Critical behaviour of the lattice gas model in the Percus-Yevick approximation

The solution of the Percus-Yevick (P.Y.) equation for the lattice gas, obtained by Levesque and Verlet, is studied in the critical region. The behaviour of the equation ofstate is similar to the one found for a fluid of sticky hard spheres in the P.Y. approximation: the critical indices have the classical value but the scaling function is non-universal, is strongly asymmetric in density with respect to the critical value and there is a spinodal curve only for the liquid phase. This suggests that these features are generally valid for the P.Y. approximation and are not specific for sticky hard spheres.     

Percolation theory and the conductivity of random close packed mixtures of hard spheres

The conductivity of random close packed mixtures of conducting and insulating spheres has been measured. The composition dependence and the critical percolation density are similar to what has been observed in crystalline systems.     

Binary nonadditive hard-sphere mixtures at high dimension

At high spatial dimension, a suitably scaled classical system of interacting particles truncates at second virial terms. A binary mixture of nonadditive hard spheres with sufficiently repulsive interaction between unlike particles decomposes at sufficiently high density into two coexisting phases. The region around the critical density behaves classically.     

Competition of percolation and phase separation in a fluid of adhesive hard spheres

Using a combination of Monte Carlo techniques, we locate the liquid-vapor critical point of adhesive hard spheres. We find that the critical point lies deep inside the gel region of the phase diagram. The (reduced) critical temperature and density are tau(c)=0.1133+/-0.0005 and rho(c)=0.508+/-0.01. We compare these results with the available theoretical predictions. Using a finite-size scaling analysis, we verify that the critical behavior of the adhesive hard sphere model is consistent with that of the 3D Ising universality class, the default for systems with short-range attractive forces.     

A new method for determining hydrodynamic effects on the collision of two spheres

A sphere falling in a fluid may collide with another sphere falling more slowly if, when the spheres are far apart vertically, the horizontal distance between their centers is less than or equal to a critical radius. Accurate prediction of aerosol particle coagulation requires a good understanding of this process. Previously reported optical techniques for measuring hydrodynamic effects on this phenomenon have inherent difficulties detecting grazing collisions and hence in determining the critical radius. In this work, a novel detection technique is demonstrated and it is shown that the critical radius may be determined from the sound generated by the collision of two spheres in a viscous liquid. The technique is shown to provide a more precise and decisive indication of when hard spheres collide.     

Critical conditions of entropy-driving nucleation in binary colloidal system

In a binary colloidal hard-sphere system, due to the entropic depletion interactions, large spheres may be pushed to pack into clusters. If a cluster is taken as a new kind of component, then the binary colloidal system turns to be a ternary one and it therefore can be dealt in the framework of a multi-component system. It is known that, under certain conditions, a cluster can grow larger and larger and turn into a nucleation, even a kind of phase transition will take place. In this paper, the critical conditions, including the critical size of the nucleating cluster and the corresponding volume fraction of the colloidal system, were determined by analyzing entropy variation through the multi-component of Carnahan–Starling (CS) state equation and the principle of entropy maximum. The results obtained in this way are in good agreement with that of the experiments. In addition, the results also show that, when the critical volume fraction of the system increases from 0.18 to 0.19, the cluster’s density ?$?$ will change from 0.74 to 0.58. Except for the size ratio of large to small spheres, the critical size of the nucleating cluster is almost independent of its density and the volume fraction of the system.     

广义相对论中负指数多层球的结构及稳定性

本文运用广义相对论讨论了满足负指数多方状态方程的流体多层球。经典引力理论与相对论性理论的差别由σ标志。σ是球体中心处的压力与密度之比。通过数值积分得到了n<0的相对论性Emden函数。在-1ed^*也增大。 关键词：     

Étude numérique du modèle de Boussinesq de convection naturelle laminaire axisymétrique permanente dans un espace annulaire compris entre deux sphères

Authors study numerically the axisymetric steady natural convection in the annular space between two vertically eccentric spheres applying the Boussinesq approximation and an integro-interpolation finite volumes method. In the case of two isothermal concentric spheres their results agree with those of the literature. Also, they obtain correlations between the average Nusselt number and the Rayleigh number quasi identical to those publish by Chiu and Scanlan. When the internal sphere is heated by the application of a constant heat flux and eccentric as compared to the supposed external sphere isothermal, they propose correlations between the average Nusselt number and the Rayleigh number that depend on the eccentricity and on the Prandtl number. According to initialising conditions of calculation, the external sphere being isothermal, authors show that there exists a critical Rayleigh number beyond which the flow can be found unicellular or bicellular. This critical Rayleigh number depends on others parameters of the system as the eccentricity and the aspect ratio when the internal sphere is isothermal as well as subjected to a uniform constant heat flux density.     

