Large NN expansion of Wilson loops in the Gross-Witten-Wadia matrix model

We study the large $N$ expansion of winding Wilson loops in the off-critical regime of the Gross-Witten-Wadia (GWW) unitary matrix model. These have been recently considered in arXiv:1705.06542 and computed by numerical methods. We present various analytical algorithms for the precise computation of both the perturbative and instanton corrections to the Wilson loops. In the gapped phase of the GWW model we present the genus five expansion of the one-cut resolvent that captures all winding loops. Then, as a complementary tool, we apply the Periwal-Shevitz orthogonal polynomial recursion to the GWW model coupled to suitable sources and show how it generates all higher genus corrections to any specific loop with given winding. The method is extended to the treatment of instanton effects including higher order $1/N$ corrections. Several explicit examples are fully worked out and a general formula for the next-to-leading correction at general winding is provided. For the simplest cases, our calculation checks exact results from the Schwinger-Dyson equations, but the presented tools have a wider range of applicability.Comment: 28 pages, 3 pdf figures. v2: minor additions, extended reference

Reactive immunization on complex networks

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks

An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion

We study the phase diagram of a minority game where three classes of agents are present. Two types of agents play a risk-loving game that we model by the standard Snowdrift Game. The behaviour of the third type of agents is coded by {\em indifference} w.r.t. the game at all: their dynamics is designed to account for risk-aversion as an innovative behavioral gambit. From this point of view, the choice of this solitary strategy is enhanced when innovation starts, while is depressed when it becomes the majority option. This implies that the payoff matrix of the game becomes dependent on the global awareness of the agents measured by the relevance of the population of the indifferent players. The resulting dynamics is non-trivial with different kinds of phase transition depending on a few model parameters. The phase diagram is studied on regular as well as complex networks

Zipf and Heaps laws from dependency structures in component systems

Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of components emerges from architectural and specific constraints in such systems. On the other hand, general regularities may unify different systems, such as the broadly studied Zipf and Heaps laws, respectively concerning the distribution of component frequencies and their number as a function of system size. Dependency structures (i.e., directed networks encoding the dependency relations between the components in a system) were proposed recently as a possible organizing principles underlying some of the regularities observed. However, the consequences of this assumption were explored only in binary component systems, where solely the presence or absence of components is considered, and multiple copies of the same component are not allowed. Here, we consider a simple model that generates, from a given ensemble of dependency structures, a statistical ensemble of sets of components, allowing for components to appear with any multiplicity. Our model is a minimal extension that is memoryless, and therefore accessible to analytical calculations. A mean-field analytical approach (analogous to the "Zipfian ensemble" in the linguistics literature) captures the relevant laws describing the component statistics as we show by comparison with numerical computations. In particular, we recover a power-law Zipf rank plot, with a set of core components, and a Heaps law displaying three consecutive regimes (linear, sub-linear and saturating) that we characterize quantitatively

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality

Modelling Sorption and Transport of Gases in Polymeric Membranes across Different Scales: A Review

Professor Giulio C. Sarti has provided outstanding contributions to the modelling of fluid sorption and transport in polymeric materials, with a special eye on industrial applications such as membrane separation, due to his Chemical Engineering background. He was the co-creator of innovative theories such as the Non-Equilibrium Theory for Glassy Polymers (NET-GP), a flexible tool to estimate the solubility of pure and mixed fluids in a wide range of polymers, and of the Standard Transport Model (STM) for estimating membrane permeability and selectivity. In this review, inspired by his rigorous and original approach to representing membrane fundamentals, we provide an overview of the most significant and up-to-date modeling tools available to estimate the main properties governing polymeric membranes in fluid separation, namely solubility and diffusivity. The paper is not meant to be comprehensive, but it focuses on those contributions that are most relevant or that show the potential to be relevant in the future. We do not restrict our view to the field of macroscopic modelling, which was the main playground of professor Sarti, but also devote our attention to Molecular and Multiscale Hierarchical Modeling. This work proposes a critical evaluation of the different approaches considered, along with their limitations and potentiality

Computational analysis of transport in three-dimensional heterogeneous materials: An OpenFOAM®-based simulation framework

© 2020, The Author(s). Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated approach to generate, study and upscale transport equations in random and periodic porous structures. The geometry generation is based on random algorithms or ballistic deposition. In particular, a new algorithm is proposed to generate random packings of ellipsoids with random orientation and tunable porosity and connectivity. The porous structure is then meshed using locally refined Cartesian-based or unstructured strategies. Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical theory of homogenisation for linear advection–diffusion–reaction operators. Existing simulation codes are extended with novel developments and integrated to produce a fully open-source simulation pipeline. A showcase of a few interesting three-dimensional applications of these computational approaches is then presented. Firstly, convergence properties and the transport and dispersion properties of a periodic arrangement of spheres are studied. Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials

Immunonutrition before esophagectomy: Impact on immune surveillance mechanisms

Preoperative oral immunonutrition was demonstrated to improve immune response and to decrease the infection rate in patients with cancer. This study aimed to assess how immunonutrition could influence the immune cell response in the mucosal microenvironment of esophageal adenocarcinoma. Therefore, A prospective cohort of consecutive patients undergoing esophagectomy for esophageal adenocarcinoma was enrolled. A subgroup of them was given preoperative oral immunonutrition with Oral Impact and was compared to those who received no preoperative supplementation. Mucosal samples from healthy esophagus were obtained at esophagectomy. Histology, immunohistochemistry, gene expression analysis, and cytofluorimetry were performed. Markers of activation of antigen-presenting cells (CD80, CD86, and HLA-I), innate immunity (TLR4 and MyD88), and cytotoxic lymphocyte infiltration and activation (CD8, CD38, CD69, and CD107) were measured. In all, 50 patients received preoperative Oral Impact and 129 patients received no nutritional support. CD80, CD86, MyD88, and CD69 messenger RNA expression was significantly increased in patients receiving immunonutrition compared to controls. In the subgroup of patients with stages I-II cancer, the rate of epithelial cells expressing CD80 and HLA-ABC was significantly higher in those receiving immunonutrition compared to controls as well as CD8+ CD28+ cell rate. Immunonutrition administration before surgery was significantly associated to increased degranulating CD8 and natural killer cells (CD107+) infiltrating the healthy esophageal mucosa. All the comparisons were adjusted for cancer stage and preoperative therapy. In conclusion, in healthy esophageal mucosa of patients undergoing esophagectomy, a 5-day course of immunonutrition enhances expression of antigen-presenting cells activity and increased CD8+ T cell activation and degranulating activity. Further studies are warranted to understand the clinical implication in terms of cancer recurrence

Spatially: Resolved heterogeneous dynamics in a strong colloidal gel

We re-examine the classical problem of irreversible colloid aggregation, showing that the application of Digital Fourier Imaging (DFI), a class of optical correlation methods that combine the power of light scattering and imaging, allows one to pick out novel useful evidence concerning the restructuring processes taking place in a strong colloidal gel. In particular, the spatially-resolved displacement fields provided by DFI strongly suggest that the temporally-intermittent local rearrangements taking place in the course of gel ageing are characterized by very long-ranged spatial correlations