Speeds of sound and isothermal compressibility of ternary liquid systems: Application of Flory’s statistical theory and hard sphere models

Speeds of sound and densities of three ternary liquid systems namely, toluene + n-heptane + n-hexane (I), cyclohexane + n-heptane + n-hexane (II) and n-hexane + n-heptane + n-decane (III) have been measured as a function of the composition at 298.15 K at atmospheric pressure. The experimental isothermal compressibility has been evaluated from measured values of speeds of sound and density. The isothermal compressibility of these mixtures has also been computed theoretically using different models for hard sphere equations of state and Flory’s statistical theory. Computed values of isothermal compressibility have been compared with experimental findings. A satisfactory agreement has been observed. The superiority of Flory’s statistical theory has been established quite reasonably over hard sphere models.      

The penetrable sphere and related models of liquid—vapour equilibrium

The equation of state of the penetrable sphere model of liquid—vapour equilibrium is calculated by three different sequences of approximations; the first is based on the virial expansion of the equivalent two-component model in powers of the densities, the second on expansion in powers of the activity, and the third on a cumulant expansion of the configurational energy in powers of the reciprocal temperature. These sequences are examined both with the inclusion of all coefficients and with the sub-sets of coefficients appropriate to the first and second Percus-Yevick (PY) approximations. The first PY approximation gives a classical critical point whose density and temperature are accurately determined. The second PY and the complete set of coefficients yield badly-behaved series from which few conclusions can be drawn.

The penetrable sphere model is generalized to a wider class of potentials and one of these, in which the configurational energy is expressed in terms of gaussian functions is related to a two-component model of Helfand and Stillinger. It is more tractable than the original model and is examined by the same sequences of approximations. They have shown that the complete series leads to a non-classical critical point in their version of the model; here we show that the first PY approximation is classical but the second nonclassical.     

Calculation of the Kirkwood–Frohlich correlation factor and dielectric constant of methanol using a statistical model and density functional theory

The geometries of methanol monomer and methanol clusters, (CH₃OH) _m , m = 2–10, were optimized using the DFT/B3LYP/6-31++G(d,p) method. For each m > 2, a number of conformers were found to satisfy the optimization condition, showing no imaginary frequency in their calculated IR spectra. With increasing m, five- and six-membered rings begin to appear with open chain branches and the calculated IR spectra approach the experimentally observed IR spectrum of liquid methanol. Using the average energy of formation of one hydrogen bond and a statistical model, the Kirkwood–Frohlich (K–F) correlation factor (g) and dielectric constant (ε) were calculated for each methanol cluster. From a plot of ε versus cluster size (m), the bulk dielectric constant was obtained by extrapolation to m→∞. The value of g averaged over all conformers is in almost complete agreement with the g value obtained in an earlier molecular dynamics simulation study by Fonseca and Ladanyi [J. Chem. Phys. 93, 8148 (1990)]. Using this value of g in the K–F equation, the dielectric constant (ε) of methanol was calculated and found to be in fair agreement with (～17% lower than) the experimental value and also with an earlier molecular dynamics simulation [Mol. Phys. 94, 435 (1998)]. The calculated ε follows the same trend in variation with temperature as the experimental ε in the range 288–318 K.     

Nordström’s scalar theory of gravity and the equivalence principle

General Relativity obeys the three equivalence principles, the “weak” one (all test bodies fall the same way in a given gravitational field), the “Einstein” one (gravity is locally effaced in a freely falling reference frame) and the “strong” one (the gravitational mass of a system equals its inertial mass to which all forms of energy, including gravitational energy, contribute). The first principle holds because matter is minimally coupled to the metric of a curved spacetime so that test bodies follow geodesics. The second holds because Minkowskian coordinates can be used in the vicinity of any event. The fact that the latter, strong, principle holds is ultimately due to the existence of superpotentials which allow to define the inertial mass of a gravitating system by means of its asymptotic gravitational field, that is, in terms of its gravitational mass. Nordström’s theory of gravity, which describes gravity by a scalar field in flat spacetime, is observationally ruled out. It is however the only theory of gravity with General Relativity to obey the strong equivalence principle. I show in this paper that this remarkable property is true beyond post-newtonian level and can be related to the existence of a “Nordström-Katz” superpotential.     

