Theory of molecular motion in liquids and glasses over broad temperature and pressure ranges

An equation for the molecular relaxation time in molten glasses is derived on the basis of hole theory. This equation is a generalization of the familiar equations of Frenkel', Shishkin, Jenckel, et al. The effects of temperature and pressure on the molecular mobility in liquids and glasses are discussed, and there is a discussion of the high-pressure plasticity of inorganic glasses.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 2, pp. 17–23, February, 1971.     

A statistical-mechanical theory of self-diffusion in glass-forming liquids

A statistical-mechanical theory of self-diffusion in glass-forming liquids is presented. A non-Markov linear Langevin equation is derived from a Newton equation by employing the Tokuyama-Mori projection operator method. The memory function is explicitly written in terms of the force-force correlation functions. The equations for the mean-square displacement, the mean-fourth displacement, and the non-Gaussian parameter are then formally derived. The present theory is applied to the glass transitions in the glass-forming liquids to discuss the crossover phenomena in the dynamics of a single particle from a short-time ballistic motion to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of analyses of the simulation results by the mean-field theory proposed recently by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that for times longer than the β-relaxation time the dynamics of a single particle is identical to that discussed in the suspensions.     

The statistical theory of the condensed system equation of state at high pressures

Abstract

One of the main problems in the statistical physics of condensed systems is the problem of the adequate equation of state to describe the thermodynamical properties of the substance in the wide range of pressure values. Here it is being solved by means of thermodynamic perturbation theory and the integral equations of the statistical theory of dense gases and liquids.     

Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering

A modification of the classical Navier–Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11–59; Navier–Stokes revisited, Physica A 349 (2005) 60–132] and then formalized by Öttinger [Beyond Equilibrium Thermodynamics, Wiley, Hoboken, 2005]. In the modified theory, a contribution for mass diffusion is included in the continuity equation. The argument was based on experimental support from thermophoresis which however depends on the correct formulation of boundary conditions. The controversy therefore remained. Since such an additional mass diffusion transport mode should contribute to dynamic light scattering spectra, the consequences of the modified theory for light scattering spectra are discussed in this work. For liquids, the new theory is consistent with measured scattering data since the modification to the spectrum is usually negligible. The effect could, however, be observable in gases.     

Quantum corrections to the radial distribution function of a fluid

The perturbation theory developed for liquids is used to derive an expression for the first-order quantum correction to the radial distribution function of a fluid. The result is given in terms of grand canonical ensemble distribution functions for the classical fluid. The equations giving the thermodynamic functions in terms of the radial distribution function are discussed, and differences in the quantum and classical cases emphasized. An equation relating the two- and three-body classical distribution functions, derived recently by Singh and Ram using an indirect method, is shown to be simply related to the second equation of the BGY hierarchy.     

丛聚的含气泡水对线性声传播的影响

含气泡水内气泡的空间分布会对线性声传播产生影响,导致实验结论与理论预测存在较大偏差.为解决这一问题,将准晶体近似引入到自洽方法中,导出了考虑空间分布时多分散含气泡水的等效声波波数.考虑到含气泡水内,气泡间存在小范围的聚集趋势(简称丛聚现象),在此基础上引入Neyman-Scott点过程描述了含气泡水内气泡的丛聚现象.分析发现,丛聚时,声速、声衰减的峰值将受到抑制,并向低频偏移,且抑制和频偏现象会随丛聚加剧而变强;随频率远离峰值段,丛聚对声传播的影响逐渐减弱.此外,考虑到空间分布的统计信息提取对相关研究的精确与否起到重要作用,引入了一种比例无偏估计,通过该方法获得了仿真环境下丛聚含气泡水模型的相速度及衰减系数,该建模及统计方法也可为相关实验工作提供理论基础.     

