Thermal expansion coefficient of ternary liquid mixture using hard sphere models and Flory’s statistical theory

The coefficients of thermal expansion (α) of ternary liquid mixtures of heterocyclic compounds viz., pyridine/quinoline with phenol in benzene have been evaluated at 308.15, 318.15 and 328.15 K, respectively. A comparative study of thermal expansivity using different models for hard sphere equation of state and Flory’s statistical theory has been made. The computed values of thermal expansivity are compared with the experimental results. The excess values of thermal expansivity have also been computed and utilized to discuss the existence and strength of intermolecular interactions in the ternary liquid system under investigation.     

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.     

Application of Donkin’s formula in the theory of energy analyzers: Part II

Studies of conic-type electric-field structures are continued. The electric field is investigated, and its potential is described by the following analytical expression. $\Phi (x,y,z) = \frac{x}{{z + \sqrt {x^2 + y^2 + z^2 } }}$ . Expression (1) is derived on the basis of Donkin’s formula. Properties of these electric fields are described in Part I [1].     

Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.     

Application of Jacobi’s last multiplier for construction of Hamiltonians of certain biological systems

The relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in biology.     

Demixing and nematic behaviour of oblate hard spherocylinders and hard spheres mixtures: Monte Carlo simulation and Parsons–Lee theory

Parsons–Lee approach is formulated for the isotropic–nematic transition in a binary mixture of oblate hard spherocylinders and hard spheres. Results for the phase coexistence and for the equation of state in both phases for fluids with different relative size and composition ranges are presented. The predicted behaviour is in agreement with Monte Carlo simulations in a qualitative fashion. The study serves to provide a rational view of how to control key aspects of the behaviour of these binary nematogenic colloidal systems. This behaviour can be tuned with an appropriate choice of the relative size and molar fractions of the depleting particles. In general, the mixture of discotic and spherical particles is stable against demixing up to very high packing fractions. We explore in detail the narrow geometrical range where demixing is predicted to be possible in the isotropic phase. The influence of molecular crowding effects on the stability of the mixture when spherical molecules are added to a system of discotic colloids is also studied.     

Application of Mie theory and fractal models to determine the optical and surface roughness of Ag–Cu thin films

Thin films of Ag/Cu were deposited by reactive DC magnetron sputtering on (001)-oriented Si and glass substrates for various deposition times (4–24 min). These films were characterized by atomic force microscopy (AFM), and a power law scaling was performed on the obtained micrographs to investigate the self-affine nature of the sample morphology, which is indicative of a fractal structure. We applied the Higuchi’s algorithm to the AFM data to determine the fractal dimension of each sample, and the Hurst exponents were computed. The deposition time dependences of these parameters and the grain size distributions estimated from the UV–visible spectra using the Mie theory, allowed us to describe a particle formation mechanism during the deposition process, in which the length of continuous paths of conductive particles increases as the deposition time is increased. In agreement with this explanation, the electrical resistance decreased with the increment of the deposition time.     

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.     

Annihilation rates of ortho—positronium in organic liquids: correlation with liquid compressibility and polarization ratio

The bubble model of ortho—positronium annihilation rates customarily employs the value of the planar-surface tension in the estimation of the (surface) energy required to expand a normal interstitial cavity to form the bubble. However, bubble radii are estimated to be only about 0.4 nm; the surface of such a small bubble is expected to have a tension different from that of the planar surface. We have replaced the surface tension parameter by the isothermal compressibility, which is thought not to have a nanostructure limitation. The model has been further improved by introducing the polarization ratio (n ² _D ? 1)/(n ² _D + 2) as a parameter, n _D being the refractive index of the organic liquid. Calculations are presented for 20 liquids.     

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.     

Monte Carlo simulations in the isothermal—isobaric ensemble: the requirement of a ‘shell’ molecule and simulations of small systems

A modification of the widely used Monte Carlo method for determining thermophysical properties in the isothermal-isobaric ensemble is presented. The new Monte Carlo method, now consistent with recent derivations describing the proper statistical mechanical formulation of the constant pressure ensemble for small systems, requires a ‘shell’ molecule to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Ensemble averages obtained with the new algorithm differ from averages calculated with the old Monte Carlo method, particularly for small system sizes, although both sets of averages become equal in the thermodynamic limit. Monte Carlo simulations in the constant pressure ensemble applied to the Lennard-Jones fluid demonstrate these differences for small systems. Peculiarities of small systems are also discussed, revealing that ‘shape’ is an important thermodynamic variable. Finally, an extension of the Monte Carlo method to mixtures is presented.     

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.     

Elastic Properties of Graphene-Like Compounds: the Keating’s and Harisson’s Models

Physics of the Solid State - The third-order elastic constants, the pressure dependences of the second-order elastic constants, the Kleinman and Grüneisen parameters, and the thermal expansion...     

Canonical local algorithms for spin systems: heat bath and Hasting’s methods

We introduce new fast canonical local algorithms for discrete and continuous spin systems. We show that for a broad selection of spin systems they compare favorably to the known ones except for the Ising 1 spins. The new procedures use discretization scheme and the necessary information have to be stored in computer memory before the simulation. The models for testing discrete spins are the Ising 1, the general Ising S or Blume-Capel model, the Potts and the clock models. The continuous spins we examine are the O(N) models, including the continuous Ising model (N = 1), the Ising model (N = 1), the XY model (N = 2), the Heisenberg model (N = 3), the Heisenberg model (N = 3), the O(4) model with applications to the SU(2) lattice gauge theory, and the general O(N) vector spins with .Received: 16 August 2004, Published online: 21 October 2004PACS: 05.70.Fh Phase transitions: general studies - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Hk Classical spin models - 75.10.Nr Spin-glass and other random models     

Application of extended Hückel theory to the geometry of molecules: propylene,methylallene and methylketene

The extended Hückel method has been applied to the calculation of the geometry of propylene, methylallene and methylketene. A good result is obtained for the CCC angle in these compounds as compared with the experimental data. The choice of the value for the H(1s) orbital exponent and the constant in the expression for the non-diagonal elements H_ij is discussed.