Thermostatistics of small systems: exact results in the microcanonical formalism

Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: (1) Stirling’s approximation can be used to evaluate the number of microstates; (2) the surface entropy can be replaced by the volume entropy; and (3) derivatives can be used even if the energy is not a continuous variable. It is also assumed that the results obtained from the microcanonical formalism agree with those from the canonical one. However, it is not clear if these assumptions are right for very small systems (10–100 particles). To answer this question, two systems with exact solutions (the Einstein model of the solid and the two-level system) have been solved with and without these approximations.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Científico Tecnológico Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Universidad Nacional de San Luis. Facultad de Cs.fisico Matematicas y Naturales. Departamento de Fisica; ArgentinaFil: Bertoldi, Dalía Surena. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Científico Tecnológico Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentin

How Good Is the Debye Model for Nanocrystals?

The question here is whether the Debye model is suited to evaluate the specific heat of nanocrystals. For this, the simplest possible nanocrystal is considered: a basic cubic structure made of atoms that interact through a harmonic potential. This simple model can be solved exactly. This allows the dispersion relation of the mechanical waves to be determined, so that calculating the exact specific heat turns out to be quite straightforward. Then, the same problem is solved using the Debye approximation. Our findings show that the specific heat of a nanocrystal evaluated exactly is higher than the value found in the thermodynamic limit, that is to say, the specific heat decreases as the nanocrystal size increases. In addition, it becomes clear that the Debye model is a poor approximation for calculating the specific heat of a nanocrystal. Naturally, the Einstein model yields an even worse result. The cause of the discrepancy is found in the role of the nanocrystal surface.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; ArgentinaFil: Mora Barzaga, Geraudys. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentin

VACÍOS URBANOS: Dimensión física o existencial

El desarrollo actual de las ciudades de nuestro país, sin planificación orgánica y con un alto grado de espontaneísmo, configura escenarios que semeja un inmenso cuerpo sin órganos, una morfología urbana y espacial y nuevas formas de ocupación del territorio, fragmentado y discontinuo, con llenos y vacíos que le otorgan una naturaleza particular, en especial en la periferia. Tomando como referencia el caso de Piura y Castilla, nuestro objetivo central fue desarrollar una perspectiva dialéctica de la manera cómo ha evolucionado el pensamiento teórico en el tratamiento de los vacíos urbanos, particularmente en la literatura urbanística, pero sin dejar de lado los aspectos relacionados con la planificación, la gestión y la naturaleza socio-espacial de estos espacios. Metodológicamente, desplegamos todo el esfuerzo para ofrecer un pormenorizado recuento del pensamiento urbanístico sobre la materia, en la perspectiva de un estado del arte que ayude a entender su dinámica. Los resultados confirman dos principales formas de abordaje del tema; la primera, enfoca el fenómeno de los vacíos urbanos, como el resultado de un modelo de ciudad contemporánea, que genera fragmentos y discontinuidad urbana; y, la segunda, como el resultado de una ciudad pos moderna, de una sociedad consumista e indiferente y desde la percepción del vacío como lugar o espacio existencial. Concluimos en el hecho de que ambas orientaciones tienen un valor agregado específico, particularmente la primera, si tomamos en cuenta las características de las ciudades en América Latina y el Perú y porque pueden ser oportunidades valiosas para transformar su actual condición

Size- And temperature-dependent magnetization of iron nanoclusters

The magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom MT, including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on MT are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.Fil: Dos Santos Mendez, Gonzalo Joaquín. Universidad de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Aparicio, Romina Marcela. Universidad de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; ArgentinaFil: Linares, D.. Universidad Nacional de San Luis. Facultad de Ciencias Físico- Matemáticas y Naturales; ArgentinaFil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; ArgentinaFil: Tranchida, J.. Sandia National Laboratory; Estados UnidosFil: Pastor, G. M.. University Of Kasel; AlemaniaFil: Bringa, Eduardo Marcial. Universidad de Mendoza; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza; Argentina. Universidad Mayor; Chil

