Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

一次脉冲偏磁场作用下硬磁泡的形成

实验研究了一次脉冲偏场作用下外延石榴石膜硬磁泡的形成规律。通过实验和计算,证明了硬泡畴壁中同号的VBL一般地说并非一个脉冲产生一对。通过双重曝光照相法揭示出软畴段的硬化与畴段运动形式的关系,发现了最适于硬泡形成的两种运动形式,并阐明了“软硬磁泡形成的分界场”H_[b]的物理意义。 关键词：     

温度对普通硬磁泡的影响

实验研究了温度对外延石榴石磁泡薄膜中硬磁泡及其相应硬条畴的影响。发现了一个与材料参量有关的临界温度T₀当试验温度T0时,硬条畴畴壁中的VBL链在升降温后不变;而当T>T₀时,VBL链消失,所有硬磁泡都软化为正常磁泡。当畴壁中的VBL处于压缩态时,较硬的硬磁泡在较低的温度下软化。软化时,VBL消失的方式是整个VBL链的解体。 关键词：     

Internal transverse fluctuation waves in a viscous liquid at a hard boundary

A liquid layer resting on a hard bottom and bounded by hard walls is considered. Analysis of the dispersion relation shows that both slowly decaying solitary waves and rapidly decaying periodic waves may arise inside the layer at the interface between stratified ～100-nm-thick near-surface regions of low-viscous liquids. Stratification is due to the orienting influence of the hard bottom and to fluctuation forces. The dispersion laws for the waves are characteristic of purely capillary waves in both a deep and shallow liquid.     

Stationary nonequilibrium states in boundary-driven Hamiltonian systems: Shear flow

We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell-demon reflection rules at the walls. These deterministic rules conserve energy but not phase space volume, and the resulting global dynamics may or may not be time reversible (or even invertible). Using rules designed to simulate moving walls, we can obtain a stationary shear flow. Assuming that for macroscopic systems this flow satisfies the Navier-Stokes equations, we compare the hydrodynamic entropy production with the average rate of phase-space volume compression. We find that they are equalwhen the velocity distribution of particles incident on the walls is a local Maxwellian. An argument for a general equality of this kind, based on the assumption of local thermodynamic equilibrium, is given. Molecular dynamic simulations of hard disks in a channel produce a steady shear flow with the predicted behavior.     

三类硬磁畴的形成及静态特性

本文提出畴壁中含有大量VBL的石榴石磁泡材料的三类硬磁畴的分类标准,描述了它们的形成方法和静态特性,并示出典型照片。从形成条件可以合理地推论,畴壁中VBL数目的增加导致硬磁畴静态特性的质的变化。 关键词：     

Wall-Induced Density Profiles and Density Correlations in Confined Takahashi Lattice Gases

We propose a general formalism to study the static properties of a system composed of particles with nearest neighbor interactions that are located on the sites of a one-dimensional lattice confined by walls (confined Takahashi lattice gas). Linear recursion relations for generalized partition functions are derived, from which thermodynamic quantities, as well as density distributions and correlation functions of arbitrary order can be determined in the presence of an external potential. Explicit results for density profiles and pair correlations near a wall are presented for various situations. As a special case of the Takahashi model we consider in particular the hard rod lattice gas, for which a system of nonlinear coupled difference equations for the occupation probabilities has been presented by Robledo and Varea. A solution of these equations is given in terms of the solution of a system of independent linear equations. Moreover, for zero external potential in the hard-rod system we specify various central regions between the confining walls, where the occupation probabilities are constant and the correlation functions are translationally invariant in the canonical ensemble. In the grand canonical ensemble such regions do not exist.     

Two disks in a box

Exact analytical expressions are derived for the thermodynamic properties of two discs in square and rhomboidal boxes with hard walls, and in a square cell with periodic boundaries. With periodic boundaries the equation of state has a van der Waals loop and a second order cusp. In a box with hard walls there is a third order “glass transition” which seems to capture the essence of the glass transition observed in systems of a few hundred hard spheres.     

Deuterium isotopic effect in 13C-N.M.R. spectra

We obtain the grand potential and the associated distribution functions for a system of hard rods on a line of finite length. These functions are shown to be related to those of a semi-infinite system bounded by one hard wall. It follows that the contact values of the density and distribution functions at the walls of the finite system are related to those at the wall of the semi-infinite system, and that the force on the walls is the density at contact. We obtain also the density and distribution functions for a system with repeating boundary conditions, which are also expressible in terms of those of the finite and semi-infinite systems.     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

约束条件下的硬球流体

利用密度泛函理论和分子动力学方法 ,对处于两平行硬墙之间的硬球流体的密度分布进行了计算 .通过比较两种方法的结果 ,发现在墙之间距离较大时 ,Rosenfeld密度泛函理论的结果与分子动力学模拟的结果符合很好 ;当两堵墙间的距离很小时 ,这两个结果之间存在明显的不一致 .另外 ,还研究了约束条件下密度分布的结构     

