Wodzicki Residue for Operators on Manifolds with Cylindrical Ends

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with cylindrical ends. The definition is based on the analysis of the associate zeta function. Using this approach, under suitable ellipticity assumptions, we also compute a two terms leading part of the Weyl formula for a positive selfadjoint operator belonging the mentioned class in the case m_1=m_2.Comment: 24 pages, picture changed, added references, corrected typo

The determination of the electron-phonon interaction from tunneling data in the two-band superconductor MgB2

We calculate the tunneling density of states (DOS) of MgB2 for different tunneling directions, by directly solving the real-axis, two-band Eliashberg equations (EE). Then we show that the numeric inversion of the standard single-band EE, if applied to the DOS of the two-band superconductor MgB2, may lead to wrong estimates of the strength of certain phonon branches (e.g. the E_2g) in the extracted electron-phonon spectral function alpha^(2)F(omega). The fine structures produced by the two-band interaction turn out to be clearly observable only for tunneling along the ab planes in high-quality single crystals. The results are compared to recent experimental data.Comment: 2 pages, 2 figures, proceedings of M2S-HTSC-VII conference, Rio de Janeiro (May 2003

TerrHum: an iPhone app for classifying forest humipedons.

The knowledge of a little number of specific terms is necessary to investigate and describe the forest topsoils: diagnostic components, diagnostic organic and organic-mineral horizons and the 17 series of humus horizons composing all the observed real forest not submerged topsoils. Diagnostic horizons are grouped in humus forms, which represent five humus systems. To become a good topsoil investigator is then only a question of field experience. No mean to do otherwise: you must go in the field with a blade and a good manual and put your hand in the soil. You have to make a hole and to observe on your knee a wall of the pit, from the top to the bottom, detecting all the characters that you find indicated in the manual. At the beginning you will be discouraged, things change from a site to another and never are exactly as in the manual. After few days of difficult survey, you will be able to know your soil even without doing a hole. Be patient and follow what it is indicated in the published first eight articles of Humusica (http://intra.tesaf.unipd.it/people/zanella/hmanual.html). On the poster, you find some examples of diagnostic properties of forest topsoils, and a dichotomy key of classification, you can copy paste and take with you in the field. An iPhone application (Terrhum) allows to bring in the field the necessary information for a fast classification of the topsoil

Bi-conformal vector fields and their applications

We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric \G to be scaled by different conformal factors. In particular, we study their infinitesimal version, called bi-conformal vector fields. We show the differential conditions characterizing them in terms of a "square root" of the metric, or equivalently of two complementary orthogonal projectors. Keeping these fixed, the set of bi-conformal vector fields is a Lie algebra which can be finite or infinite dimensional according to the dimensionality of the projectors. We determine (i) when an infinite-dimensional case is feasible and its properties, and (ii) a normal system for the generators in the finite-dimensional case. Its integrability conditions are also analyzed, which in particular provides the maximum number of linearly independent solutions. We identify the corresponding maximal spaces, and show a necessary geometric condition for a metric tensor to be a double-twisted product. More general ``breakable'' spaces are briefly considered. Many known symmetries are included, such as conformal Killing vectors, Kerr-Schild vector fields, kinematic self-similarity, causal symmetries, and rigid motions.Comment: Replaced version with some changes in the terminology and a new theorem. To appear in Classical and Quantum Gravit

Current Challenges and Opportunities in Microstructure-Related Properties of Advanced High-Strength Steels