Mortality from gastrointestinal congenital anomalies at 264 hospitals in 74 low-income, middle-income, and high-income countries: a multicentre, international, prospective cohort study

Summary Background Congenital anomalies are the fifth leading cause of mortality in children younger than 5 years globally. Many gastrointestinal congenital anomalies are fatal without timely access to neonatal surgical care, but few studies have been done on these conditions in low-income and middle-income countries (LMICs). We compared outcomes of the seven most common gastrointestinal congenital anomalies in low-income, middle-income, and high-income countries globally, and identified factors associated with mortality. Methods We did a multicentre, international prospective cohort study of patients younger than 16 years, presenting to hospital for the first time with oesophageal atresia, congenital diaphragmatic hernia, intestinal atresia, gastroschisis, exomphalos, anorectal malformation, and Hirschsprung’s disease. Recruitment was of consecutive patients for a minimum of 1 month between October, 2018, and April, 2019. We collected data on patient demographics, clinical status, interventions, and outcomes using the REDCap platform. Patients were followed up for 30 days after primary intervention, or 30 days after admission if they did not receive an intervention. The primary outcome was all-cause, in-hospital mortality for all conditions combined and each condition individually, stratified by country income status. We did a complete case analysis. Findings We included 3849 patients with 3975 study conditions (560 with oesophageal atresia, 448 with congenital diaphragmatic hernia, 681 with intestinal atresia, 453 with gastroschisis, 325 with exomphalos, 991 with anorectal malformation, and 517 with Hirschsprung’s disease) from 264 hospitals (89 in high-income countries, 166 in middleincome countries, and nine in low-income countries) in 74 countries. Of the 3849 patients, 2231 (58·0%) were male. Median gestational age at birth was 38 weeks (IQR 36–39) and median bodyweight at presentation was 2·8 kg (2·3–3·3). Mortality among all patients was 37 (39·8%) of 93 in low-income countries, 583 (20·4%) of 2860 in middle-income countries, and 50 (5·6%) of 896 in high-income countries (p<0·0001 between all country income groups). Gastroschisis had the greatest difference in mortality between country income strata (nine [90·0%] of ten in lowincome countries, 97 [31·9%] of 304 in middle-income countries, and two [1·4%] of 139 in high-income countries; p≤0·0001 between all country income groups). Factors significantly associated with higher mortality for all patients combined included country income status (low-income vs high-income countries, risk ratio 2·78 [95% CI 1·88–4·11], p<0·0001; middle-income vs high-income countries, 2·11 [1·59–2·79], p<0·0001), sepsis at presentation (1·20 [1·04–1·40], p=0·016), higher American Society of Anesthesiologists (ASA) score at primary intervention (ASA 4–5 vs ASA 1–2, 1·82 [1·40–2·35], p<0·0001; ASA 3 vs ASA 1–2, 1·58, [1·30–1·92], p<0·0001]), surgical safety checklist not used (1·39 [1·02–1·90], p=0·035), and ventilation or parenteral nutrition unavailable when needed (ventilation 1·96, [1·41–2·71], p=0·0001; parenteral nutrition 1·35, [1·05–1·74], p=0·018). Administration of parenteral nutrition (0·61, [0·47–0·79], p=0·0002) and use of a peripherally inserted central catheter (0·65 [0·50–0·86], p=0·0024) or percutaneous central line (0·69 [0·48–1·00], p=0·049) were associated with lower mortality. Interpretation Unacceptable differences in mortality exist for gastrointestinal congenital anomalies between lowincome, middle-income, and high-income countries. Improving access to quality neonatal surgical care in LMICs will be vital to achieve Sustainable Development Goal 3.2 of ending preventable deaths in neonates and children younger than 5 years by 2030

Statistical mechanics of few-particle systems: Exact results for two useful models

