Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical and ellipsoidal cavities. Results have been compared with two previously studied geometries, the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based in the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained which express the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the analyzed different geometries. We obtain analytically the external work, the pressure on the wall, the pressure in the homogeneous zone, the wall-fluid surface tension, the line tension and other similar properties

The supreme turbinate and the drainage of the posterior ethmoids: a computed tomographic study

Background: It is generally acknowledged that the posterior ethmoidal cells drain under the superior nasal turbinate (SorNT) or, rarely, under the supreme nasal turbinate (SmeNT), and the sphenoid ostium (SO) opens to the sphenoethmoidal recess. However, detailed relations between these structures are variable, complex and still not clear. There is no reliable data on the prevalence of SmeNT and drainage of the posterior ethmoidal cells under this structure. The aim of this study was to re-evaluate the anatomy of the aforementioned region. Materials and methods: Multiplanar and three-dimensional reconstruction analysis of 100 thin slice paranasal sinus computed tomography scans. Results: SmeNT was identified in 77 subjects (136 sides). It formed the ostium to the posterior ethmoidal cell adjacent to the skull base or orbit in 58 subjects (91 sides). This cell drained independently from the remaining posterior ethmoidal cells. The sphenoethmoidal (Onodi) cell drained to supreme meatus in 41 subjects (54 sides), and to superior meatus in 37 subjects (49 sides). SO was always located medial to the posteroinferior attachment of SmeNT, or SorNT (in absence of SmeNT). Conclusions: Patients with divergent drainage of the posterior ethmoids (with posterior ethmoidal cell draining to the supreme meatus) may require more extensive surgery to avoid persistence or recurrence of inflammatory disease. SmeNT is more common than thought, but due to its posterior and superior location to SorNT, it is rarely seen intraoperatively. If SmeNT is present, SO is always located medial to its posteroinferior attachment. (Folia Morphol 2018; 77, 1: 110–115

Assessment of the concentration of nitric oxide in exhaled air (FeNO) in primary school children in Krakow and Ruzomberk in relation to air pollution in these cities.

The measurement of the exhaled nitric oxide (FeNO) is a recognized biomarker in the detection and monitoring of airway inflammatory infections, this including asthma. Due to its simplicity, and noninvasiveness, it is more and more widely used in diagnostics of children. Few studies indicate the relationship between FeNO and atmospheric air pollution. The goal of the following study was the measuring of FeNO for 8-9 year old children in Krakow and Ruzomberok and relating the results of these measurements to the level of air pollution in the PM10 and PM2,5 range. 250 children aged 8-9 (125 in Krakow and 125 in Ruzomberok) attending third grades of primary schools, have constituted the research group. The measurement has been taken in accordance with the applicable standards with the application of a MediSOFT Belgium analyzer with a disposable head with an antibacterial filter. The results of the measurements have been referred to the PM10 and PM2,5 concentration of particulate matter in the air. Within the group of 125 children participating in the study in Krakow, the FeNO levels were normal for 104 (83.2%) children and increased for 21 (16.8%) children. During the period of the study, the average PM10 concentration was 55,7 µg/m3 and PM2,5 was 37.0 µg/m3. As far as the group of 125 children examined in Ruzomberok, the FeNO levels were correct (5-20 ppb) for 114 (91,2%) children and increased (21-55) for 11 child­ren (8.8%). During the period of the study, the average PM10 concentration was 24.1 µg/m3 and PM2,5 was 15.4 µg/m3. As one can see from the comparison, 1.9 times more increased FeNO levels have been recorded in Krakow than in Ruzomberok (18.6 vs 8.8%), and, within the range of the heavily increased values (>50 ppb), this difference was as much as 4 times greater (3.2% vs 0.8%). These results correlate with the PM10 and PM2,5 levels in Krakow, which are respectively 2.3 and 2.4 times higher than those in Ruzomberok

Virial series for inhomogeneous fluids applied to the Lennard-Jones wall-fluid surface tension at planar and curved walls

We formulate a straightforward scheme of statistical mechanics for inhomogeneous systems that includes the virial series in powers of the activity for the grand free energy and density distributions. There, cluster integrals formulated for inhomogeneous systems play a main role. We center on second order terms that were analyzed in the case of hard-wall confinement, focusing in planar, spherical and cylindrical walls. Further analysis was devoted to the Lennard-Jones system and its generalization the 2k-k potential. For this interaction potentials the second cluster integral was evaluated analytically. We obtained the fluid-substrate surface tension at second order for the planar, spherical and cylindrical confinement. Spherical and cylindrical cases were analyzed using a series expansion in the radius including higher order terms. We detected a $\ln R^{-1}/R^{2}$ dependence of the surface tension for the standard Lennard-Jones system confined by spherical and cylindrical walls, no matter if particles are inside or outside of the hard-walls. The analysis was extended to bending and Gaussian curvatures, where exact expressions were also obtained.Comment: 15 pages, 6 figure

Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories

A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.Comment: A modified and expanded version of a second part of the paper which previously appeared as gr-qc/0702097v1. The first, modified part is now published as gr-qc/0702097v2 and as a separate paper in Class. Qu. Grav. The present paper matches the published versio

A mechanochemical strategy for IRMOF assembly based on pre-designed oxo-zinc precursors.

We demonstrate a mechanochemical strategy that allowed the first successful mechanosynthesis of IRMOFs based on an oxo-centred secondary building unit (SBU). The presented study indicates that controlling the acid-base relationship between reagents is key to mechanochemical synthesis of IRMOFs, revealing a pre-assembled oxo-zinc amidate cluster as an efficient precursor for IRMOF mechanosynthesis.The authors would like to acknowledge the project operated within the Foundation for Polish Science Team Programme co-financed by the EU ‘‘European Regional Development Fund’’ TEAM/2011–7/8, and the European Union in the framework of Regional Development Fund through the Joint UW and WUT International PhD Program of Foundation for Polish Science – “Towards Advanced Functional Materials and Novel Devices” (MPD/2010/4) (D.P.) for financial support.This is the accepted manuscript. The final version was published in Chemical Communications and is available at http://pubs.rsc.org/en/Content/ArticleLanding/2015/CC/c4cc09917f#!divAbstract

Measurement of nitric oxide in exhaled air in primary school children in Ružomberok.

Nowadays, there are a number of respiratory illnesses that directly affect children. Exhaled nitric oxide measurement (FeNO) is one of the modern methods of investigation used for diagnosing and controlling allergic eosinophilic airway inflammation. It is a simple, painless and time-saving method for the patient. Because of its non-invasiveness and simplicity, it is a valuable diagnostic method, especially in younger children. Measurement of FeNO is a recognized biomarker and an accurate quantitative indicator in the detection, assessment and monitoring of airway inflammation, including asthma. However, only a few studies assess the relationship between FeNO and level of air pollution. The aim of our study is to determine the relationship between FeNO in third-grade students of primary schools and the level of air pollution in Ruzomberok. 146 children aged 8-10 years were included in the research. This is the first stage of a wider research project involving FeNO measurements in children at different times of the year. The goal of the research is to determine the concentration of FeNO in the studied group of children in the autumn when air pollution is lower than in second stage which is observed in winter. The study showed elevated values of FeNO>20 ppb in 11% of the tested children and correct values <20 ppb in 89% of them. Level of average air pollution in survey days for PM10 ranged from 23 to 40 μg/m3 and for NO2 – from 28 to 44 μg/m3. The study shows that the significant majority of children have normal levels of nitric oxide in the exhaled air when air pollution is low. Analysis of the second phase of FeNO measurements in winter, when air pollution was higher, will allow to compare the results and assess the correlation between the FeNO value and air pollution

Oscillatory behavior of closed isotropic models in second order gravity theory

Homogeneous and isotropic models are studied in the Jordan frame of the second order gravity theory. The late time evolution of the models is analysed with the methods of the dynamical systems. The normal form of the dynamical system has periodic solutions for a large set of initial conditions. This implies that an initially expanding closed isotropic universe may exhibit oscillatory behaviour.Comment: 16 pages, 3 figures. With some minor improvements. To appear in General Relativity and Gravitatio

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

Wetting transitions of Ne

We report studies of the wetting behavior of Ne on very weakly attractive surfaces, carried out with the Grand Canonical Monte Carlo method. The Ne-Ne interaction was taken to be of Lennard-Jones form, while the Ne-surface interaction was derived from an ab initio calculation of Chizmeshya et al. Nonwetting behavior was found for Li, Rb, and Cs in the temperature regime explored (i.e., T < 42 K). Drying behavior was manifested in a depleted fluid density near the Cs surface. In contrast, for the case of Mg (a more attractive potential) a prewetting transition was found near T= 28 K. This temperature was found to shift slightly when a corrugated potential was used instead of a uniform potential. The isotherm shape and the density profiles did not differ qualitatively between these cases.Comment: 22 pages, 12 figures, submitted to Phys. Rev.