Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution

The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to previous studies, where the radial distribution function $g(r)$ was obtained numerically from the structure factor by Fourier inversion, we provide a fully analytic representation of $g(r)$ up to any desired distance. The solution is employed to perform an extensive study of the equation of state, the excess internal energy per particle, the residual multiparticle entropy, the structure factor, the radial distribution function, and the direct correlation function. In addition, scatter plots of the bridge function versus the indirect correlation function are used to gauge the reliability of the hypernetted-chain, Percus--Yevick, and Martynov--Sarkisov closures. Finally, the Fisher--Widom and Widom lines are obtained in the case of the triangle-well model.Comment: 19 pages, 9 figure

Equation of state of hard-disk fluids under single-file confinement

The exact transfer-matrix solution for the longitudinal equilibrium properties of the single-file hard-disk fluid is used to study the limiting low- and high-pressure behaviors analytically as functions of the pore width. In the low-pressure regime, the exact third and fourth virial coefficients are obtained, which involve single and double integrals, respectively. Moreover, we show that the standard irreducible diagrams do not provide a complete account of the virial coefficients in confined geometries. The asymptotic equation of state in the high-pressure limit is seen to present a simple pole at the close-packing linear density, as in the hard-rod fluid, but, in contrast to the latter case, the residue is $2$. Since, for an arbitrary pressure, the exact transfer-matrix treatment requires the numerical solution of an eigenvalue integral equation, we propose here two simple approximations to the equation of state, with different complexity levels, and carry out an extensive assessment of their validity and practical convenience vs the exact solution and available computer simulations.Comment: 14 pages, 9 figures, 4 appendices; v3: minor change

Structural properties of hard-disk fluids under single-file confinement

The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse limit. Standard statistical-mechanical results are used as a starting point to derive thermodynamic and structural properties of the one-dimensional mixture, where the condition that all particles have the same chemical potential must be taken into account. Analytical results are then provided for the $n$th neighbor probability distribution function, the radial distribution function, and the structure factor, a very good agreement being observed upon comparison with simulation data from the literature. Moreover, we have analyzed the scaling form for the disappearance of defects in the zigzag configuration for high pressure, and have obtained the translational correlation length and the structural crossover in the oscillation frequency for asymptotically large distances.Comment: 15 pages, 12 figures; v2: new subsections and 4 new figures added; v3: minor change

La castellanización de Li Livres dou Tresor de Brunetto Latini en la corte de Sancho IV (1284-1295): algunas notas sobre la recepción de la Ética aristotélica

This article focuses on the translation into Castilian of Brunetto Latini’s Li Livres dou tresor. This translation was ordered by king Sancho IV around 1293, and included the first extant abridged version of Aristotle’s Nicomachean Ethics (Summa Alexandrinorum) in Castilian. Nevertheless, the Aristotelian ethics would not become popular until the fifteenth century. This article aims at qualifying the initial reception of Libro del tesoro. Therefore, the interpolations of short explanations in the translation to Castilian are analyzed. It is observed that the effort to clarify the meaning of some concepts is evident in the chapters on ethics and does impinge on the Aristotelian notion of happiness or eudaimonia.Este trabajo se centra en la traducción al castellano de la obra de Brunetto Latini, Li Livres dou tresor. Dicha traducción —requerida por el rey castellano Sancho IV en torno a 1293— permitió la aparición de la primera versión abreviada, en castellano, de la Ética a Nicómaco de Aristóteles (Summa Alexandrinorum); sorprendentemente la ética aristotélica no alcanzaría popularidad hasta el siglo XV. Este trabajo trata de ahondar en el tipo de recepción inicial que tuvo el Libro del tesoro, para lo cual se analizan las interpolaciones de breves explicaciones en la traducción al castellano. Se observa que el esfuerzo por aclarar el sentido de algunos conceptos se da mayoritariamente en la parte de la Ética a Nicómaco y afecta en particular a la noción de eudaimonía

Ordering properties of anisotropic hard bodies in one-dimensional channels

The phase behavior and structural properties of hard anisotropic particles (prisms and dumbbells) are examined in one-dimensional channels using the Parsons--Lee (PL) theory, and the transfer-matrix and neighbor-distribution methods. The particles are allowed to move freely along the channel, while their orientations are constrained such that one particle can occupy only two or three different lengths along the channel. In this confinement setting, hard prisms behave as an additive mixture, while hard dumbbells behave as a non-additive one. We prove that all methods provide exact results for the phase properties of hard prisms, while only the neighbor-distribution and transfer-matrix methods are exact for hard dumbbells. This shows that non-additive effects are incorrectly included into the PL theory, which is a successful theory of the isotropic-nematic phase transition of rod-like particles in higher dimensions. In the one-dimensional channel, the orientational ordering develops continuously with increasing density, i.e., the system is isotropic only at zero density, while it becomes perfectly ordered at the close-packing density. We show that there is no orientational correlation in the hard prism system, while the hard dumbbells are orientationally correlated with diverging correlation length at close packing. On the other hand, positional correlations are present for all the systems, the associated correlation length diverging at close packing.Comment: 14 pages, 6 figures; v2: minor change

Ultrathin carbon nanotube with single, double, and triple bonds

A metastable carbon nanotube with single, double, and triple bonds has been predicted from abinitio simulation. It results from the relaxation of an ideal carbon nanotube with chirality (2,1), without any potential barrier between the ideal nanotube and the new structure. Ten-membered carbon rings are formed by breaking carbon bonds between adjacent hexagons; eight-membered rings, already present in the ideal structure, become the smallest rings. This structure is stable in molecular dynamics simulations at temperatures up to 1000K. Raman, infrared, and optical absorption spectra are simulated to allow its identification in the laboratory. The structure can be described as a double helical chain with alternating single, double, and triple bonds, where the chains are bridged by single bondsThis work was supported by Grants No. SB2010-0119 (MEC), No. CTQ2010-19232 (MICIN), and No. A1/035856/11 (AECID

Economic Analysis of Biodiesel Production from Waste Vegetable Oil in Mexicali, Baja California

Mexicali, capital of Baja California, Mexico, has a motor vehicle fleet of diesel estimated at 14,000 units and cargo transport. The transport cargo sector with 11,861 units, consumes about 169 million liters of diesel. The diesel used in Baja California comes from southern Mexico and is one of the causes of CO2 emissions that affect air quality in Mexicali, it is therefore important to explore options for replacing it with biodiesel, which produces less CO2 and can be obtained from waste material. Thus, in the analysis, was considered the use of waste vegetable oil from the Mexicali restaurant industry as a raw material for the production of 4.78 million liters of biodiesel energy equivalent to 4.45 million liters of diesel. The environmental benefit involving the replacement of such a volume of diesel with biodiesel is to reduce emissions by about 9,700 tons of CO2, 22 tons of SOx and 11 tons of PM10. To determine the economic feasibility of producing biodiesel, were applied the methodologies of net present value and internal rate of return. The results indicate that the production of biodiesel is profitable. However, the recovery time of investment, coupled with the uncertainty presented by the biofuels market, make necessary a policy that implements local tax resources to support the promotion, production and use of biodiesel for the transport sector. Therefore, under the circumstances considered in this analysis, the production of biodiesel is feasible if it is developed a synergy among the productive sectors, education and government. Key words: Biodiesel; Economic analysis; Waste vegetable oil; Transport cargo secto