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.

An extensive numerical study of level-spacing properties of rational and irrational polygonal billiard systems is carried out. It is found that level statistics of both rational and irrational polygonal billiards deviate from a Gaussian-orthogonal-ensemble-type fluctuation. It is also explored in detail whether the polygonal billiards with the infinite genus number provide different level-spacing characteristics from those with the finite genus number. Some delicate problems in dealing with several types of pseudointegrable systems are also discussed.

The conditions for the existence of negative-energy electrostatic waves (which could be nonlinearly unstable and cause anomalous transport) are investigated for the case of an inhomogeneous force-free Vlasov-Maxwell equilibrium with sheared magnetic field. The method of investigation consists in evaluating the general expression for the second-order wave energy derived by Morrison and Pfirsch [Phys. Rev. A 40, 3898 (1989); Phys. Fluids B 2, 1105 (1990)] in the form given by Correa-Restrepo and Pfirsch [Phys. Rev. A 45, 2512 (1992)]. In Cartesian coordinates, the equilibrium magnetic field is given by ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$=${\mathit{B}}^{\mathrm{}\left(0\right)\mathrm{}}$(sinay${\mathbf{e}}_{\mathit{x}}$+cosay${\mathbf{e}}_{\mathit{z}}$). In this case, there is an electric current parallel to the magnetic field, and the charged particles of any species belong (according to the values of their constants of the motion) to either one of two essentially different groups, either to the group of gyrating particles (the overwhelming majority in all cases of interest), which move around the field lines, their motion being confined to a certain y region around y=${\mathit{scrY}}_{\nu }$, or to the group of swinging particles, which move freely in the y direction. The two groups of particles must be investigated separately.

Owing to the presence of the electric current associated with nonvanishing a, the equilibrium distribution function ${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$=${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$(scrH,scrU) [with scrH(v) the energy and scrU(v,y) a certain velocity variable] of at least one particle species ν must be anisotropic, unlike in the homogeneous case. If any ${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$ has the property ${\mathit{v}}_{\mathit{y}}$∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$>0 for some scrH and scrU, negative-energy waves exist for any wave number k, irrespective of its magnitude and orientation. If ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0 holds, only the waves with a component ${\mathbf{k}}_{\mathrm{\parallel }0}$ of k in the direction of ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$(${\mathit{y}}_0$) can possess negative energy. If ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0, but A≡${\mathit{k}}_{\mathrm{\parallel }0}^2$〈${\mathit{w}}_{\mathrm{\parallel }0}$〉 〈${\mathbf{e}}_{\mathit{B}}$(${\mathit{y}}_0$)⋅(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂v)〉≳0(${\mathit{w}}_{\mathrm{\parallel }}$0 is a parallel velocity, the 〈 〉 represent a certain averaging process), there are negative-energy waves with no restriction imposed on either ${\mathit{k}}_{\mathrm{\parallel }0}$ (other than ${\mathit{k}}_{\mathrm{\parallel }0}$≠0) or the spatial variation of the perturbation perpendicular to ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$.

This result agrees with that obtained for a homogeneous plasma by Morrison and Pfirsch [Phys. Fluids B 3 (2), 271 (1991)] in the context of drift-kinetic theory. If both ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0 and A<0, negative-energy modes also exist. In this case, the characteristic length for the variation of the perturbation perpendicular to ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$ is ≲${\mathit{a}}^{\mathrm{-}1}$, which, since ${\mathit{a}}^{\mathrm{-}1}$ is the shear length and is usually very large, is not an important restriction, and the possible parallel wave numbers are generally limited to a certain interval related to the magnitude of the gyroradius of the gyrating particles, this also being so in the homogeneous case. The results of that case are of course regained by taking the limit of vanishing shear, a→0. The present results show that large perpendicular wave numbers ${\mathit{k}}_{\mathrm{\perp }}$ are not necessary for the existence of negative-energy waves in the system under consideration, a feature that enhances the relevance of these modes.

Experiments on the grid excitation and subsequent propagation of solitons in a positive-ion–negative-ion–electron plasma are described. In the experiments, the ratio of the negative-ion density to the positive-ion density in a quasineutral plasma is a parameter that can be varied. Hence solitons that are described by either the Korteweg–de Vries or the modified Korteweg–de Vries equations can be experimentally investigated.

A recent model treating the structure of ‘‘simple plasmas’’ as that of high-temperature liquid metals is used here to calculate the equation of state of dense beryllium plasmas, for values of compression between 0.2 and 6, and temperatures up to 100 eV. This model gets rid of the standard simplified descriptions of ionic distributions (isolated ion sphere, uniform positive background, etc.); it applies when the electronic structure justifies the use of a binary pair interaction. This interaction is calculated, for every density and temperature, using the self-consistent electronic charge density obtained in a density-functional-theory calculation. The statistical mechanics of the ion fluid is treated via a modified hypernetted-chain integral equation. The various contributions to the equation of state are presented and discussed, and comparisons with other theories are made.

The uniformity of electron temperature (${\mathit{T}}_{\mathit{e}}$) along an x-ray laser plasma produced by a line-focused laser was investigated with precise space- and time-resolved measurements. Thomson scattering of a uv probe by the plasma was used to measure the spatial variation of ${\mathit{T}}_{\mathit{e}}$ along the line focus. This characterization was complemented by spatially resolved L-shell x-ray spectroscopy. Electron temperatures obtained from the n=4→2 F-like to Ne-like line ratios agree well with the results from Thomson scattering. Interferometry and x-ray imaging were also used to aid in the diagnosis of the plasma. The inhomogeneities observed are typical of those to be expected in x-ray laser experiments and can lead to significant reduction of the inferred gain on the Ne-like transitions.