Evolution of slow magnetoacoustic perturbations is used to demonstrate a new mechanism of plane Couette flow shear energy transformation. The initial uniform magnetic field is considered to be directed along the unperturbed flow velocity. We find that the amplification of waves is nonordinary—it occurs in a limited time interval and is anomalously strong. The unusual behavior is manifested also by the fact that the characteristic length scale of perturbation diminishes down to the dissipative scales not only due to nonlinear cascade processes, but due to a linear drift in the k space as well.

We consider the effect of viscosity on Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities by deriving a moment equation for fluids with arbitrary density and viscosity profiles, including surface tension. We apply our result to the classical case of two semi-infinite fluids with densities ${\mathrm{\rho }}_1$ and ${\mathrm{\rho }}_2$ and viscosities ${\mathrm{\mu }}_1$ and ${\mathrm{\mu }}_2$. Treating a shock as an instantaneous acceleration we find that perturbations at the interface undergo damped oscillations when viscosity and surface tension are both present. For pure viscosity the amplitude η(t) evolves according to η(t)/η(0)=1+(ΔvA/2kν)(1-${\mathit{e}}^{\mathrm{-}2\mathit{k}2}$νt) where Δv is the jump velocity imparted by the shock, A=(${\mathrm{\rho }}_2$-${\mathrm{\rho }}_1$)/(${\mathrm{\rho }}_2$+${\mathrm{\rho }}_1$), ν=(${\mathrm{\mu }}_1$+${\mathrm{\mu }}_2$)/(${\mathrm{\rho }}_1$+${\mathrm{\rho }}_2$), k=2π/λ is the wave number of the perturbation, and t is time. We also consider the turbulent energy in accelerating fluids and calculate the reduction in ${\mathit{E}}_{\mathrm{turbulent}}$ as a function of ν, and propose experiments to measure the effect of viscosity on RT and RM instabilities.

The problem of Brownian motion in shear flows is analyzed using a path-integral approach and a piecewise-linearized velocity profile. In this way, the complete two-dimensional conditional probability distribution is found and the unimodal-bimodal transition in the longitudinal distribution is consistently described. A remarkable aspect is the appearance of a transient trimodal regime.

In a previous publication [Z. Y. Chen, A. Abbaci, S. Tang, and J.V. Sengers, Phys. Rev. A 42, 4470 (1990)] a renormalized Landau expansion was constructed for the thermodynamic free energy of one-component fluids that incorporates the crossover from singular thermodynamic behavior at the critical point to regular behavior far away from the critical point. In the present paper the approach is extended to obtain a crossover free energy for binary fluid mixtures in the region around the vapor-liquid critical line. The thermodynamic equations thus obtained are compared with experimental equation-of-state and specific-heat data for mixtures of carbon dioxide and ethane.

We present results of computer simulations of the motion of shock fronts in a variety of one-dimensional stochastic lattice models with parallel and serial dynamics, infinite and finite temperatures, and ferromagnetic and antiferromagnetic particle interactions. We find that fluctuations in the shock location, about an average determined by evolving an ensemble of systems with the same initial conditions, generically grow in time like ${\mathit{t}}^{1/3}$. We discuss the robustness of the ${\mathit{t}}^{1/3}$ growth and determine the density dependence of the coefficient in a simple case. We compare this with models where the dynamics are specially tuned so that the growth is reduced to ${\mathit{t}}^{1/4}$, and with the situation where the ensemble members have different initial conditions, in which case the growth is like ${\mathit{t}}^{1/2}$.

The two-point correlation function of an ensemble of interacting closed self-avoiding surfaces on a cubic lattice is analyzed in the disordered phase, which corresponds to the paramagnetic region in a related spin formulation. Mean-field theory and Monte Carlo simulations predict the existence of a disorder line which corresponds to a transition from an exponential decay to an oscillatory damped behavior of the two-point correlation function. The relevance of the results for the description of amphiphilic systems in a microemulsion phase is discussed. The scattering function is also calculated for a bicontinuous phase coexisting with the paramagnetic phase.

The energy ${\mathit{V}}_0$ of the bottom of the conduction band (relative to vacuum) of quasifree positrons in rare-gas fluids is calculated as a function of fluid density. The calculations are performed within the framework of the Wigner-Seitz approximation [Phys. Rev. 43, 804 (1933)] for nonpolar fluids, using a semiempirical analytical potential to model the positron–rare-gas-atom interactions. For all the rare gases studied, ${\mathit{V}}_0$ is negative and decreases almost linearly with increasing density. Extended to the solid-phase density range, our ${\mathit{V}}_0$ calculations are in good agreement with available experimental data for rare-gas crystals.