A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Phase transition in metallic plasmas

An estimate is made for the energy of a virtual atomic structure on the metallic side of the metal-nonmetal transition in a dense plasma. On the assumption of a nearly uniform valence electron density, the interatomic interaction is treated as a Madelung energy, which is found to be approximately one-third of that for the one-component plasma model. Our estimate is verified by solving numerically the pseudowave equation for the valence electrons in ellipsoidal atomic cells which are compatible with the percolation structure of overlapping classically accessible spheres. The critical value of the Coulomb coupling parameter has been shown to agree with experiment at the liquid-gas critical points of cesium and rubidium, which can be identified with the plasma-phase-transition critical points. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 11, 849–854 (10 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Theory of polar liquids

Two recent contributions to the statistical theory of polar fluids, namely the perturbation theory of Stell, Rasaiah and Narang (SRN) and the meanspherical-approximation (MSA) results of Wertheim, and of Nienhuis and Deutch, are compared and contrasted for the conceptually simple model of hard spheres, diameter R, with central point dipoles, of strength μ (dipolar hard spheres). It is shown that the MSA approach replaces correlation functions which enter correctly into the SRN theory by their low-density limits : to this extent it is unsatisfactory. On the other hand the MSA work does suggest reasons why the naive Padé approximant featuring in SRN theory may be expected to do reasonable justice to the physics of the problem. Numerical comparisons of the excess free-energy (as compared with non-polar hard spheres) as a function of reduced density, ρ* = ρR ³, are given at two temperatures, T* = 2 and T* = 0·25, where T* = kTR ³/μ². Similar curves, for T* = 1 and T* = 0·5, are available from the authors. The gas-liquid (T*, ρ*)-phase boundary is located, near the critical point, on both theories, as are the vapour pressure curves. These are calculated using the Carnahan-Starling equation of state for hard spheres ; and critical comment is made in justification of employing this in the context of MSA results for the excess quantities. The two theories are found to have appreciably different numerical consequences.     

Perturbation expansions and series acceleration procedures. Part I. ε-convergence and critical parameters

A simple acceleration of convergence technique known as the ‘ε-convergence algorithm’ (ea) is applied to determine the critical temperatures and exponents. Several illustrations involving well-known series expansions appropriate to two- and three-dimensional Ising models, three-dimensional Heisenberg models, etc., are given. Apart from this, a few recently studied ferrimagnetic systems have also been analysed to emphasise the generality of the approach. Where exact solutions are available, our estimates obtained from this procedure are in excellent agreement. In the case of other models, the critical parameters we have obtained are consistent with other estimates such as those of the Padé approximants and group theoretic methods. The same procedure is applied to the partial virial series for hard spheres and hard discs and it is demonstrated that the divergence of pressure occurs when the close-packing density is reached. The asymptotic form for the virial equation of state is found to beP/ρkT ∼ (1 −ρ/ρ _c ⁻¹ for hard spheres and hard discs. Apart from the estimation of ‘critical parameters’, we have applied theea and the parametrised Euler transformation to sum the partial, truncated virial series for hard spheres and hard discs. The resulting values of pressure so obtained, compare favourably with the molecular dynamics results.     

