The homogeneous-shear (HS) technique has been used extensively to study shear flow, but it uses artificial methods to remove the viscous heat generated. In reality the viscous heat is removed from the system by conduction out through the boundaries. This inevitably leads to characteristic gradients in temperature, density, and shear rate. While at low shear rates these effects may be neglected, and the use of HS justified, at high shear rates they certainly cannot, and doubts remain as to the validity of HS in this regime. In this study we make careful comparisons between HS and a more-realistic sliding-boundary method. HS gives very similar results when conditions corresponding to different regions within the sliding system are used. The use of HS simulations at shear rates where energy is generated at a rate faster than can be realistically removed by any natural process is called into question.

We investigate the influence of a horizontal plane Poiseuille shear flow transversal to the convective roll chain of the Rayleigh-Bénard problem. Using a one-dimensional (1D) amplitude equation and a 2D numerical simulation of the basic field equations, we study how different boundary conditions at the inlet and outlet of the channel affect nonlinear convection. If convection is suppressed near the cell apertures, spatially localized traveling-wave states appear with a uniquely selected bulk wavelength. For convectively unstable parameters this pattern is pushed out of the channel; however, the system becomes very sensitive to perturbations, and noise-driven structures occur. Phase-pinning boundary conditions lead for very small flows to stationary roll patterns with a space-dependent wavelength decreasing downstream. Strengthening the throughflow causes local Eckhaus instabilities, which finally generate a transition to propagating rolls.

The linear stability of pure-fluid Rayleigh-Bénard convection in a finite cell of arbitrary geometry can be formulated as a self-adjoint eigenvalue problem. This, when coupled with perturbation theory, allows one to deduce how the sidewalls affect its stability. In particular, it is shown that for almost all boundary conditions the difference between the onset Rayleigh number and its infinite-cell limit scales like ${\mathit{L}}^{\mathrm{-}2}$ as the cell dimension L tends to ∞, and near the sidewall the temperature and velocity are of order ${\mathit{L}}^{\mathrm{-}1}$ compared to their bulk values. The validity of replacing the true thermal boundary condition by a frequently used mathematically simpler homogeneous one is also demonstrated.

We investigate how the criteria for two prototype instabilities in one-dimensional pattern-forming systems, namely for the Eckhaus instability and for the Benjamin-Feir instability, change as one goes from a continuous bifurcation to a spatially periodic or spatially and/or time-periodic state to the corresponding weakly inverted, i.e., hysteretic, cases. We also give the generalization to two-dimensional patterns in systems with anisotropy as they arise, for example, for hydrodynamic instabilities in nematic liquid crystals.

The stability behavior of the conductive state of binary gas mixtures in the Rayleigh-Bénard setup is significantly altered in comparison to binary liquid mixtures due to their different thermodynamic and transport properties. In particular, the Dufour effect influences dramatically the topology and the existence ranges of the oscillatory and stationary instabilities for Dufour and Lewis numbers that are typical in gas mixtures. We present a detailed investigation of the changes of the stability properties for several types of boundary conditions including the realistic no-slip, impermeable ones.

For a dense gas equilibrium mixture of 65 at.% He and 35 at.% Ne at T=39.3 K and p=114 bar, we determine from neutron scattering the total dynamic structure factor S(k,ω) as a function of frequency ω for wave numbers 4<k<28 ${\mathrm{nm}}^{\mathrm{-}1}$. For all k, S(k,ω) is a sum of four Lorentzians; two located at ω=±${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{}\left(1\right)\mathrm{}}$(k) (directly visible for smaller k) and two located at ω=±${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{}\left(2\right)\mathrm{}}$(k) (not visible). ${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{}\left(1\right)\mathrm{}}$(k)>ck can be attributed to fast oscillations of the light He particles (fast sound) and ${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{}\left(2\right)\mathrm{}}$(k)<ck to slow oscillations of the heavy Ne particles (slow sound), where c is the hydrodynamic (k→0) sound velocity of the total mixture. ${\mathrm{\omega }}_{\mathit{s}}^{\mathrm{}\left(1\right)\mathrm{}}$(k) is virtually indistinguishable from the (extended) sound dispersion measured in pure helium at T=39.3 K and p=114 bar. A kinetic model, consistent with our experiment, predicts that fast sound vanishes at k=0.7 ${\mathrm{nm}}^{\mathrm{-}1}$ and that slow sound merges into hydrodynamic sound then.