On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models

Daganzo’s criticisms of second-order fluid approximations of traffic flow [C. Daganzo, Transpn. Res. B. 29, 277 (1995)] and Aw and Rascle’s proposal how to overcome them [A. Aw, M. Rascle, SIAM J. Appl. Math. 60, 916 (2000)] have stimulated an intensive scientific activity in the field of traffic modeling. Here, we will revisit their arguments and the interpretations behind them. We will start by analyzing the linear stability of traffic models, which is a widely established approach to study the ability of traffic models to describe emergent traffic jams. Besides deriving a collection of useful formulas for stability analyses, the main attention is put on the characteristic speeds, which are related to the group velocities of the linearized model equations. Most macroscopic traffic models with a dynamic velocity equation appear to predict two characteristic speeds, one of which is faster than the average velocity. This has been claimed to constitute a theoretical inconsistency. We will carefully discuss arguments for and against this view. In particular, we will shed some new light on the problem by comparing Payne’s macroscopic traffic model with the Aw-Rascle model and macroscopic with microscopic traffic models.     

Classical mechanics via general relativity and Maxwell’s theory: a bit of magic

In the 1950’s Herman Bondi observed that a very effective way to study gravitational radiation was to use null surfaces as part of the coordinate system for analyzing the Einstein (Einstein–Maxwell) equations. A particular class of such surfaces, (referred to as Bondi null surfaces) with their associated null tetrad, has now been the main tool for this analysis for many years; their use—until recently—has been almost ubiquitous. Several years ago we realized that there was an attractive alternative to the use of Bondi coordinates, namely to use coordinates (in the asymptotic null future space–time region) that were as close to ordinary flat-space light-cones as possible—very different from Bondi surfaces. There were initially serious impediments to this program: these new null surfaces (referred to as asymptotically shear-free surfaces, ASF) were determined by solving a non-linear differential equation (the “good-cut” equation) whose solutions were most often complex. Eventually these problems were overcome and the program was implemented. In a series of papers, using the ASF null surfaces to study the asymptotically flat Einstein (or Einstein–Maxwell) equations, a variety of surprising (strange) results were obtained. Using only the Einstein and Maxwell equations, we found a large number of the basic relations of classical mechanics. They included very detailed conservation laws, well know kinematic relations and dynamic equations and even the Abraham–Lorentz–Dirac radiation reaction force and the rocket force. As interesting as these were, they came with a serious enigma. These relations from classical mechanics had no relationship with the physical space–time. The space for the action of these relations was the parameter space of solutions of the good-cut equation—a complex space, known as H-space. The enigma—what possible relationship did these standard appearing classical relations have with physical space–time? It is the purpose of this work to establish such a relationship—objects in H-space are related to structures in physical space–time. For example, a complex world-line in H-space becomes in physical space–time an asymptotically shear-free null geodesic congruence where its twist describes its intrinsic spin and if charged, its magnetic dipole.     

The corrections to scaling within Mazenko’s theory in the limit of low and high dimensions

We consider corrections to scaling within an approximate theory developed by Mazenko for nonconserved order parameter in the limit of low (d → 1) and high (d → ∞) dimensions. The corrections to scaling considered here follows from the departures of the initial condition from the scaling morphology. Including corrections to scaling, the equal time correlation function has the form: C(r, t) = f ₀(r/L)+L ^−ω f ₁(r/L)+…, where L is a characteristic length scale (i.e. domain size). The correction-to-scaling exponent ω and the correction-to-scaling functions f ₁(x) are calculated for both low and high dimensions. In both dimensions the value of ω is found to be ω = 4 similar to 1D Glauber model and OJK theory (the theory developed by Ohta, Jasnow and Kawasaki).     

Photon Green’s functions for a consistent theory of absorption and emission in nanostructure-based solar cell devices

The light-matter interaction in planar nanostructures with applications in photovoltaic devices is investigated by means of a microscopic quantum-kinetic theory based on the non-equilibrium Green’s function formalism. The Dyson and Keldysh equations for the Green’s functions of photons are solved numerically. The result is used to couple the optical and electronic degrees of freedom via respective self-energies. The numerical approach for the solution of the optical problem is verified against a standard transfer-matrix formalism and applied to the computation of absorption and emission characteristics in ultra-thin-absorber solar cells.     

