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We establish a criterion for the flatness of a principal circle bundle in terms of the intrinsically harmonic form problem. It states that the flatness is equivalent to the intrinsic harmonicity of a certain natural associated form.

Advanced materials and their applications have become a key field of research, and it looks like this trend is not going to change soon. For that reason, the need for systematic and efficient methods for organizing knowledge in the field and conduct computational or experimental investigations is stronger than ever. In this work, we present a basic implementation of MAMBO - an ontology for molecular materials and their applications in real-life scenarios. The development of MAMBO has been guided by the needs of the research community involved in the development of novel materials with functional properties, with particular attention to the nanoscale. MAMBO aims at extending the current work in the field, while retaining a modular nature in order to allow straightforward extension of concepts and relations to neighboring domains. Our work is expected to enable the systematic integration of computational and experimental data in specific domains of interest (nanomaterials, molecular materials, organic an polymeric materials, supramolecular and bio-organic systems, etc.). Moreover, MAMBO is developed with a strong focus on the applications of data-driven frameworks for the design of novel materials with tailored characteristics.

Recent advances in computational and experimental technologies applied to the design and development of novel materials have brought out the need for systematic, rational and efficient methods for the organization of knowledge in the field. In this work, we present the initial steps carried out in the development of MAMBO - an ontology focused on the organization of concepts and knowledge in the field of materials based on molecules and targeted to applications. Our approach is guided by the needs of the communities involved in the development of novel molecular materials with functional properties at the nanoscale. As such, MAMBO aims at bridging the gaps of ongoing efforts in the development of ontologies in the materials science domain. By extending current work in the field, the modular nature of MAMBO also allows straightforward extension of concepts and relations to neighboring domains. Our work is expected to enable the systematic integration of computational and experimental data in specific domains of interest (nanomaterials, molecular materials, organic an polymeric materials, supramolecular and bio-organic systems, etc.). Moreover, MAMBO can be applied to the development of data-driven integrated predictive frameworks for the design of novel materials with tailored functional properties., Comment: To appear in the proceedings of the DORIC-MM workshop, 2021

Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological relevance, the properties of molecular materials are related to the link between molecular structure and phenomena occurring across a wide set of spatial scales, from the nanoscale to the macroscale. Here, we describe an approach for predicting the properties of molecular aggregates based on multiscale simulations and machine learning.

Two-dimensional and layered materials, such as graphene, have emerged in recent years for their potential use in several applications in technology, for example in electronics, bioelectronics, optoelectronics and related fields. Phosphorene, which can be considered as an analogous of graphene made of phosphorus atoms, is a relatively new two-dimensional system with peculiar structural, electronic, and mechanical properties. Despite the remarkable potential for applications, phosphorene suffers from severe limitations, hampering its use in practical uses. For example, phosphorene undergoes severe degradation phenomena in ordinary environments, leading to a very limited stability. Phosphorene is therefore very difficult to handle in real applications. In this paper, we briefly outline the concepts behind the application of predictive computational approaches to complex systems based on phosphorene, leading to the definition of practical strategies that can be applied to the development of stable, high-performance devices for electronics.

A computational approach for predictive simulations of the nanoscale morphology in the early steps of the formation of the interface between metals and organic molecular semiconductors is presented. Despite the relevance of the metal-molecule junction for the development of electronic applications, structural details at the interface are often difficult to assess. Our approach, based on the integration of density functional theory with methods for the simulation of growth dynamics, allows to unravel the structural details of the formation of gold aggregates onto molecular materials. Simulations are applied to investigations of the initial steps in the formation of gold clusters at the interface with prototypical p-type and n-type organic molecular semiconductors. Results show a striking correlation between the morphology of the metal-organic interface, the details of the molecular structure and the peculiar metal-molecule interaction, also highlighting the role of fabrication conditions.

In this article we collect results obtained by the authors jointly with other authors and we discuss old and new ideas. In particular we discuss singularities of the exponential map, completeness and homogeneity for Riemannian Hilbert quotient manifolds. We also extend a Theorem due to Nomizu and Ozeki to infinite dimensional Riemannian Hilbert manifolds.

In [15] Robert Osserman proved that the image of the Gauss map of a complete, non flat minimal surface in R^3 with finite total curvature miss at most 3 points. In this paper we prove that the Gauss map of such a minimal immersions omit at most 2 points. This is a sharp result since the Gauss map of the catenoid omits exactly two points. In fact we prove this result for a wider class of isometric immersions, that share the basic differential topological properties of the complete minimal surfaces of finite total curvature., Comment: 22 pages. Result about the missing points by the Gauss map of a wide class of complete parabolic surfaces in the 3 dimensional Euclidean space with finite total curvature and the Gauss map extending continuously to a compact Riemann surfaces including the minimal surfaces. If it is no flat then the Gauss map can not miss more than 2 points of the sphere

In this paper we will construct a Weierstrass type representation for minimal surfaces in 4-dimensional Lorentzian Damek-Ricci spaces and we give some examples of such surfaces., Comment: 10 pages

In this paper we will show the existence and uniqueness of the solution of the Bj\"orling problem for minimal surfaces in a 3-dimensional Lorentzian Lie group., Comment: 16 pages

We prove existence and uniqueness of the solution of the Bj\"orling problem for minimal surfaces in a three-dimensional Lie group., Comment: 10 pages

We investigate the problem of the stability of the number of conjugate or focal points (counted with multiplicity) along a semi-Riemannian geodesic $\gamma$. For a Riemannian or a non spacelike Lorentzian geodesic, such number is equal to the intersection number (Maslov index) of a continuous curve with a subvariety of codimension one of the Lagrangian Grassmannian of a symplectic space. Such intersection number is proven to be stable in a large variety of circumstances. In the general semi-Riemannian case, under suitable hypotheses this number is equal to an algebraic count of the multiplicities of the conjugate points, and it is related to the spectral properties of a non self-adjoint differential operator. This last relation gives a weak extension of the classical Morse Index Theorem in Riemannian and Lorentzian geometry. In this paper we reprove some results that were incorrectly stated by Helfer in a previous reference; in particular, a counterexample to one of Helfer's results, which is essential for the theory, is given. In the last part of the paper we discuss a general technique for the construction of examples and counterexamples in the index theory for semi-Riemannian metrics, in which some new phenomena appear., Comment: 58 pages, LaTeX2e, amsart class some references updated and minor changes in the abstract and in the Introduction in the replacement of Aug. 13th, 1999 Revised version of April 24th, 2000: added Remark 6.2.2, minor modifications in the Introduction