Lyotropic nematic liquid crystals, like their thermotropic counterparts, exhibit collective reorientation modes known as director fluctuations. In this work we consider the effect of director fluctuations on the transverse spin relaxation of quadrupolar nuclei in uniaxial lyotropic nematic liquid crystals, reporting ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ (labeled surfactant) and ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ (counterion) relaxation data from the calamitic (${\mathit{N}}_{\mathit{C}}^{+}$) and discotic (${\mathit{N}}_{\mathit{D}}^{\mathrm{-}}$) phases of the system sodium dodecyl sulphate-decanol-water. The transverse relaxation is found to be dominated by a large contribution to the secular zero-frequency spectral density from diffusion-modulated (counterion) or viscoelastic (surfactant) director fluctuations. The existing theory of nuclear-spin relaxation by director fluctuations is extended to include the effect of translational diffusion on the fourth-order director-fluctuation time correlation functions. In contrast to thermotropic nematics, the second-order director-fluctuation contribution to the nonsecular high-frequency spectral densities is negligible in lyotropic nematic liquid crystals at conventional magnetic fields. This is a consequence of the much longer short-wavelength cutoff in lyotropic liquid crystals. The large zero-frequency spectral density, however, allows us to deduce the viscoelastic properties of the nematic phases, obtaining effective elastic constants of 0.3–1.0 pN in the investigated temperature range. The nematic order parameter is found to be significantly influenced by collective modes as well as by local micelle reorientation. For the oblate micelles in the ${\mathit{N}}_{\mathit{D}}^{\mathrm{-}}$ phase, the local modes are most important, whereas the reverse is true for the prolate micelles in the ${\mathit{N}}_{\mathit{C}}^{+}$ phase. In the surfactant case, the longest-wavelength-director-fluctuation modes are too slow to motionally average the nuclear-quadrupole coupling, resulting in a static broadening of the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$ satellites.

It is shown that every true macroscopic variable in a set that provides the complete macroscopic description of a medium has a significant conserved part. Upon taking this into account it becomes possible to extend significantly the validity range of the simplest theory of viscoelasticity, which is developed from first principles in the present paper. Because of such an extension a dimensionless parameter, the value of which characterizes the degree of the solidification of the viscoelastic fluids, naturally appears in the theory. The expressions for the elastic constants and the transport coefficients through equal-time correlation of microscopic quantities and Green-Kubo-type formulas are obtained. The behavior of the transverse and longitudinal oscillations in simple viscoelastic fluids as well as the related behavior of the transverse momentum and density autocorrelation functions is studied. The results are in agreement with experiments. In particular, it turns out that liquid Ar at the triple point is partly solidified.

The twist, splay, and bend Fréedericksz transitions induced by electric or magnetic fields in zero-field undistorted nematic cells are known to be second order, except the bend transition induced by an electric field, which can be first order. By a theoretical analysis, we show that similar transitions, with threshold and symmetry breaking, can be obtained in zero-field distorted cells—the distortion being imposed by a +${\mathit{cphi}}_{\mathit{b}}$ and a -${\mathit{cphi}}_{\mathit{b}}$ rotation of the director at the two boundary planes—with pure twist, predominantly splay and predominantly bend distortion. The transitions that are second order for ${\mathit{cphi}}_{\mathit{b}}$→0 preserve their order for any value of ${\mathit{cphi}}_{\mathit{b}}$, and the critical field is an increasing function of such angle, whereas the first-order bend transition induced by an electric field becomes second order above a critical value of ${\mathit{cphi}}_{\mathit{b}}$. We discuss the stability of the possible director configurations and the role of the critical fluctuations in driving the transitions.

In this paper we extend the variational modified hypernetted-chain theory to multicomponent liquids. Following the hypothesis of universality of the bridge functions we use the additive hard-sphere Percus-Yevick bridge functions. This can be seen as a first step in a bootstrap procedure. The theory is applied to binary mixtures interacting via Lennard-Jones potentials, and its accuracy is assessed by comparing with simulation results. We also compare this theory with others regarded to be of comparable accuracy.