The statistical mechanics of small clusters (n ∼ 10-50 elements) of harmonic oscillators and two-level systems is studied exactly, following the microcanonical, canonical and grand canonical formalisms. For clusters with several hundred particles, the results from the three formalisms coincide with those found in the thermodynamic limit. However, for clusters formed by a few tens of elements, the three ensembles yield different results. For a cluster with a few tens of harmonic oscillators, when the heat capacity per oscillator is evaluated within the canonical formalism, it reaches a limit value equal to k B, as in the thermodynamic case, while within the microcanonical formalism the limit value is k B(1-1/n). This difference could be measured experimentally. For a cluster with a few tens of two-level systems, the heat capacity evaluated within the canonical and microcanonical ensembles also presents differences that could be detected experimentally. Both the microcanonical and grand canonical formalism show that the entropy is non-additive for systems this small, while the canonical ensemble reaches the opposite conclusion. These results suggest that the microcanonical ensemble is the most appropriate for dealing with systems with tens of particles.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentin

How to use thermodynamics to deal with some thermal systems out of equilibrium

Se muestra de una manera didáctica que un sistema térmico fuera de equilibrio puede ser tratado con las herramientas usuales de la termodinámica si se lo fracciona en secciones lo suficientemente pequeñas como para que las magnitudes termodinámicas tengan valores constantes en su interior. Para ejemplificar este procedimiento, se analiza el caso de un gas ideal en un gradiente térmico y se muestra que eso implica la aparición de un gradiente en la densidad. También se menciona el caso de la conducción térmica en una varilla metálica en el que puede calcularse explícitamente la producción de entropía tanto en los reservorios como en la varilla propiamente dicha.It is shown at a level suitable for an undergraduate student that thermodynamics can be use to deal with certain thermal systems out of equilibrium. The trick is to cut the system in parts or slides small enough so that the thermodynamics magnitudes have constant values inside them. As an example, an ideal gas in a thermal gradient is considered. It is shown that a density gradient appears as a consequence of the thermal one. It is also briefly considered the heat conduction in a rod; it is shown that the entropy production rate can be calculated both for the reservoirs and the rod.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentina. Universidad Nacional de San Luis; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentin

Where are the particles when the box is hot?

We consider the known problem of a particle in a one-dimensional box, i.e. in an infinite potential well. Specifically, we evaluate the probability density for finding a particle in a certain position when the system is in contact with a reservoir at a temperature T ≠ 0. We observe that, when the T is increased, the density tends to become uniform in the box, except in a 'boundary layer' close to the walls. Then, we consider two particles in the box, discriminating between bosons and fermions. The particles are first analyzed without accounting for the spin. Evaluating the thermalized probability density in this way, results in a clear difference between bosons and spinless fermions. Next, we consider the complete wave function for spin-1/2fermions, and the probability density changes significantly with respect to the spinless case. This shows that disregarding the electron spin for the sake of simplicity may lead to misleading results.Fil: Miranda, Enrique Nestor. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentin

Boltzmann or Gibbs Entropy?: Thermostatistics of Two Models with Few Particles

We study the statistical mechanics of small clusters (N ~ 10 - 100) for two-level systems and harmonic oscillators. Both Boltzmann’s and Gibbs’s definitions of entropy are used. The properties of the studied systems are evaluated numerically but exactly; this means that Stirling’s approximation was not used in the calculation and that the discrete nature of energy was taken into account. Results show that, for the two-level system, using Gibbs entropy prevents temperatures from assuming negative values; however, they reach very high values that are not plausible in physical terms. In the case of harmonic oscillators, there are no significant differences when using either definition of entropy. Both systems show that for N = 100 the exact results evaluated with statistical mechanics coincide with those found in the thermodynamic limit. This suggests that thermodynamics can be applied to systems as small as these.Fil: Miranda, Enrique Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Provincia de Mendoza. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales. Universidad Nacional de Cuyo. Instituto Argentino de Nivología, Glaciología y Ciencias Ambientales; Argentin