An exact formalism to study the thermodynamic properties of hard-sphere systems under spherical confinement

This paper presents a modified grand canonical ensemble which provides a new simple and efficient scheme to study few-body fluid-like inhomogeneous systems under confinement. The new formalism is implemented to investigate the exact thermodynamic properties of a hard sphere (HS) fluid-like system with up to three particles confined in a spherical cavity. In addition, the partition function of this system was used to analyze the surface thermodynamic properties of the many-HS system and to derive the exact curvature dependence of both the surface tension and adsorption in powers of the density. The expressions for the surface tension and the adsorption were also obtained for the many- HS system outside of a fixed hard spherical object. We used these results to derive the dependence of the fluid-substrate Tolman length up to first order in density.Comment: 6 figures. The paper includes new exact results about hard spheres fluid-like system

Fluids confined in wedges and by edges: Virial series for the line-thermodynamic properties of hard spheres

This work is devoted to analyze the relation between the thermodynamic properties of a confined fluid and the shape of its confining vessel. Recently, new insights in this topic were found through the study of cluster integrals for inhomogeneous fluids that revealed the dependence on the vessel shape of the low density behavior of the system. Here, the statistical mechanics and thermodynamics of fluids confined in wedges or by edges is revisited, focusing on their cluster integrals. In particular, the well known hard sphere fluid, which was not studied in this framework so far, is analyzed under confinement and its thermodynamic properties are analytically studied up to order two in the density. Furthermore, the analysis is extended to the confinement produced by a corrugated wall. These results rely on the obtained analytic expression for the second cluster integral of the confined hard sphere system as a function of the opening dihedral angle 0 < β < 2π. It enables a unified approach to both wedges and edges.Fil: Urrutia, Ignacio. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

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

Quantitation of buried contamination by use of solvents

Experiments directed at determining the potential of reclaimed silicone polymers for reuse are described

Quantitation of buried contamination by use of solvents

Spore recovery form cured silicone potting compounds using amine solvents to degrade the cured polymers was investigated. A complete list of solvents and a description of the effect of each on two different silicone polymers is provided

Analysis and testing of two-dimensional vented Coanda ejectors with asymmetric variable area mixing sections

The analysis of asymmetric, curved (Coanda) ejector flow has been completed using a finite difference technique and a quasi-orthogonal streamline coordinate system. The boundary layer type jet mixing analysis accounts for the effect of streamline curvature in pressure gradients normal to the streamlines and on eddy viscosities. The analysis assured perfect gases, free of pressure discontinuities and flow separation and treated three compound flows of supersonic and subsonic streams. Flow parameters and ejector performance were measured in a vented Coanda flow geometry for the verification of the computer analysis. A primary converging nozzle with a discharge geometry of 0.003175 m x 0.2032 m was supplied with 0.283 cu m/sec of air at about 241.3 KPa absolute stagnation pressure and 82 C stagnation temperature. One mixing section geometry was used with a 0.127 m constant radius Coanda surface. Eight tests were run at spacing between the Coanda surface and primary nozzle 0.01915 m and 0.318 m and at three angles of Coanda turning: 22.5 deg, 45.0 deg, and 75.0 deg. The wall static pressures, the loci of maximum stagnation pressures, and the stagnation pressure profiles agree well between analytical and experimental results

Energy Balance During Backpacking

Energy expenditure and energy intake were determined in three Subjects during a 160-kilometer backpacking trip. Prior to the trip, heart rate and oxygen consumption during treadmill walking while carrying a backpack were measured. Subjects recorded heart rate during hiking. Heart rate Was used to estimate energy expenditure based on the heart rate: oxygen consumption relationship (Heart Rate Method). Expenditure was also estimated from distance walked and elevation gained (Terrain Method). Subjects recorded food consumption, and were weighed upon finishing the hike. Mean heart rate during biking was 105 +/- 12 beats per Minute. According to the Heart Rate Method, net expenditure averaged 3410 +/- 955 kilocalories on days 1-4, and 2586 +/- 974 kilocalories on day 5. Net expenditure from the Terrain Method was approximately 28% lower. Gross expenditure, using the Heart Rate Method, averaged 4928 +/- 1050 kilocalories on days 1-4, and 3550 +/- 1052 kilocalories on day 5. Energy intake averaged 2134 +/- 625 kilocalories on days 1-4,and 1117 +/- 320 kilocalories on day 5. Expected weight loss due to the caloric deficit was 1.8 +/- 0.4 kilograms, and actual weight loss was 1.7 +/- 0.6 kilograms. Subjects expended nearly 5000 kilocalories per clay and did not consume sufficient food to maintain body mass

The homeodomain protein PAL-1 specifies a lineage-specific regulatory network in the C. elegans embryo

Maternal and zygotic activities of the homeodomain protein PAL-1 specify the identity and maintain the development of the multipotent C blastomere lineage in the C. elegans embryo. To identify PAL-1 regulatory target genes, we used microarrays to compare transcript abundance in wild-type embryos with mutant embryos lacking a C blastomere and to mutant embryos with extra C blastomeres. pal-1-dependent C-lineage expression was verified for select candidate target genes by reporter gene analysis, though many of the target genes are expressed in additional lineages as well. The set of validated target genes includes 12 transcription factors, an uncharacterized wingless ligand and five uncharacterized genes. Phenotypic analysis demonstrates that the identified PAL-1 target genes affect specification, differentiation and morphogenesis of C-lineage cells. In particular, we show that cell fate-specific genes (or tissue identity genes) and a posterior HOX gene are activated in lineage-specific fashion. Transcription of targets is initiated in four temporal phases, which together with their spatial expression patterns leads to a model of the regulatory network specified by PAL-1

Mean properties and Free Energy of a few hard spheres confined in a spherical cavity

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is taken also as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N=4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.Comment: 11 pages, 9 figures and two table