Thermodynamics and criticality of supersymmetric spin chains with long-range interactions

We study the thermodynamics and critical behavior of su($m|n$) supersymmetric spin chains of Haldane-Shastry type with a chemical potential term. We obtain a closed-form expression for the partition function and deduce a description of the spectrum in terms of the supersymmetric version of Haldane's motifs, which we apply to obtain an analytic expression for the free energy per site in the thermodynamic limit. By studying the low-temperature behavior of the free energy, we characterize the critical behavior of the chains with $1\le m,n\le2$, determining the critical regions and the corresponding central charge. We also show that in the su($2|1$), su($1|2$) and su($2|2$) chains the bosonic or fermionic densities can undergo first-order (discontinuous) phase transitions at $T=0$, in contrast with the previously studied su(2) case.Comment: 44 pages, 10 figures. Minor corrections, references adde

Key Production Parameters to Obtain Transparent Nanocellular PMMA

Transparent nanocellular polymethylmethacrylate (PMMA) with relative density around 0.4 is produced for the first time by using the gas dissolution foaming technique. The processing conditions and the typical characteristics of the cellular structure needed to manufacture this novel material are discovered. It is proved that low saturation temperatures (−32 °C) combined with high saturation pressures (6, 10, 20 MPa) allow increasing the solubility of PMMA up to values not reached before. In particular, the highest CO2 uptake ever reported for PMMA, (i.e., 48 wt%) is found for a saturation pressure of 20 MPa and a saturation temperature of −32 °C. Due to these processing conditions, cell nucleation densities of 1016 nuclei cm−3 and cell sizes clearly below 50 nm are achieved. The nanocellular polymers obtained, with cell sizes ten times smaller than the wavelength of visible light and very homogeneous cellular structures, show a significant transparency

Self-regulation in family foster children

This poster presents research on foster children’s capacities for self-regulation and its relation to adversity history. Children in family foster care are a vulnerable population due to their experiences of maltreatment and separation from primary caregivers. Research has shown high rates of behavioral problems and impulsivity in these children, as well as other difficulties such as poor academic adjustment. Recent theory and research advances suggest some of these problems are due to deficits in self-regulatory capacities, such as executive functions or emotion regulation. Early adversity in key developmental stages, like that suffered by many foster children, can undermine the normative development of these capacities and, consequently, their psychosocial adjustment. This study explores this topic in a sample of foster children between 4 and 8 years old who were living in non-relative foster families for at least six months in Southern Spain. We used the Behavior Rating Inventory of Executive Function (BRIEF; Gioia, Isquith, Guy, & Kenworthy, 2000), a widely used parent-reported questionnaire, to assess self-regulation in the foster children. The BRIEF was answered by the primary foster caregiver during a home visit. The information regarding adverse events and trajectory in the child protection services was obtained through case records in collaboration with caseworkers. The results of this study show us information about the capacities of self-regulation of children in family foster care. Due to the centrality of self-regulation in development and the fact that it remains responsive to well-designed interventions beyond early childhood, interventions for foster children and families should consider targeting this dimension to improve their outcomes

Transparent nanocellular PMMA: Characterization and modeling of the optical properties

In this work, the optical properties of transparent nanocellular polymethylmethacrylate (PMMA) have been studied, experimental and theoretically. Transmittance measurements of samples presenting different cell sizes (14, 24, 39 and 225 nm) and a constant relative density of around 0.45 have been carried out obtaining values as high as 0.94 for the sample with the smaller cell size and a thickness of 0.05 mm. In addition, the light absorption coefficient has been measured as a function of cell size and wavelength. It has been found that the transmittance has a strong dependence with the wavelength, presenting these transparent materials Rayleigh scattering. On the other hand, the transmission of visible light through these nanocellular materials has been modelled for the first time. The developed model reproduces with good accuracy the trends observed in the experimental results and provides remarkable insights into the physics mechanisms controlling the optical behavior of these materials

Modeling the heat transfer by conduction of nanocellular polymers with bimodal cellular structures