Using molecular-dynamics computer simulation, we study the dynamical behavior of the isotropic and nematic phases of highly anisotropic molecular fluids. The interactions are modeled by means of the Gay-Berne potential with anisotropy parameters κ=3 and κ’=5. The linear-velocity autocorrelation function shows no evidence of a negative region in the isotropic phase, even at the higher densities considered. The self-diffusion coefficient parallel to the molecular axis shows an anomalous increase with density as the system enters the nematic region. This enhancement in parallel diffusion is also observed in the isotropic side of the transition as a precursor effect. The molecular reorientation is discussed in the light of different theoretical models. The Debye diffusion model appears to explain the reorientational mechanism in the nematic phase. None of the models gives a satisfactory account of the reorientation process in the isotropic phase.

We show that the length scale ${\mathrm{\alpha }}^{\mathrm{-}1}$, which appears in the interfacial binding potential of the effective Hamiltonian description of wetting transitions, should be identified with the ‘‘true’’ or exponential range of the pair-correlation function of the bulk (wetting) phase, rather than the Ornstein-Zernike (second-moment) bulk correlation length ${\xi }_{\mathit{b}}$. Since ${\mathrm{\alpha }}^{\mathrm{-}1}$>${\xi }_{\mathit{b}}$, this implies that the parameter ω=${\mathit{k}}_{\mathit{B}}$T${\mathrm{\alpha }}^2$/4πΣ̃, which determines the values of critical exponents for critical wetting in three dimensions, is significantly smaller than initial estimates of this quantity. For the simple-cubic Ising model (α${\xi }_{\mathit{b}}$${)}^{\mathrm{-}1}$≊1.46 for T≳${\mathit{T}}_{\mathit{R}}$, the roughening temperature, and depending on the magnitude of the interfacial stiffness Σ̃, we conclude ω≲0.5 is appropriate for such temperatures. We discuss the implications for recent Monte Carlo studies of critical wetting.

The role of the Percus-Yevick hard-sphere bridge function in the modified hypernetted-chain integral equation is examined within the context of Lado’s criterion [F. Lado, S. M. Foiles, and N. W. Ashcroft, Phys. Rev. A 28, 2374 (1983)]. It is found that the commonly used Lado’s criterion, which takes advantage of the analytical simplicity of the Percus-Yevick hard-sphere bridge function, is inadequate for determining an accurate static pair-correlation function. Following Rosenfeld [Y. Rosenfeld, Phys. Rev. A 29, 2877 (1984)], we reconsider Lado’s criterion in the so-called variational modified hypernetted-chain theory. The main idea is to construct a free-energy functional satisfying the virial-energy thermodynamic self-consistency. It turns out that the widely used Gibbs-Bogoliubov inequality is equivalent to this integral approach of Lado’s criterion. Detailed comparison between the presently obtained structural and thermodynamic quantities for liquid alkali metals and those calculated also in the modified hypernetted-chain theory but with the one-component-plasma reference system leads us to a better understanding of the universality property of the bridge function.

Studies in two dimensions have been made of the evolution of an initially linear interface between two liquid areas by both continuum hydrodynamics and molecular dynamics. It was found that at both levels the interface evolves into a fractal curve. While the limiting fractal dimensionalities (D) of the continuum and molecular interfaces differ, this difference is no greater than that that can be induced in the hydrodynamic results by marked changes in the initial conditions and/or fluid parameters. There is, however, a marked qualitative difference in the initial values of D. This is discussed and shown to be a natural consequence of the molecular discreteness of the real liquids.

A three-parameter equation is proposed to describe the separation temperatures and hexagonal-mesophase melting temperatures of nonionic n-alkyl oligo-oxyethylene surfactants in water. The temperature of the separation point is well reproduced by the equation starting from a simple balance principle of hydrophilic and hydrophobic parts in the amphiphile monomer. The oxyethylene of the amphiphile contributes a stabilizing effect. This part tends to increase the separation temperature. Increasing the size of the hydrocarbon part lowers the separation temperature. Thus, micelle size or form (spheres or cylinders), or the properties of the critical process (critical exponents) are not primary determinants of the separation temperature. The hexagonal-phase melting temperature depends strongly on the length of the monomer-oxyethylene part; the hydrocarbon part has a smaller effect.

We develop a method for calculating the physical and geometric properties of atomic clusters in a very general aggregation model. Our method accommodates an arbitrary interparticle potential. It also allows the use of a very wide range of pairing criteria for specifying which configuations are considered to form clusters. We develop an exact differential equation satisfied by the generating function for the quantities {${\mathit{n}}_{\mathit{c}}$(k)}, where ${\mathit{n}}_{\mathit{c}}$(k) is the mean number per unit volume of clusters containing exactly k atoms. We discuss economic methods of solving this equation; a second paper is planned to discuss numerical solutions in detail. We show that the analog, for continuum percolation, of the virial theorem is an exact rate equation of Smoluchowski type for the cluster densities, in which the time is replaced by the total particle density. In this equation, the rate constants are given by contact values of connectedness functions. Applications of this rate equation are discussed. We also give an exact equation for the generating function for cluster volumes. Extensions of the method to calculate cluster free energies economically are described.

