Nucleon and pion structure with lattice QCD simulations at physical value of the pion mass

We present results on the nucleon scalar, axial, and tensor charges as well as on the momentum fraction, and the helicity and transversity moments. The pion momentum fraction is also presented. The computation of these key observables is carried out using lattice QCD simulations at a physical value of the pion mass. The evaluation is based on gauge configurations generated with two degenerate sea quarks of twisted mass fermions with a clover term. We investigate excited states contributions with the nucleon quantum numbers by analyzing three sink-source time separations. We find that, for the scalar charge, excited states contribute significantly and to a less degree to the nucleon momentum fraction and helicity moment. Our result for the nucleon axial charge agrees with the experimental value. Furthermore, we predict a value of 1.027(62) in the MS¯¯¯¯¯ scheme at 2 GeV for the isovector nucleon tensor charge directly at the physical point. The pion momentum fraction is found to be ⟨x⟩π±u−d=0.214(15)(+12−9) in the MS¯¯¯¯¯ at 2 GeV.

An Urn Model for Cascading Failures on a Lattice

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

Multi-scale micro-structure generation strategy for up-scaling transport in clays

Clays and claystones are used as backfill and barrier materials in the design of waste repositories, because they act as hydraulic barriers and retain contaminants. Transport through such barriers occurs mainly by molecular diffusion. There is thus an interest to relate the diffusion properties of clays to their structural properties. In previous work, we have developed a concept for up-scaling pore-scale molecular diffusion coefficients using a grid-based model for the sample pore structure. Here we present an operational algorithm which can generate such model pore structures of polymineral materials. The obtained pore maps match the rock’s mineralogical components and its macroscopic properties such as porosity, grain and pore size distributions. Representative ensembles of grains in 2D or 3D are created by a lattice Monte Carlo (MC) method, which minimizes the interfacial energy of grains starting from an initial grain distribution. Pores are generated at grain boundaries and/or within grains. The method is general and allows to generate anisotropic structures with grains of approximately predetermined shapes, or with mixtures of different grain types. A specific focus of this study was on the simulation of clay-like materials. The generated clay pore maps were then used to derive upscaled effective diffusion coefficients for non-sorbing tracers using a homogenization technique. The large number of generated maps allowed to check the relations between micro-structural features of clays and their effective transport parameters, as is required to explain and extrapolate experimental diffusion results. As examples, we present a set of 2D and 3D simulations and investigated the effects of nanopores within particles (interlayer pores) and micropores between particles. Archie’s simple power law is followed in systems with only micropores. When nanopores are present, additional parameters are required; the data reveal that effective diffusion coefficients could be described by a sum of two power functions, related to the micro- and nanoporosity. We further used the model to investigate the relationships between particle orientation and effective transport properties of the sample.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.