Nanocellular polymers are a new generation of materials with the potential of being used as very efficient thermal insulators. It has been proved experimentally that these materials present the Knudsen effect, which strongly reduces the conductivity of the gas phase. There are theoretical equations to predict the thermal conductivity due to this Knudsen effect, but all the models consider an average cell size. In this work, we propose a model to predict the thermal conductivity due to the conduction mechanisms of nanocellular materials with bimodal cellular structures, that is, with two populations of cells, micro and nanocellular. The novelty of our work is to consider not only the average cell size, but the cell size distribution. The predictions of the model are compared with the experimental conductivity of two real bimodal systems based on poly(methyl methacrylate) (PMMA), and it is proved that this new model provides more accurate estimations of the conductivity than the models that do not consider the bimodality. Furthermore, this model could be applied to monomodal nanocellular polymers. In particular, for monomodal materials presenting a wide cell size distribution and at low densities, the model predicts important variations in comparison with the current models in the literature. This result indicates that the cell size distribution must be included in the estimations of the thermal conductivity of nanocellular polymer

Nanocellular Polymers with a Gradient Cellular Structure Based on Poly(methyl methacrylate)/Thermoplastic Polyurethane Blends Produced by Gas Dissolution Foaming

Graded structures and nanocellular polymers are two examples of advanced cellular morphologies. In this work, a methodology to obtain low-density graded nanocellular polymers based on poly(methyl methacrylate) (PMMA)/ thermoplastic polyurethane (TPU) blends produced by gas dissolution foaming is reported. A systematic study of the effect of the processing condition is presented. Results show that the melt-blending results in a solid nanostructured material formed by nanometric TPU domains. The PMMA/ TPU foamed samples show a gradient cellular structure, with a homogeneous nanocellular core. In the core, the TPU domains act as nucleating sites, enhancing nucleation compared to pure PMMA and allowing the change from a microcellular to a nanocellular structure. Nonetheless, the outer region shows a gradient of cell sizes from nano- to micron-sized cells. This gradient structure is attributed to a non-constant pressure profile in the samples due to gas desorption before foaming. The nucleation in the PMMA/ TPU increases as the saturation pressure increases. Regarding the effect of the foaming conditions, it is proved that it is necessary to have a fine control to avoid degeneration of the cellular materials. Graded nanocellular polymers with relative densities of 0.16–0.30 and cell sizes ranging 310–480 nm (in the nanocellular core) are obtained

Overcoming the Challenge of Producing Large and Flat Nanocellular Polymers: A Study with PMMA

Although nanocellular polymers are interesting materials with improved properties in comparison with conventional or microcellular polymers, the production of large and flat parts of those materials is still challenging. Herein, gas dissolution foaming process is used to produce large and flat nanocellular polymethylmethacrylate samples. In order to do that, the foaming step is performed in a hot press. The methodology is optimized to produce flat samples with dimensions of 100 × 100 × 6 mm3, relative densities in the range 0.25–0.55 and cell sizes around 250 nm. Additionally, foaming parameters are modified to study their influence on the final cellular structure, and the materials produced in this paper are compared with samples produced by using a most conventional approach in which foaming step is conducted in a thermal bath. Results obtained show that an increment in the foaming temperature leads to a reduction in relative density and an increase of cell nucleation density. Moreover, differences in the final cellular structure for materials produced by both foaming routes are studied, proving that although there exist some differences, the mechanisms governing the nucleation and growing are the same in both processes, leading to the production of homogeneous materials with very similar cellular structures

Low-density PMMA/MAM nanocellular polymers using low MAM contents: Production and characterization