This is a viewpoint paper on recent progress in the understanding of the microstructure–property relations of advanced high-strength steels (AHSS). These alloys constitute a class of high-strength, formable steels that are designed mainly as sheet products for the transportation sector. AHSS have often very complex and hierarchical microstructures consisting of ferrite, austenite, bainite, or martensite matrix or of duplex or even multiphase mixtures of these constituents, sometimes enriched with precipitates. This complexity makes it challenging to establish reliable and mechanism-based microstructure–property relationships. A number of excellent studies already exist about the different types of AHSS (such as dual-phase steels, complex phase steels, transformation-induced plasticity steels, twinning-induced plasticity steels, bainitic steels, quenching and partitioning steels, press hardening steels, etc.) and several overviews appeared in which their engineering features related to mechanical properties and forming were discussed. This article reviews recent progress in the understanding of microstructures and alloy design in this field, placing particular attention on the deformation and strain hardening mechanisms of Mn-containing steels that utilize complex dislocation substructures, nanoscale precipitation patterns, deformation-driven transformation, and twinning effects. Recent developments on microalloyed nanoprecipitation hardened and press hardening steels are also reviewed. Besides providing a critical discussion of their microstructures and properties, vital features such as their resistance to hydrogen embrittlement and damage formation are also evaluated. We also present latest progress in advanced characterization and modeling techniques applied to AHSS. Finally, emerging topics such as machine learning, through-process simulation, and additive manufacturing of AHSS are discussed. The aim of this viewpoint is to identify similarities in the deformation and damage mechanisms among these various types of advanced steels and to use these observations for their further development and maturation.</p

Spatially structured environmental filtering of collembolan traits in late successional salt marsh vegetation

Both the environment and the spatial configuration of habitat patches are important factors that shape community composition and affect species diversity patterns. Species have traits that allow them to respond to their environment. Our current knowledge on environment to species traits relationships is limited in spite of its potential importance for understanding community assembly and ecosystem function. The aim of our study was to examine the relative roles of environmental and spatial variables for the small-scale variation in Collembola (springtail) communities in a Dutch salt marsh. We used a trait-based approach in combination with spatial statistics and variance partitioning, between environmental and spatial variables, to examine the important ecological factors that drive community composition. Turnover of trait diversity across space was lower than for species diversity. Most of the variation in community composition was explained by small-scale spatial variation in topography, on a scale of 4-6 m, most likely because it determines the effect of inundation, which restricts where habitat generalists can persist. There were only small pure spatial effects on species and trait diversity, indicating that biotic interactions or dispersal limitation probably were less important for structuring the community at this scale. Our results suggest that for springtails, life form (i.e. whether they live in the soil or litter or on the surface/in vegetation) is an important and useful trait to understand community assembly. Hence, using traits in addition to species identity when analysing environment-organism relationships results in a better understanding of the factors affecting community composition

A Standardized Morpho-Functional Classification of the Planet’s Humipedons

It was time to take stock. We modified the humipedon classification key published in 2018 to make it easier and more practical. This morpho-functional taxonomy of the topsoil (humipedon) was only available in English; we also translated it into French and Italian. A standardized morphofunctional classification of humipedons (roughly the top 30–40 cm of soil: organic and organomineral surface horizons) would allow for a better understanding of the functioning of the soil ecosystem. This paper provides the founding principles of the classification of humipedon into humus systems and forms. With the recognition of a few diagnostic horizons, all humus systems can be determined. The humus forms that make up these humus systems are revealed by measuring the thicknesses of the diagnostic horizons. In the final part of the article, several figures represent the screenshots of a mobile phone or tablet application that allows for a fast recall of the diagnostic elements of the classification in the field. The article attempts to promote a standardized classification of humipedons for a global and shared management of soil at planet level

A standardized morpho-functional classification of the planet’s humipedons

It was time to take stock. We modified the humipedon classification key published in 2018 to make it easier and more practical. This morpho-functional taxonomy of the topsoil (humipedon) was only available in English; we also translated it into French and Italian. A standardized morphofunctional classification of humipedons (roughly the top 30–40 cm of soil: organic and organomineral surface horizons) would allow for a better understanding of the functioning of the soil ecosystem. This paper provides the founding principles of the classification of humipedon into humus systems and forms. With the recognition of a few diagnostic horizons, all humus systems can be determined. The humus forms that make up these humus systems are revealed by measuring the thicknesses of the diagnostic horizons. In the final part of the article, several figures represent the screenshots of a mobile phone or tablet application that allows for a fast recall of the diagnostic elements of the classification in the field. The article attempts to promote a standardized classification of humipedons for a global and shared management of soil at planet level