In three different phase-separated binary liquid mixtures we have observed stationary capillary rises in which the meniscus curvature is inconsistent with the sign of the rise. This ‘‘inverted-meniscus’’ configuration occurs within approximately 50 mK of the mixture’s critical temperature and shows no sign of decay after much longer than the characteristic time for relaxation. We also report experiments showing that perturbation of the wetting layer inside the capillary tube can dramatically affect the capillary rise. This motivates three scenarios in which the behavior of the wetting layer foils an equilibrium capillary rise measurement of the contact angle and produces an inverted meniscus.

Experimental data are presented for the dielectric constant ε and the electric conductivity σ near the consolute point of a binary liquid mixture nitroethane–3-methylpentane. Fitting the data for ε and σ as a function of temperature, we find for both a 1-α power-law singularity with an α value consistent with the Ising value α=0.11. The temperature dependence of the amplitude of the observed low-frequency Maxwell-Wagner critical dispersion has been explained on the basis of a droplet model for the critical fluctuations.

We present an analytical equation of state for convex-molecule fluids in any number of dimensions, based on statistical-mechanical perturbation theory for hard convex bodies. The second virial coefficient is calculated exactly. Two temperature-dependent parameters in addition to the second virial coefficient arise, an effective molecular volume (or van der Waals covolume) and a scaling factor for the average contact pair distribution function of hard convex bodies. The equation is tested against computer simulations and perturbation calculations for the model of rodlike molecules interacting via a Kihara (12,6) potential. This model allows the two temperature-dependent parameters to be calculated from the intermolecular potential by simple quadrature, without further approximations for averaging over molecular orientations. The agreement is quite good.

An analytical equation of state for real molecular fluids is presented, based on an extension of a previously presented perturbation theory for hard convex bodies [Song and Mason, preceding paper, Phys. Rev. A 42, xxxx (1990)]. It is a fifth-order polynomial in the density and seems to be valid over the range from the dilute gas to the metastable liquid, both below and above the critical temperature. The temperature-dependent parameters of the equation can be calculated if the intermolecular pair potential is known. However, knowledge of just the second virial coefficient plus some liquid densities is sufficient to predict reasonably accurate parameters and hence the whole p-v-T surface. Three scaling constants characterize the equation: an interaction energy, an interaction distance, and a dimensionless nonsphericity or inner hard-core parameter. The equation is tested with experimental p-v-T data for eight selected systems: ${\mathrm{N}}_2$, ${\mathrm{CO}}_2$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, ${\mathrm{C}}_3$${\mathrm{H}}_8$, ${\mathrm{CF}}_4$, ${\mathrm{SF}}_6$, ${\mathrm{NH}}_3$, and ${\mathrm{H}}_2$O. Agreement is quite remarkable.

We construct a nonlocal theory of elasticity for a nematic polymer composed of rigid or semiflexible molecules. We then introduce a mean-field theory for the calculation of wave-vector-dependent elastic moduli. Because the length of the molecules can be comparable to observable elastic distortions, the wave-vector dependence of the Frank moduli, i.e., their nonlocality, can be quite important. For rodlike molecules we obtain analytic results valid for arbitrary wave vector and strong nematic ordering. For flexible chains we are unable to obtain analytic results for the nonlocal elastic constants except in the limit of chains whose lengths are short compared to their global persistence length. However, our formalism is readily amenable to numerical techniques which should allow future consideration of the interplay of nonlocality and flexibility.

We show, both through theory and light-scattering experiments, how the order-parameter fluctuations in a nematic liquid crystal can be decomposed into two parts: a critical part consisting of fluctuations in the magnitude of the order and a noncritical part, the well-known director fluctuations. Mean-field theory is shown to predict some new and interesting relations between these two components, most of which are confirmed by experiment.

A simple model for the adhesion of vesicles to interfaces and membranes is introduced and theoretically studied. It is shown that adhering (or bound) vesicles can exhibit a large variety of different shapes. The notion of a contact angle governed by tension is found to be applicable only for a restricted subset of these shapes. Furthermore, the vesicle undergoes a nontrivial adhesion transition from a free to a bound state. This transition is governed by the balance between the overall bending and adhesion energies, and occurs even in the absence of shape fluctuations.

The scaling behavior of the elastic properties of colloidal gels that are well above the gelation threshold is studied both theoretically and experimentally. A scaling theory was developed by considering the structure of the gel network as a collection of flocs, which are fractal objects closely packed throughout the sample. Two regimes are found based on the relative value of the elastic constant of the interfloc links to that of the flocs. In the strong-link (interfloc) regime, the elastic constant of the gels increases but the limit of linearity decreases with increasing particle concentration, whereas in the weak-link regime both the elastic constant and the limit of linearity increase with increasing particle concentration. Rheological studies on the elastic behavior of two types of boehmite alumina gels, Catapal and Dispal powders, were performed. Both types of gels in the concentration range studied showed the strong-link behavior and the results are in good agreement with the theoretical predictions. The value of the fractal dimension of the flocs D≃1.95, deduced from the rheological measurements, is in agreement with the value D≃2.04 deduced from the static light-scattering measurements on dilute suspensions. Therefore the scaling theory we developed also enables us to extract structural information from the rheological measurements.

