite filled with 1 wt%. The composite with the higher A-silica concentration shows lower space charge accumulation and a lower charge current value. Besides, much deeper traps and lower trap density are observed in the composite with 2 wt% A-silica addition compared to the one with a lower concentration. Surprisingly, the presence of silica clusters with dimensions of more than 200 nm exhibit a positive effect on reducing the space charge accumulation. However, the real cause of this improvement might be due to change of the electron distribution stemming from the amine-amine hydrogen bond formation, or the change of the chain mobility due to the presence of occluded polymer macromolecules constrained inside the high structure silica clusters. Both phenomena may lead to a higher energetic barrier of charge de-trapping, thus increasing the depth of the charge traps

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

Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.