Thermal transport property of Ge34 and d-Ge investigated by molecular dynamics and the Slack’s equation

In this study,we evaluate the values of lattice thermal conductivity κ L of type II Ge clathrate (Ge 34) and diamond phase Ge crystal (d-Ge) with the equilibrium molecular dynamics (EMD) method and the Slack's equation.The key parameters of the Slack's equation are derived from the thermodynamic properties obtained from the lattice dynamics (LD) calculations.The empirical Tersoff's potential is used in both EMD and LD simulations.The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values.The predictions of the Slack's equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge.In a temperature range of 200-1000 K,the κ L value of d-Ge is about several times larger than that of Ge 34.     

Structure-based design and analysis of MAO-B inhibitors for Parkinson’s disease: using in silico approaches

Parkinson’s disease (PD) is a degenerative disorder of the CNS, characterized by cerebral depletion of dopamine (DA), hence one of the approaches to delay the depletion of DA is to inhibit its oxidative deamination. Monoamine oxidases (MAO) carry out the oxidative deamination of monoamines like DA. These are intracellular enzymes, located on the outer mitochondrial membrane. MAO-A and MAO-B are the two subtypes of which MAO-B is the most predominant enzyme and is commonly found in the brain. Inhibition of the MAO-B enzyme boosts the effect of both endogenous and exogenous DA. In this study, we have carried out crystal structure analysis and structure-based design of MAO-B inhibitors. We also performed molecular dynamics, flexible docking, induced-fit docking and ADME prediction of the newly designed compounds.     

High dielectric properties of polymer-based ternary blend films using fillers’ synergy between asymmetrical Na-bearing OH–C60 and insulative diamond

Polymer/highly-conductive carbon composites are used as dielectrics. However, a high dielectric loss is induced by leakage current. In this study, ternary polymer composites with hydroxyfullerene and diamond were fabricated. Ternary composites exhibited more promising dielectric traits compared with polymer/hydroxyfullerene composites. A high dielectric constant was achieved using polar hydroxyfullerene. A significantly reduced dielectric loss was achieved owing to insulative diamond. Polymer/hydroxyfullerene interaction and branching of leakage current were studied. The best ternary composite showed a dielectric constant of ∼26 and dielectric loss of ∼0.21 at 20 Hz. This work may enable the large-scale fabrication of advanced dielectrics.     

Comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models" by D. Helbing and A.F. Johansson

There has been a debate in the transportation research community over the validity of a class of traffic flow models. These models have the peculiar property that one of its characteristic speeds is faster than that of vehicular traffic. This note attempts to provide an overview of the diverging views on how to interpret this property, and specific comments on the interpretation of Helbing and Johansson [On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00182-7]. We showed that having faster-than-traffic characteristics does produce counterintuitive predictions, and they cannot be explained away by a linear stability analysis. As such, the existence of such characteristics must be justified by the physics of traffic, and verified through empirical observations.     

Electrostatic force between rings and discs of charge inside a grounded metallic pipe using the Green’s function technique

We derive analytic formulae for the electrostatic force between ring and disc charge distributions inside a grounded metallic pipe using the Green’s function technique. These distribution models are useful in the modeling of electron beams commonly employed in microwave tubes. We analyze the electric force between two discs, between two rings, and between a disc and a ring and we compare the results for the electric potential, field, and force to numerical ones obtained from a 3D electrostatic solver. Present expressions were developed to avoid an oscillatory noise when the field diverges by axial proximity between source and observer.     

Reply to comment on “On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models” by H.M. Zhang

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.     

Comparative analysis of the characteristics of the elastic scattering of protons by lithium isotopes 6, 7, 8, 9Li, performed using Glauber’s multiple diffraction scattering theory

Differential cross sections and vector analyzing powers are calculated for the elastic scattering of protons by lithium isotopes ⁶Li, ⁷Li, ⁸Li, and ⁹Li at energies of 60 and 200 MeV. The calculations are performed using Glauber??s multiple diffraction scattering theory in the two-particle (for ⁷Li) and three-particle (for ^6,8,9Li) models with realistic intercluster interaction potentials. An analysis of the relationship between the differential elastic scattering cross section and various wave functions, calculated using different interaction potentials, is presented for the ^{8, 9}Li isotopes.