Numerical integration of the fluctuating hydrodynamic equations

An approach to numerically integrate the Landau-Lifshitz fluctuating hydrodynamic equations is outlined. The method is applied to one-dimensional systems obeying the nonlinear Fourier equation and the full hydrodynamic equations for a dilute gas. Static spatial correlation functions are obtained from computer-generated sample trajectories (time series). They are found to show the emergence of long-range behavior whenever a temperature gradient is applied. The results are in very good agreement with those obtained from solving the correlation equations directly.     

Existence theory of the linear equations appearing in the Chapman-Enskog solutions to two kinetic equations for liquids

The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.Sloan Foundation Fellow 1968–70. Guggenheim Fellow 1969–70.     

Molecular associations in binary mixtures of pyridine and chlorobenzene in benzene solution using microwave absorption data

The dielectric relaxation time (τ) of binary mixtures of different molar concentrations of pyridine (C₅H₅N) and chlorobenzene (C₆H₅Cl) in benzene solution at different temperatures (25, 30, 35 and 40 °C) has been calculated by using standard microwave techniques and Gopala Krishna's single frequency (9.875 GHz) concentration variation method. The energy parameters (ΔH_ε, ΔF_ε, and ΔS_ε) for the dielectric relaxation process of the binary mixture containing 0.5 mol fraction of pyridine have been calculated at the respective temperatures. Comparisons have been made with the corresponding energy parameters for the viscous flow (ΔH_η, ΔF_η, and ΔS_η). From the observations it is found that the dielectric relaxation process can be treated as the rate process. Based upon above studies, solute–solvent type of molecular associations arising from the interaction of chlorobenzene and benzene and pyridine and benzene molecules has been proposed. No solute–solute type of molecular association has been observed.     

On the derivation of quantum kinetic equations. I. Collision expansions

A straightforward scheme for deriving quantum kinetic equations is presented. It is based on Bogoliubov's initiai condition of vanishing correlations in the infinite past and consists in the elimination of an initial oneparticle Wigner function between two nonlinear functionals. By performing the elimination to second order in the density the quantum analog of the Choh-Uhlenbeck three-particle collision term is obtained. The scheme may be extended to include relativistic particles as well as particles with internal degrees of freedom.This investigation is part of the research program of the Stichting voor fundamenteel onderzoek der materie (FOM), which is financially supported by the Organisatie voor zuiver-wetenschappelijk onderzoek (ZWO).     

Time Evolution in Macroscopic Systems. I. Equations of Motion

Time evolution of macroscopic systems is re-examined primarily through further analysis and extension of the equation of motion for the density matrix (t). Because contains both classical and quantum-mechanical probabilities it is necessary to account for changes in both in the presence of external influences, yet standard treatments tend to neglect the former. A model of time-dependent classical probabilities is presented to illustrate the required type of extension to the conventional time-evolution equation, and it is shown that such an extension is already contained in the definition of the density matrix.     

The statistical mechanical resolution of a thermodynamic “paradox”

We discuss a thermodynamic paradox suggested by Fallows and Greenleaf. Using quantum statistical mechanics, we analyze the problem in detail, showing why no paradox arises.This work was carried out some time ago, circulated as a MIT internal report, and has since enjoyed a modest popularity. We are pleased to publish it more broadly in this volume dedicated to the memory of such an outstanding researcher as Prof. P. Résibois. (MOS)     

Ergodic Properties for a Quantum Nonlinear Dynamics

We present a quantum system composed of infinitely many particles, subject to a nonquadratic Hamiltonian, for which it is possible to investigate the long time behavior of the dynamics and its ergodic properties. We do so both for the KMS states and for a large class of locally normal invariant states, whose very existence is already of some interest.     

On the Asymptotic Convergence of the Transient and Steady-State Fluctuation Theorems

Nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady-state forms of the fluctuation theorem. In the case of planar Poiseuille flow, we find that the transient form, valid for all times, converges to the steady-state predictions on microscopic time scales. Further, we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady-state fluctuation theorem.     