Low-density nanocellular polymers are required to take advantage of the full potential of these materials as high efficient thermal insulators. However, their production is still a challenging task. One promising approach is the use of nanostructured polymer blends of poly(methyl methacrylate) (PMMA) and a block copolymer poly(methyl methacrylate)-poly(butyl acrylate)-poly(methyl methacrylate) (MAM), which are useful for promoting nucleation but seem to present a severe drawback, as apparently avoid low relative densities. In this work, new strategies to overcome this limitation and produce low-density nanocellular materials based on these blends are investigated. First, the effect of very low amounts of the MAM copolymer is analysed. It is detected that nanostructuration can be prevented using low copolymer contents, but nucleation is still enhanced as a result of the copolymer molecules with high CO2 affinity dispersed in the matrix, so nanocellular polymers are obtained using very low percentages of the copolymer. Second, the influence of the foaming temperature is studied. Results show that for systems in which there is not a clear nanostructuration, cells can grow more freely and smaller relative densities can be achieved. For these studies, blends of PMMA with MAM with copolymer contents from 10 wt% and as low as 0.1 wt% are used. For the first time, the production strategies proposed in this work have allowed obtaining low density (relative density 0.23) nanocellular polymers based on PMMA/MAM blends. Graphical abstrac

Diseño de una metodología matemática para la construcción de mapas estratégicos de un cuadro de mando integral, utilizando mapas cognitivos difusos y optimización

El propósito principal del presente proyecto es desarrollar una metodología para la generación de mapas estratégicos capaz de adaptarse a diferentes modelos organizacionales. La metodología propone reducir la subjetividad inmersa en las decisiones complejas de escogencia de los objetivos que deben, o no, participar en el mapa, así como de las relaciones de causa y efecto entre objetivos para construir la estrategia, que permita a una compañía lograr la consecución de sus propósitos. Para el cumplimiento del propósito se utiliza la herramienta de análisis multicriterio denominada mapas cognitivos difusos, que pondera las importancias de las relaciones entre pares de objetivos y de los objetivos de forma global en el mapa, suministradas por los tomadores de decisiones, usando herramientas de lógica difusa. La información obtenida se utiliza como insumo para un modelo de optimización que escoge las relaciones y objetivos mejor calificados por los expertos cumpliendo con las condiciones lógicas de dichas estructuras.The main purpose of the present project is to develop a methodology for the generation of strategic maps capable of adapting to different organizational models. The methodology proposes to reduce the subjectivity immersed in the complex choice decisions of the objectives that must, or not, participate in the map, as well as the cause and effect relationships between objectives to build the strategy, which allows a company to achieve the achievement of its purposes. For the fulfillment of the purpose, the multicriteria analysis tool called diffuse cognitive maps is used, which weights the importance of relations between pairs of objectives and objectives in a global way on the map, provided by decision makers, using logic tools diffuse The information obtained is used as an input for an optimization model that chooses the relationships and objectives best qualified by the experts, complying with the logical conditions of said structuresMagíster en Ingeniería IndustrialMaestrí

Extended eigenvalues of composition operators

A complex scalar lambda is said to be an extended eigenvalue of a bounded linear operator A on a complex Hilbert space if there is a nonzero operator X such that AX = lambda XA. The results in this paper provide a full solution to the problem of computing the extended eigenvalues for those composition operators C-phi induced on the Hardy space H-2(D) by linear fractional transformations phi of the unit disk. (c) 2021 Universidad de Sevilla. Published by Elsevier IncThe first and fourth authors were supported by Ministerio de Ciencia, Innovacion y Universidades under Grant MTM 2015-63699-P, and by Fondo Europeo de Desarrollo Regional under Grant PGC2018-094215-B-I00. The second author was also supported by Fondo Europeo de Desarrollo Regional under Grant PGC2018-101514-B-I00, and by Junta de Andalucia under Grant FEDER-UCA18-108415. The first author visited Western Michigan University at an early stage of this research. He would like to acknowledge the warm hospitality received from the third author. He is grateful to the Mathematics Department of WMU for covering local expenses and for the commitment to this global engagement.The third author visited Universidad de Sevilla several times at later stages of this research. He would like to thank the first and fourth authors for making possible this cooperation. He also acknowledges the Ministerio de Ciencia, Innovacion y Universidades for the sponsorship under Grant MTM 2015-6399-P, and the people at Instituto de Matematicas for the organization of his visits