Mechanism for creation of critical phenomena in liquids

In the present paper, we study general methods of solving the Ornstein-Zernike equation to find out what refinements are to be introduced into these equations for them to describe properties of liquids not only in the regular domain of the phase diagram but also in a neighborhood of the critical point. This approach enabled us to obtain, by using the Ornstein-Zernike equation, practically all known results of scaling theory and to establish some specific features of critical phenomena that were not known earlier.     

The refined theory of transversely isotropic piezoelectric rectangular beams

The problem of deducing one-dimensional theory from two-dimensional theory for a transversely isotropic piezoelectric rectangular beam is investigated. Based on the piezoelasticity theory, the refined theory of piezoelectric beams is derived by using the general solution of transversely isotropic piezoelasticity and Lur’e method without ad hoc assumptions. Based on the refined theory of piezoelectric beams, the exact equations for the beams without transverse surface loadings are derived, which consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beams under transverse loadings are derived directly from the refined beam theory. As a special case, the governing differential equations for transversely isotropic elastic beams are obtained from the corresponding equations of piezoelectric beams. To illustrate the application of the beam theory developed, a uniformly loaded and simply supported piezoelectric beam is examined.     

A theory of electric polarisation in liquids : I. Nonpolar liquids

The static dielectric constant of nonpolar liquids is described by analyzing the pair distribution function and the dipole-dipole interaction into a finite set of Fourier components. In a mean field approximation the theory leads to a final formula that does not contain any adjustable parameter, and proves to work better than the Clausius-Mossotti equation. The theory explains in a satisfactory way the temperature and pressure dependence of the dielectric constant of nonpolar liquids, as well as the temperature variation of the refractive index of many organic polar liquids.     

Changes in the refractive indices of absorbing liquids under the action of pulsed laser radiation

Changes in the refractive indices of weakly absorbing liquids exposed to pulsed laser radiation have been calculated as functions of space and time based on numerical solution of equations for continuous media motion in the Lagrange form, the heat-conduction equation, and the Lorentz–Lorenz formula.     

The refined theory of deep rectangular beams based on general solutions of elasticity

The problem of deducing one-dimensional theory from two-dimensional theory for a homogeneous isotropic beam is investigated. Based on elasticity theory, the refined theory of rectangular beams is derived by using Papkovich-Neuber solution and Lur’e method without ad hoc assumptions. It is shown that the displacements and stresses of the beam can be represented by the angle of rotation and the deflection of the neutral surface. Based on the refined beam theory, the exact equations for the beam without transverse surface loadings are derived and consist of two governing differential equations: the fourth-order equation and the transcendental equation. The approximate equations for the beam under transverse loadings are derived directly from the refined beam theory and are almost the same as the governing equations of Timoshenko beam theory. In two examples, it is shown that the new theory provides better results than Levinson’s beam theory when compared with those obtained from the linear theory of elasticity.     

Dynamic Theory of Die Swell for Entangled Polymeric Liquids in Tube Extrusion: Correlations of Total and Ultimate Extrudate Swell Effects to Growth Time, Shear Stress and Aspect Ratio Under the Free States

利用挤出胀大动力学理论研究稳态剪切流下HDPE 和PBD液体的挤出胀大行为,建立了自由动态下线团回复和挤出胀大增长时间的回复机制和动力学. 结果表明在自由回复过程中自由线团回复和挤出物胀大增长可分为两个区域(瞬间和推迟区)、三个增长阶段(瞬间、推迟和最终阶段). 证明了自由线团回复和挤出胀大增长可表征为增长时间、剪切应力和长径比的函数。从而从动力学理论推倒出了三种挤出胀大效应(瞬间、推迟和最终)同分子结果参数和挤出操作条件间的相关性. 并建立了总合(TESE)和最终(UESE)两组挤出胀大效应的普适方程.     