We study an electrorheological fluid consisting of spherical dielectric particles in a liquid of low dielectric constant. At a fixed temperature, there are two critical electric fields ${\mathit{E}}_{\mathit{c}2}$<${\mathit{E}}_{\mathit{c}1}$. When the applied field E<${\mathit{E}}_{\mathit{c}2}$, the system is a fluid with no long-range order. When ${\mathit{E}}_{\mathit{c}2}$<E<${\mathit{E}}_{\mathit{c}1}$, the particles form chains between two electrodes, but the distribution of these chains is random. This state is similar to an induced nematic liquid crystal. As E exceeds ${\mathit{E}}_{\mathit{c}1}$, the system is a solid whose ideal structure is a body-centered tetragonal lattice with ${\mathbf{a}}_1$= √6 ax^, ${\mathbf{a}}_2$= √6 ay^, and ${\mathbf{a}}_3$=2az, where a is the radius of dielectric spheres and z^ is the field direction.

Thermodynamic perturbation theory and density-functional approximations are systematically combined to produce a model of Lennard-Jones solids and solid-liquid coexistence. The perturbation theory is based on expanding the free energy about that of the fcc hard-sphere solid, which is described by an accurate nonperturbative density-functional theory. Approximations made throughout the development are systematically checked against results of Monte Carlo simulations. The Gaussian approximation used for describing the solid density is shown to be a good approximation for the stable solid; however, anisotropies in the structure that are not captured by the Gaussian approximation become pronounced at densities corresponding to metastable solids. The free energies of both the solid and the liquid Lennard-Jones phases and the phase diagram predicted by the density-functional thermodynamic perturbation model are in good agreement with Monte Carlo simulations for temperatures in the range 0.75≤kT/ɛ≤100.

We describe a light-scattering technique capable of probing the dynamics of thickness fluctuations in lipid bilayers. The technique, which we call reflectance fluctuation spectroscopy (RFS), is keenly sensitive to light scattered from the squeeze modes of motion in a thin liquid film, and insensitive to light scattered from the bend modes. A laser beam is focused to a small spot on the film, and the power in the specularly reflected beam is recorded in real time. Thickness fluctuations associated with the squeeze modes of motion give rise to fluctuations in the power of the specularly reflected light. The frequency spectrum of the fluctuations in detected power (RFS spectrum) can be analyzed to yield values for the film viscosity and thickness compressibility. We present two independent theoretical derivations of the RFS spectrum and show that scattering from the bend mode can be neglected. The theoretical expression for the RFS spectrum is compared with experimental spectra obtained from glycerylmono-oleate–decane bilayers. The fit of the theory to the data is excellent and the values deduced for the film viscosity and thickness compressibility are reasonable.

We have quantitatively determined the nature of the surface order of the outermost layer of monolayer and multilayer Langmuir-Blodgett films of cadmium arachidate, in air and under water, using atomic-force microscopy. Molecular-resolution images of 1200-${\mathrm{nm}}^2$ areas show that the alkyl chains of 2–5-layer films have a noncentered rectangular lattice with lattice constants of 0.482±0.004 and 0.748±0.006 nm, in good agreement with diffraction measurements of bulk aliphatic systems. We show unambiguously that the unit cell consists of two molecules. In contrast with the highly ordered multilayers, monolayer films have a disordered surface. Images taken under water of the head-group surface show that the bilayer surface is disordered, while thicker films show order of the alkyl chains. The presence of an underlying head-group–head-group interface with its associated cadmium ion bridging is shown to be the critical feature needed to obtain a stable and ordered surface layer.

Based on the same bending energy of the spontaneous curvature model, three shape equations for axisymmetric vesicles are derived from different variational methods. They are degenerate for the spherical vesicle, while for the cylindrical vesicle, two of them are the same. They all have a special toroidal solution, Clifford tori, but the constraints on the Lagrange multipliers ΔP and λ and the spontaneous curvature ${\mathit{c}}_0$ are different. We consider the physical mode of variation and introduce an arbitrary parameter for the axisymmetric action; we get the shape equation in terms of this parameter from it. When this parameter is identified as the parameter ρ, it reduces to the same equation that is from the general shape equation.

Results obtained on electrical conductivity, dielectric relaxation (static permittivity and characteristic frequency), and dynamic viscosity are presented for microemulsions with very different components (water-based or waterless, ternary or quaternary). However, they do have in common the fact that they all correspond to the model of a distribution of spheres, subjected to Brownian motion, dispersed in a continuous medium. For all these systems the associated dynamic percolation model is qualitatively verified. Moreover when the conditions of application of the asymptotic laws of the theory are satisfied, the scale exponents are the same (approximately equal to 2 above the threshold and - 1.2 below it) for all the systems, in agreement with the theoretical predictions. This reflects the fact that all these systems belong to the same class of universality.