杂质对硬球系统团簇成核临界条件的影响

通过CS状态方程及熵极大原理在多元胶体系统研究了杂质对硬球系统团簇成核临界条件的影响. 极少量元素或杂质的小胶球对系统成核的临界条件的影响也是不可忽略的: 成核的临界体积分量显著地降低;此外,研究还发现杂质对成核的临界尺寸影响较少.     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

直径任意分布球填充的数值模拟

提出球填充数值算法的新分类方法.改进原有的松弛算法,使其能够模拟直径任意分布的球填充问题,采用可变循环周期使不同球数情形下的填充率基本保持不变.算例数据表明,该算法的填充率和配位数均高于原算法.由于采用背景网格搜索和双向链表组数据结构,使得邻接球搜索效率有相当大的提高,算法的时间复杂度为O(N)(N为球数).在一台AMD Athlon 3200+PC上,对于10000个等径球的随机密排列,只需217s,填充率即可达到0.64.     

Incompressible Einstein–Maxwell fluids with specified electric fields

The Einstein–Maxwell equations describing static charged spheres with uniform density and variable electric field intensity are studied. The special case of constant electric field is also studied. The evolution of the model is governed by a hypergeometric differential equation which has a general solution in terms of special functions. Several classes of exact solutions are identified which may be considered as charged generalizations of the incompressible Schwarzschild interior model. An analysis of the physical features is undertaken for the uniform case. It is demonstrated that uniform density spheres with constant electric field intensity are not realizable with isotropic pressures. This highlights the necessity of studying the criteria for physical admissability of gravitating spheres in general relativity which are solutions to the Einstein–Maxwell equations.     

Experimental evidence of zero forward scattering by magnetic spheres

Magnetically induced diffraction patterns by micron sized magnetic spheres dispersed in a ferrofluid disappear at a certain critical magnetic field. This critical field is found to depend on the concentration of the ferrofluid and on the volume of the magnetic spheres. We attribute this effect to the zero forward scattering by magnetic spheres as predicted by Kerker, Wang, and Giles [J. Opt. Soc. Am. 73, 765 (1983)]. We suggest that such a dispersion can be used to study the optical analogues of localization of electrons in condensed matter, the Hall effect, and the anisotropic diffusion, etc. The combination of the micron sized magnetic spheres and the ferrofluid will also be useful to design magnetically tunable photonic devices.     

Phase equilibria of charge-, size-, and shape-asymmetric model electrolytes

The low-temperature phase behavior of two 2:1 hard-core electrolyte models has been investigated by Monte Carlo simulations. In the first model, both bivalent cations and monovalent anions are spherical, and the charges are located at the ion's centers; in the second model, bivalent cations are modeled as rigid dimers composed of two tangent hard spheres, each carrying a positive charge at the center. It is found that the critical temperature and the critical density are strongly affected by the size asymmetry and the shape of the ions. The results presented in this work provide insights into the behavior of charged colloidal suspensions and polyelectrolytes, where large, symmetric or asymmetric ionic species carrying like charges can attract each other and give rise to thermodynamically unstable conditions.     

Statistical Analysis of Simulated Random Packings of Spheres

This paper describes two algorithms for the generation of random packings of spheres with arbitrary diameter distribution. The first algorithm is the force‐biased algorithm of Mościński and Bargieł. It produces isotropic packings of very high density. The second algorithm is the Jodrey‐Tory sedimentation algorithm, which simulates successive packing of a container with spheres following gravitation. It yields packings of a lower density and of weak anisotropy. The results obtained with these algorithms for the cases of log‐normal and two‐point sphere diameter distributions are analysed statistically, i. e. standard characteristics of spatial statistics such as porosity (or volume fraction), pair correlation function of the system of sphere centres and spherical contact distribution function of the set‐theoretical union of all spheres are determined. Furthermore, the mean coordination numbers are analysed. These results are compared for both algorithms and with data from the literature based on other numerical simulations or from experiments with real spheres.     

Sphere-shaped SiGe micro/nanostructures with tunable Ge composition and size formed by laser irradiation

SiGe spheres with different diameters are successfully fabricated on a virtual SiGe template using a laser irradiation method. The results from scanning electron microscopy and micro-Raman spectroscopy reveal that the diameter and Ge composition of the SiGe spheres can be well controlled by adjusting the laser energy density. In addition, the transmission electron microscopy results show that Ge composition inside the Si Ge spheres is almost uniform in a well-defined, nearly spherical outline. As a convenient method to prepare sphere-shaped SiGe micro/nanostructures with tunable Ge composition and size, this technique is expected to be useful for Si Ge-based material growth and micro/optoelectronic device fabrication.