缠结高分子液体在管中挤出胀大动力学理论：一组新的增长和最终挤出胀大比方程

基于O-W-F本构方程和自由回复机制，从Poioeuille流出发建立了一种新的缠结高分子液体挤出胀大动力学理论，该理论能有效地预测高分子流体的动静态挤出胀大行为同高分子粘弹性参数和成型条件间的相关性. 基于稳态剪切量可分解为自由“回复线团”和“不可回复热耗”两部分事实，定义了一个稳态剪切下自由“回复线团”和“不可回复热耗”的配分函数和它们两者间分配指数上可回复和不可回复构象分数，从而在理论上得到了瞬时、推迟和最终三者可回复形变量和可回复线团量同配分函数、分配指数上可回复构象分数、分子粘弹性参数和成型条件     

Density functional theory of liquids, some extensions and applications

The density functional theory(DFT) of nonuniform liquids plays an important role in classical many-body theory because of its (mathematical)simplicity and (physical)clarity. Some extensions and applications of DFT, including a new proposal for an m-body hypernetted-chain(HNC) equation for the static structure of liquids are presented.     

Microscopic derivation of Landau's transport theory of Fermi liquids

The linearized version of Landau's transport theory of Fermi liquids is derived using Green's-function techniques. The transport equation includes high-frequency corrections in the collision integral and describes situations which vary on a scale larger than atomic. Landau's expressions for the densities and currents of conserved quantities are verified by a comparison with exact expressions.     

Weakly nonlinear propagation of focused ultrasound in bubbly liquids with a thermal effect: Derivation of two cases of Khokolov–Zabolotskaya–Kuznetsoz equations

A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived. Especially, the dissipation term depends on three factors, i.e., interfacial liquid viscosity, liquid compressibility, and thermal conductivity of gas inside bubbles; the thermal conduction is evaluated by using four types of temperature gradient models. Finally, we numerically solve the derived KZK equation and show a moderate temperature rise appropriate to medical applications.     

Quasiclassical boundary conditions for Fermi liquids at surfaces

The general boundary conditions at surfaces are derived within the quasiclassical theory of superfluidity in Fermi liquids (superconductors, superfluid³He). These conditions supplement the transport-like equations first introduced into the theory of superconductivity by G. Eilenberger, and allow a quantitative analysis of superfluids near a wall.     

Application of methods of the scattering theory in the statistical theory of liquids

This paper is devoted to the application of the projection methods of the nonrelativistic quantum theory of scattering (the method of Petrov-Bubnov-Galerkin (PBG) and the Bubnov-Galerkin (BG) method) in the statistical theory of liquids. By means of the projection PBG method we have found a new family of equations both for the correlation functions and for the radial distribution function (RDF). In the generalized equation for the RDF we have obtained new terms which are linear and quadratic in the density and the latter are absent in all the previous theories. By means of the projection BG principle the approximate eigenfunctions of the Liouville operator in a liquid were obtained as a linear combination of the Kihara functions. It was shown that the spectrum of the collective excitations is determined by the complex Fourier transformation of the force acting on an arbitrary particle in a liquid.     

Vitrification in a 2D Ising model with mobile bonds

A bond-disordered two-dimensional Ising model is used to simulate Kauzmann's mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to nearest neighbors at the same rate as the spins flip. For slow cooling, the theoretical minimum energy configuration is approached, characterized by an amorphous distribution of locally optimally arranged impurity bonds. Rapid cooling to low temperatures regularly finds bond configurations of higher energy, which are both a priori rare and severely restrictive to spin movement, providing a simple realization of kinetic vitrification. A supercooled liquid regime is also found, and characterized by a change in sign of the field derivative of the spin-glass susceptibility at a finite temperature. Received 3 August 2000 and Received in final form 9 March 2001     

Optoacoustic effects in absorbing liquids under the action of pulsed bessel light

The excitation of acoustic oscillations in absorbing liquids exposed to pulsed Bessel light beams has been considered theoretically. Spatial profiles of refractive index diffraction patterns and the kinetics of their excitation and relaxation have been studied based on a numerical solution of continuous medium motion equations in a Lagrangian form and a heat-transfer equation and using the Lorentz–Lorenz formula. The conditions for optimal excitation of spatially localized acoustic pulses have been determined.