The dynamics of the transition from supercooled liquid to glass is examined in terms of several probes: ergodic measures, self-diffusion coefficients, the Van Hove self-correlation functions, and the shear viscosity. Constant-pressure molecular-dynamics calculations at several temperatures are performed for a Lennard-Jones mixture and binary mixtures of soft spheres. The temperature dependence of the ergodicity diffusion parameters for both systems follow the Vogel-Fulcher law. On the other hand, the self-diffusion coefficients exhibit Arrhenius behavior for the soft-sphere system, but Vogel-Fulcher behavior for the Lennard-Jones system. These observations suggest that loss of effective ergodicity may be the universal feature of glass-forming substances. Various probes of the dynamics of the mixtures studied here suggest that the mechanism for mass transport dramatically changes from a simple diffusive process to one that involves activated transitions. The temperature at which this occurs is higher than the glass transition temperature ${\mathit{T}}_{\mathit{g}}$ and lies in the range 1.1<T/${\mathit{T}}_{\mathit{g}}$<1.3. In this temperature range the effective ergodic times also increase very rapidly and suggest that the relaxation process is dominated by the presence of barriers in configuration space. We also show that the Stokes-Einstein relation between the shear viscosity and the self-diffusion coefficients starts to break down in the temperature range where the ergodic convergence times increase dramatically.

We report numerical simulation of the deposition of spherical particles on a planar surface, by ballistic, straight-line trajectory transport, and assuming irreversible adhesion on contact with the surface or previously deposited particles. Our data indicate that the deposit formed has a loosely layered structure within a few diameters from the surface. This structure can be explained by a model of growth via chain formation. Away from the surface we found evidence of a monotonic, power-law approach to the bulk density. Both density and contact-statistics results suggest that the deposit formed is sparse: the space-filling fraction is about 15%, and the average number of contacts is 2. The morphology of the deposit both near the surface and in the bulk seems to be a result of competition of screening and branching; nearly half of all the spheres are either single-contact dangling ends, or branching nodes with more than two contacts.

We apply the differential formulation of the generalized effective liquid approximation to the study of hard-sphere and hard-disk freezing. We show that the thermodynamic properties of the solid phase are rather insensitive to the compressibility factor of the fluid phase used to map the solid onto the effective liquid. The solid-fluid coexistence data instead are quite dependent on the equation of state describing the fluid phase. Very accurate results, as compared with the simulation data, are obtained for both the freezing of hard spheres and hard disks.

The influence of dipolar forces on the structural and thermodynamic properties of hard spherocylinders is investigated in the isotropic and smectic phases using Monte Carlo simulations. Irrespective of the characteristics of the dipole moment, location (from center to the end of the molecule), strength (${\mathrm{\mu }}^{\mathrm{*}}$ varying from 0 to √6 ), and direction (from parallel to perpendicular to the molecular axis), the stable smectic-A phase is found to have a monolayer structure. In the case of a longitudinal dipole moment the layers are unpolarized; for transverse dipole moments the simulation results give some indication for a net polarization of the system parallel to the smectic planes, although this result should be taken with care because of the slow relaxation of the system towards equilibrium.

The formation of ferroelectric liquid crystals by simple dipolar models is investigated using density-functional theory and absolute-stability analysis. It is emphasized that for such systems well-defined results can only be found by specifying exactly how the long-range dipolar interactions are treated. Explicit formal expressions are derived for mean-reaction-field boundary conditions and these are combined with integral-equation approximations in order to obtain numerical results for fluids of dipolar hard and soft spheres. The calculations predict isotropic-to-ferroelectric nematic transitions in qualitative agreement with computer simulations. The quantitative agreement, however, is rather poor.

Rapid-solidification experiments on metallic alloys in the last decade have provided widespread observations of a novel ‘‘banded structure.’’ We report the results of numerical and analytical studies of the interface dynamics underlying the formation of this structure in a model of directional solidification which includes both solute and heat diffusion and nonequilibrium effects. The thrust of these studies is on the unsteady dynamics of the planar interface and thermal effects. The main conclusion is that the origin of banding can be related to relaxation oscillations of the solidification front, characterized by large variations of the interface velocity, which are dramatically affected by latent-heat diffusion. Without the latter, the oscillations are found to be reasonably well approximated by the phenomenological model of Carrard et al. [Acta Metall. 40, 983 (1992)], and the band spacing is inversely proportional to the temperature gradient. In contrast, with latent-heat diffusion the band spacing is insensitive to the temperature gradient, but is controlled instead by the interplay of solute and heat diffusion. The smallness of the solutal diffusivity to thermal diffusivity ratio is exploited to explain analytically this effect and to derive considerably simpler equations of interface motion that provide an efficient numerical means to study the nonplanar interface dynamics expected to cause dark bands. A reasonable agreement with experiment is found for the spacing of banded structures dominated by light-band microsegregation-free regions in Al-Fe alloys.

The usual theories of selection in dendritic growth involve an analytical extension in the complex plane and a search of singularities for the profile function. We show here that the complex plane is in fact the liquid phase and that the zone of singularity lies on the growth axis. We find a selection mechanism, by using localized perturbations, for the dendritic growth even when the surface tension is isotropic. We show that it is possible to act on the complex plane and to modify at distances the growth rate and the shape of the solidification front. Moreover, we stress here the influence of localized perturbations on the measurement of the constant of stability ${\mathrm{\sigma }}^{\mathrm{*}}$ of the needle crystal.