Local Isometric immersions of pseudo-spherical surfaces and evolution equations

The class of differential equations describing pseudo-spherical surfaces, first introduced by Chern and Tenenblat [3], is characterized by the property that to each solution of a differential equation, within the class, there corresponds a 2-dimensional Riemannian metric of curvature equal to $-1$. The class of differential equations describing pseudo-spherical surfaces carries close ties to the property of complete integrability, as manifested by the existence of infinite hierarchies of conservation laws and associated linear problems. As such, it contains many important known examples of integrable equations, like the sine-Gordon, Liouville and KdV equations. It also gives rise to many new families of integrable equations. The question we address in this paper concerns the local isometric immersion of pseudo-spherical surfaces in ${\bf E}^{3}$ from the perspective of the differential equations that give rise to the metrics. Indeed, a classical theorem in the differential geometry of surfaces states that any pseudo-spherical surface can be locally isometrically immersed in ${\bf E}^{3}$. In the case of the sine-Gordon equation, one can derive an expression for the second fundamental form of the immersion that depends only on a jet of finite order of the solution of the pde. A natural question is to know if this remarkable property extends to equations other than the sine-Gordon equation within the class of differential equations describing pseudo-spherical surfaces. In an earlier paper [11], we have shown that this property fails to hold for all other second order equations, except for those belonging to a very special class of evolution equations. In the present paper, we consider a class of evolution equations for $u(x,t)$ of order $k\geq 3$ describing pseudo-spherical surfaces. We show that whenever an isometric immersion in ${\bf E}^3$ exists, depending on a jet of finite order of $u$, then the coefficients of the second fundamental forms are functions of the independent variables $x$ and $t$ only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and Applications, pp.N

CURSO DIÁRIO E SAZONAL DO POTENCIAL HÍDRICO FOLIAR DE MOGNO EM SISTEMAAGROFLORESTAL1

Este trabalho objetivou avaliar o curso diário e sazonal do potencial hídrico foliar de mogno (Swietenia macrophylla King) (Meliaceae) em sistema agroflorestal (SAF). O experimento foi realizado em árvores de S. macrophylla plantadas num sistema agroflorestal instalado no Campo Experimental da Embrapa Amazônia Ocidental, Manaus, AM. Avaliou-se o potencial hídrico foliar (Ψf) dos cursos diário e sazonal nos anos 2004 e 2005, por meio da utilização de bomba de pressão tipo Scholander. Os resultados indicaram que os valores do Ψf de S. macrophylla, de modo geral, foram superiores no início da manhã e no final da tarde, com redução acentuada ao meio-dia, e que, em relação à sazonalidade de precipitação, as menores taxas foram reportadas para a época menos chuvosa, variando de -26 bar em 2004 para -31bar em 2005. Verificou-se que o potencial hídrico de Swietenia macrophylla em sistema agroflorestal sofreu reduções significativas em razão dos baixos índices pluviométricos entre junho e outubro de 2005

NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

Xenarthrans – anteaters, sloths, and armadillos – have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with 24 domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, ten anteaters, and six sloths. Our dataset includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data-paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the south of the USA, Mexico, and Caribbean countries at the northern portion of the Neotropics, to its austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n=5,941), and Cyclopes sp. has the fewest (n=240). The armadillo species with the most data is Dasypus novemcinctus (n=11,588), and the least recorded for Calyptophractus retusus (n=33). With regards to sloth species, Bradypus variegatus has the most records (n=962), and Bradypus pygmaeus has the fewest (n=12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other datasets of Neotropical Series which will become available very soon (i.e. Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans dataset

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Volume I. Introduction to DUNE

The preponderance of matter over antimatter in the early universe, the dynamics of the supernovae that produced the heavy elements necessary for life, and whether protons eventually decay—these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our universe, its current state, and its eventual fate. The Deep Underground Neutrino Experiment (DUNE) is an international world-class experiment dedicated to addressing these questions as it searches for leptonic charge-parity symmetry violation, stands ready to capture supernova neutrino bursts, and seeks to observe nucleon decay as a signature of a grand unified theory underlying the standard model. The DUNE far detector technical design report (TDR) describes the DUNE physics program and the technical designs of the single- and dual-phase DUNE liquid argon TPC far detector modules. This TDR is intended to justify the technical choices for the far detector that flow down from the high-level physics goals through requirements at all levels of the Project. Volume I contains an executive summary that introduces the DUNE science program, the far detector and the strategy for its modular designs, and the organization and management of the Project. The remainder of Volume I provides more detail on the science program that drives the choice of detector technologies and on the technologies themselves. It also introduces the designs for the DUNE near detector and the DUNE computing model, for which DUNE is planning design reports. Volume II of this TDR describes DUNE\u27s physics program in detail. Volume III describes the technical coordination required for the far detector design, construction, installation, and integration, and its organizational structure. Volume IV describes the single-phase far detector technology. A planned Volume V will describe the dual-phase technology

Deep Underground Neutrino Experiment (DUNE), far detector technical design report, volume III: DUNE far detector technical coordination

The preponderance of matter over antimatter in the early universe, the dynamics of the supernovae that produced the heavy elements necessary for life, and whether protons eventually decay—these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our universe, its current state, and its eventual fate. The Deep Underground Neutrino Experiment (DUNE) is an international world-class experiment dedicated to addressing these questions as it searches for leptonic charge-parity symmetry violation, stands ready to capture supernova neutrino bursts, and seeks to observe nucleon decay as a signature of a grand unified theory underlying the standard model. The DUNE far detector technical design report (TDR) describes the DUNE physics program and the technical designs of the single- and dual-phase DUNE liquid argon TPC far detector modules. Volume III of this TDR describes how the activities required to design, construct, fabricate, install, and commission the DUNE far detector modules are organized and managed. This volume details the organizational structures that will carry out and/or oversee the planned far detector activities safely, successfully, on time, and on budget. It presents overviews of the facilities, supporting infrastructure, and detectors for context, and it outlines the project-related functions and methodologies used by the DUNE technical coordination organization, focusing on the areas of integration engineering, technical reviews, quality assurance and control, and safety oversight. Because of its more advanced stage of development, functional examples presented in this volume focus primarily on the single-phase (SP) detector module