Freezing and glass transition of hard spheres in cavities

Dynamical and static properties of N=13-4000 hard spheres in spherical cavities with smooth and rough walls have been calculated by molecular-dynamics computer simulations. We use a dynamical criterion to distinguish between fluidlike and solidlike states. The associated crossover densities show a strong dependence both on the system size and on the surface roughness. For large N, these crossover densities tend to the bulk glass transition density for rough walls and to the bulk crystallization density for smooth walls. The crossover densities for finite N are found to be significantly smaller than the corresponding bulk densities. A detailed examination of the layer-resolved radial- and tangential mean-square displacements reveals qualitatively different dynamics for smooth and rough cavities.     

Numerical solutions of the acoustic eigenvalue equation in the rectangular room with arbitrary (uniform) wall impedances

Two numerical procedures for finding the acoustic eigenvalues in the rectangular room with arbitrary (uniform) wall impedances are developed. One numerical procedure applies Newton's method. Here, starting with soft walls, the eigenvalues are found by increasing the impedances of each wall pair in small increments up to the terminal impedances. Another procedure poses the eigenvalue problem as one of homotopic continuation from a non-physical reference configuration in which all eigenvalues are known and obvious. The continuation is performed by the numerical integration of two differential equations. The latter procedure was found to be faster and finds all possible solutions. The set of eigenvalues allowed the room modal natural frequencies and damping constants to be obtained. From sound decays measured in a hard-walled rectangular room, and from the collective-modal-decay curve, the impedances of the hard walls are estimated. These are then used to find the reverberation times of the modes in the room with the floor lined with sound absorbing material of known acoustic impedance. It was found that a single reverberation time, for all modes, is only supported in the rectangular room with hard walls and at the higher frequency bands, consistent with Sabine's theory, which assumes a diffuse sound field. In the rectangular room with hard walls and at the lower frequency bands, and in the rectangular room with the floor lined with sound absorbing material and for all frequency bands, modes with rather distinctive reverberation times may produce sound decays not always consistent with Sabine's prediction.     

2-Dimensional polymers confined in a strip

Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance ( is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and monomer density at the wall are compared to theoretical predictions.Received: 14 August 2003, Published online: 8 December 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 07.05.Tp Computer modeling and simulation - 61.41. + e Polymers, elastomers, and plastics     

Monte Carlo simulation of a confined hard ellipse fluid

The structural and thermodynamic properties of a confined hard ellipse fluid are studied using Monte Carlo simulation. The angular, average number densities and order parameters of hard ellipses confined between hard parallel walls are obtained for various bulk densities, aspect ratios and wall separations. The results show that the effect of the existence of the wall on the molecular fluid structure, either on their directions or their locations, with respect to the bulk, especially close to the walls, is significant. For this system the pressure is also obtained and it is shown that the average density at the wall is proportional to the pressure, βP=〈ρ_w〉. Our simulation results show that the order parameters depend on the number of the particles in the box unless it exceeds thousand.     

Shielded distribution approximation for a wall-bounded classical fluid

We investigate lower order distribution functions in classical fluids in the presence of large-scale inhomogeneities, in particular those imposed by wall contacts. The consequences of the effective shielding of a wall by the nearest particle of the set being considered are determined in the context of two distribution function hierarchies, kinematic and dynamic in origin. The effects of both flat and spherical, hard and soft walls are considered, as well as those of curved and double walls. A few correction sequences to the basic shielding approximation are discussed.Supported in part by the Department of Energy under contract DE-AC02-76 ERO 3077.     

Maximum Sound Absorption by a Helmholtz Resonator in a Room at Low Frequencies

Acoustical Physics - The paper considers the problem of sound absorption by a Helmholtz resonator in a room with perfectly hard walls. The resonator parameters are determined that yield the maximum...     

Controlling domain wall chirality by combining hard and soft magnetic materials in planar nanostructures with wire-ring morphology

Vortex domain walls (DWs) are characterized by their chirality, an important property that needs to be controlled for the use of such walls in potential technological applications. In this work we explore a wire-ring structure in which we have alternate hard and soft magnetic materials. Our results evidence that, depending on the materials, it is possible to control the DW chirality when it goes through the ring section. Therefore, this system can be used as a device that controls domain wall chirality.     

微通道板的新应用——X射线准直器

应用微通道板通道玻璃表面对大角入射的X射线吸收和小角入射的X射线全反射的特性,讨论适用于硬X射线和软X射线准直的两种类型微通道板,分析影响准直性能的因素。最后,对硬X射线微通道板准直器的辐射通量与通用准直器的进行比较。