Methodological problems of the temperature control (thermostat) in nonequilibrium-molecular-dynamics simulations of dense liquids undergoing a stationary planar shear flow are addressed. They arise in connection with a transition into a shear-induced ordered state at high shear rates which goes along with inhomogeneities of the fields of density, temperature, and velocity gradient (shear rate) on the length scale of a particle diameter. We demonstrate that a meaningful local description of the thermodynamic fields can be achieved by a smoothing procedure. In particular, the local temperature is related to the width of a local Maxwellian velocity-distribution function. These results are employed for a formulation of a so-called profile-unbiased thermostat which fulfills the criterion of the local-equilibrium hypothesis.

Light-scattering studies of the liquid-glass transition of ${\mathrm{Ca}}_{0.4}$${\mathrm{K}}_{0.6}$(${\mathrm{NO}}_3$${)}_{1.4}$ have been carried out from 305 to 23°C. Composite spectra covering over four decades in frequency were obtained by combining data obtained with a Sandercock tandem Fabry-Pérot interferometer and Raman spectra. Two-step relaxation processes were observed in the supercooled liquid near the glass transition. The α relaxation exhibits a temperature-independent stretching for T>${\mathit{T}}_{\mathit{c}}$ with ${\mathit{T}}_{\mathit{c}}$≊105 °C, which is about 45°C above the glass transition temperature. The β-relaxation frequency scale indicates critical slowing down when the temperature approaches ${\mathit{T}}_{\mathit{c}}$ from either above or below. Scaling analyses for both α and β relaxations provide good agreement with the predictions of mode-coupling theory.

We have investigated the phenomenon of intense dynamic light scattering at the nonequilibrium crystal-melt interface in succinonitrile and naphthalene, in order to resolve the ongoing controversy over its origin. Of the several models that have been proposed to explain this phenomenon, the microbubble model of H. Z. Cummins et al. [Solid State Commun. 60, 857 (1986)] and the mesophase model proposed by J. Bilgram and co-workers [P. Boni, J. H. Bilgram, and W. Kanzig, Phys. Rev. A 28, 2953 (1983)] are the only two still considered to be consistent with most of the experimental observations. In these experiments the angular dependence of the scattered light was investigated. In the mesophase model the angular dependence of the scattered light is described by the Ornstein-Zernike form I(q)=${\mathit{I}}_0$(1+${\mathit{q}}^2$${\xi }^2$${)}^{\mathrm{-}1}$, whereas light scattered by bubbles can be modeled by the Mie scattering theory. The data for both materials were found to be incompatible with the Ornstein-Zernike form, but could be reasonably well fit by the Mie theory. The behavior of the onset of scattering was also investigated, and it was found that the product ${\mathit{R}}_0$${\mathit{t}}_0$${\mathit{v}}_{\mathit{g}}^2$ was a constant, where ${\mathit{R}}_0$ is the onset radius, ${\mathit{t}}_0$ the onset time, and ${\mathit{v}}_{\mathit{g}}$ the crystal growth velocity. This result is consistent with the analysis of Mesquita et al. [Phys. Rev. B 38, 1550 (1988)], in which the onset of the scattering was modeled by considering the rate of buildup of dissolved gas at the advancing crystal-melt interface. The time taken for the disappearance of the scattering after growth was terminated was also investigated. Lastly, the gases dissolved in our samples of succinonitrile were identified by mass spectroscopy and found to have a composition similar to air.

We solve exactly a one-dimensional reversible coagulation A+A?A in a discrete spatial formalism using a technique involving the probability ${\mathit{E}}_{\mathit{n}}$(t) of finding an empty interval n at time t, introduced by Burschka, Doering, and ben-Avraham (BDB) [Phys. Rev. Lett. 63, 700 (1989)]. Our results show that the lattice effect (finite lattice spacing l) does not change qualitatively a dynamic phase transition predicted by BDB in a spatial continuum formalism, and can be minimized quantitatively by choosing a small value of the equilibrium concentration. The continuum results can be obtained by setting l→0 in the discrete solution.