Light scattering from a nonequilibrium fluid undergoing a planar Poiseuille-Couette flow

We calculate the Rayleigh-Brillouin spectrum of a Newtonian fluid undergoing a planar Poiseuille-Couette flow using the fluctuating hydrodynamic approach of Landau and Lifshitz. Our results reduce to the corresponding results for pure Couette flow when the pressure gradient is made to vanish. The Brillouin spectrum is obtainable from that appropriate to Couette flow by a simple rescaling. There are very minute corrections which impart asymmetry to the Brillouin lines as well as the Rayleigh line, and these can be selectively picked up by suitable choice of the scattering geometry.     

On the derivation of quantum kinetic equations. II. Nonlocal Uehling-Uhlenbeck equation

The binary and triple collision terms of the quantum kinetic equation derived previously are analyzed in the weak coupling approximation. In this approximation the equation appears to be a nonlocal Markovian extension of the kinetic equation due to Uehling and Uhlenbeck. After linearization, its relationship with non-Markovian formulations found in the literature is studied.This investigation is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO).     

Molecular model for the VLE p- T-x relationships of binary mixtures

An analytical expression for the pressure-temperature-composition relations in the vapour - liquid equilibrium of non-polar binary mixtures is proposed. The model is based on a simple analytical expression for the vapour pressure of pure non-polar fluids, which, for a given temperature, requires as input only the Lennard- Jones molecular parameters and the acentric factor of the substance. The equilibrium mixture pressure is then expressed as a function of the vapour pressure of each component and of a mixture contribution. The molecular parameters required for this mixture contribution are related to the molecular parameters of the pure component through a modified Lorentz-Berthelot mixing rule, where the interaction parameters are given as simple functions of the temperature and composition, with eight appropriate constants for each binary mixture. We show that the model permits one to reproduce or predict in a simple way the pressure (for a given liquid mole fraction) or the liquid composition (for a given pressure).     

Self-consistent derivation of subgrid stresses for large-scale fluid equations

A self-consistent procedure for deriving subgrid scale models for a complex system of equations is presented. When applied to the Navier-Stokes equation for incompressible flow it reproduces the differential version of the stress-similarity model with a correct coefficient. As an example the complete system of equations is derived for an ocean global circulation model.     

On the derivation of the Burnett hydrodynamic equations from the Hilbert expansion

We have derived the Burnett-order transport equations by applying the Hilbert expansion to the steady BGK equation. The pressure tensor and heat flux vector are computed for potentials of the form r^−μ. The calculated transport coefficients are compared with those obtained by means of the Chapman-Enskog expansion.     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999     

Correlation functions for simple fluids in a finite system under nonequilibrium constraints

The Landau-Lifschitz fluctuating hydrodynamics formalism is applied to study the statistical properties of simple fluids in a finite system under nonequilibrium constraints. The boundary conditions are explicitly taken into account so that the results can be compared with particle simulations. Two scenarios are investigated: a fluid subjected to a constant shear and a fluid subjected to a constant temperature gradient. By considering a fluid with vanishing thermal expansivity, exact results are obtained for the static and dynamic correlation functions.     

Induced twisted-grain-boundary phases in the binary mixtures of a cholesteric and a nematic compound

Thermodynamical, optical-texture and dielectric studies have been performed to study the phase diagram of the binary system of 5-cholesten-3β-ol-octanoate and 4-n-nonyloxybenzoic acid. It is observed that low concentrations of 5-cholesten-3β-ol-octanoate (2–30?mol?%) in 4-n-nonyloxybenzoic acid induce a mean-field phase diagram derived by Renn within the framework of the chiral Chen–Lubenski model. Various optical textures of the twisted-grain-boundary (TGB) phases under different conditions of molecular anchoring have been observed. Weak transitions related to the TGB phases have been detected by temperature dependent dielectric spectroscopy.     

Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid

The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boiling-saturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 60°, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 0° to 30° and 60° to 90°.     

Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. In this work, the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles, free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis. The momentum space distribution is determined by a random walk argument, and the position space distribution is determined by employing the equiprobability and ergodicity principles. The expressions for energy, entropy, free energy, and pressures are then deduced, and the relation among external force, drift velocity, and temperature is also established. Moreover, the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.     

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.