We simulate two-phase flow in a porous medium, which is represented by random, isotropic two- and three-dimensional networks containing up to 80 000 interconnected pore spaces. The simulations are sufficiently large that macroscopic properties of the flow may be determined. For unstable viscous floods, we show that the displacements are compact with a fractal interface between the fluids. The fractal dimension is found as a function of viscosity ratio. For invasion percolation, where the displacement is controlled by capillary forces, and for viscous fingering, we calculate relative permeabilities in an averaged two-phase Darcy equation, which we show are functions of mean saturation. The relative permeabilities also depend on flow rate, which means that the two-phase Darcy equation is nonlinear, even with microscopic linear Poiseuille flow.

In laser interaction, absorption of x rays by Kα lines has been shown to be a powerful diagnostic of electronic temperature and integrated density in a dense absorbing plasma. Integrated densities measured in these experiments are lower than expected, especially in implosions where density is high. We present here an experiment and calculations that show that absorption saturates rapidly with increasing thicknesses of the absorber. An aluminum layer of variable thickness is heated by the soft x rays emitted by a samarium layer deposited on the laser-irradiated side of a planar target. We have measured the optical depth of the Kα transitions of ${\mathrm{Al}}^{6+}$ to ${\mathrm{Al}}^{8+}$ ions as a function of the layer thickness. A strong nonlinear behavior is observed as predicted by the calculations. This type of saturation is explained by the high number of superimposed absorbing lines, and it is strongly dependent on the ratio between the linewidth and the instrumental resolution. Such a saturation effect is general for line absorption and does not appear on film when the instrumental broadening is larger than the line profile.

This is a continuation of our previous work [Phys. Rev. B 40, 2477 (1989)] on the liquid-gas transition for systems ranging from simple fluids through polymer solutions and microemulsions. We provide here the crossover calculations for various measurable quantities of the magnetic type defined in the text. Our calculations performed with the help of the field-theoretic methods reproduce, in the case of simple fluids, the results of Nelson and Rudnick [Phys. Rev. B 13, 2208 (1976)], who used the Wilson-Fisher style of renormalization. In the case of polymers, the results obtained are in very good agreement with available Monte Carlo and experimental data.

Three recent weighted-density-functional (WDF) theories are critically examined in terms of their ability to describe correctly the structure of a hard-sphere fluid at a hard wall. A new derivation of the Curtin-Ashcroft WDF theory is given that clarifies the basic approximations behind this formulation and brings out the close relationship between their work and the WDF theories of Meister-Kroll and Groot–van der Eerden. The condition that the second functional derivative of the approximate Helmholtz free-energy functional yields the correct two-particle direct-correlation function in the homogeneous limit is found to be of crucial importance in determining good liquid structures.

We study the freezing properties of systems with inverse-power and Yukawa interactions (soft spheres), using recently developed weighted-density-functional theories. We find that the modified weighted-density-functional approximation (MWDA) of Denton and Ashcroft yields results for the liquid to face-centered-cubic (fcc) structure transition that represent a significant improvement over those of earlier ‘‘second-order’’ density-functional freezing theories; however, this theory, like the earlier ones, fails to predict any liquid to body-centered-cubic (bcc) transition, even under conditions where the computer simulations indicate that this should be the equilibrium solid structure. In addition, we show that both the modified effective-liquid approximation (MELA) of Baus [J. Phys. Condens. Matter 2, 2111 (1990)] and the generalized effective-liquid approximation of Lutsko and Baus [Phys. Rev. Lett. 64, 761 (1990)], while giving excellent results for the freezing of hard spheres, fail completely to predict freezing into either fcc or bcc solid phases for soft inverse-power potentials. We also give an alternate derivation of the MWDA that makes clearer its connection to earlier theories.

The clustering process in sodium di(2-ethylhexyl)sulfosuccinate–${\mathrm{H}}_2$O–iso-octane microemulsions has been studied by dielectric relaxation spectroscopy and small-angle x-ray scattering (SAXS). The SAXS experiments are interpreted using the pair-correlation function for the microemulsion droplets obtained from the multicomponent sticky hard-sphere-droplet model. The results indicate the presence of a strong interaction between the droplets and the solvent medium. The structural parameters extracted from this analysis are used to calculate the correction term to the Clausius-Mossotti equation for the polarizability of the microemulsion system. Good agreement is found between the observed and calculated polarizabilities.

We propose a deterministic model of diffusion-limited aggregation (DLA), based on the concept of an infinite hierarchy of voids connected by narrow channels. This hierarchical model reproduces many features of DLA: (1) The growth-site probability distribution shows multifractal behavior, (2) the minimum growth probability decreases with size L as ln${\mathit{p}}_{\min }$(L)∼-(lnL${)}^2$, and (3) the maximum growth probability scales as ${\mathit{p}}_{\max }$(L)∼${\mathit{L}}_{\min }^{\mathrm{-}\mathrm{\alpha }}$.

The η model for the dielectric breakdown is extended to the case where double power laws apply. It is shown that a crossover phenomenon between the diffusion-limited aggregation (DLA) fractal and the η fractal occurs in the extended η model. Through the use of the dimensional analysis, a dimensionless parameter is found to govern the crossover. It is shown that when η<1 the crossover from the DLA fractal to the η fractal occurs with increasing size, and if η>1 the inverse crossover from the η fractal to the DLA fractal appears. It is also shown that the crossover radius is controlled by changing the applied field. The global flow diagram in the two-parameter space is obtained by using a two-parameter position-space renormalization-group approach. The crossover exponent and the crossover radius are calculated. The crossover phenomenon is described in terms of a thermodynamic representation of the two-phase equilibrium.

We explore the connectivity properties of diffusing particles with short-range interactions for dimensions d=1,2. We consider both ‘‘blind’’ and ‘‘myopic’’ diffusion rules (for the blind case, the walker chooses the next step from among all neighbor sites while in the myopic case the walker chooses from among only the unblocked sites). We show that—for all d—the equilibrium state of a system of particles diffusing according to the blind rule, at density ρ, is equivalent to the lattice gas with interaction parameter J=0 and chemical potential μ=2 ${\sinh }^{\mathrm{-}1}${[(2ρ-1${)}^2$/4ρ(1-ρ)${]}^{1/2}$}. The connectivity properties of the blind diffusion system are described by random site percolation in all dimensions. The myopic diffusion system is more complicated. For d=1, the equilibrium state of a system of particles diffusing according to the myopic rule, with particle density ρ, is equivalent to a lattice gas with J=-ln(2) and μ=ln(2)+2 ${\sinh }^{\mathrm{-}1}${[(2ρ-1${)}^2$/2ρ(1-ρ)${]}^{1/2}$}. Also, for d=1, the number of clusters of size s is approximately ${\mathit{n}}_{\mathit{s}}$=ρ${\mathit{p}}_{\mathrm{eff}}^{\mathit{s}\mathrm{-}1}$(1-${\mathit{p}}_{\mathrm{eff}}$${)}^2$, where ${\mathit{p}}_{\mathrm{eff}}$≤ρ. An approximation for ${\mathit{p}}_{\mathrm{eff}}$ is given that agrees closely with Monte Carlo simulations. For d=2, the myopic diffusion system has no mapping to the lattice-gas model. Rather, it undergoes a percolation transition at a threshold density ${\mathrm{\rho }}_{\mathit{c}}$. On the square lattice, ${\mathrm{\rho }}_{\mathit{c}}$=0.617±0.004, a value that is higher than the threshold for random site percolation. However, percolation and myopic diffusion appear to be in the same universality class.

It has been proposed [J. L. Bobin, Opt. Commun. 55, 413 (1985)] that the presence of a plasma can, under certain conditions, enhance the accelerating electric field in an inverse free-electron laser. In this scheme, the beat wave generated by a laser and an undulator is expected to couple to the plasma oscillations generated by the electron beam streaming through the plasma. We have undertaken an analytical and numerical study of the proposed acceleration scheme. Our results show that the electric field is dominantly the self-field of the electron beam, and the plasma makes a negligible contribution to the electric field. Based on our analysis, we propose an alternative method of acceleration that employs a high-current electron beam to generate a beat wave that is subsequently used to accelerate a higher-energy beam. We show that an accelerating electric field ∼1 MeV/cm can be achieved with an electron beam of current density ∼20 kA/${\mathrm{cm}}^2$. The results of the analytical study agree well with numerical results from a two-dimensional computer code. The parameters of a proof-of-principle experiment are presented.

A nonlinear theory is presented unifying the concepts of the photon accelerator and the plasma wake-field generator. For a weakly relativistic nonlinearity an upper limit of frequency up-conversion, which is attainable for an electromagnetic bunch that is accelerated in a periodic plasma field, is found. This limitation is directly attributed to the existence of localized nonlinear wave structures trapped in a deformation of the plasma-wave lattice.

First-principles calculations of the shear modulus tensor are presented for the bcc crystalline and rapidly quenched Coulomb solids produced by the Monte Carlo simulation method. The shear moduli are calculated for temperatures up to the melting conditions, including the effects of thermal fluctuations. An effective shear modulus appropriate to an approximate ‘‘isotropic’’ body is introduced through averages over directions.