Equations for correlation functions in nonequilibrium systems are derived using a generalization of the diagrammatic Keldysh method. The four field operators of the correlation function are ordered on a time contour that consists of four axes extending from -∞ to +∞ and from +∞ to -∞ (doubled Keldysh contour). For those correlation functions that may be considered as correlation functions of one-particle Green-functions’ fluctuations, a closed system of equations is obtained in the case of weak interaction of the particles with the scattering system. Its structure may be related to the Langevin approach: on the left-hand side a linear operator acts on each of two pairs of the correlation-function arguments, each of these two operators being just the operator of the linearized quantum kinetic equation. The expression for the right-hand side of this equation is derived. It has the meaning of the correlation function of extraneous Langevin sources, and the equation may be called the quantum Boltzmann-Langevin equation. In the quasi-classical limit it reduces to the usual Boltzmann-Langevin equation for the particles’ distribution-function fluctuations. Possible applications of the method are discussed.

Pattern selection in binary-fluid convection with a positive separation ratio S is studied. Relative stability between rolls and squares in an unbounded plane layer with experimentally relaistic boundary conditions (fixed temperature, no-slip, and no solutal flux) at the top and bottom is determined. For a mixture with Lewis number τ=0.02 and Prandtl number σ=10 confined between perfectly conducting boundaries, squares are stable whenever S>${\mathit{S}}_3$=1.01×${10}^{\mathrm{-}5}$.

Experiments on convective turbulence have revealed a number of unexpected changes in measured signals. Most notable are (i) the transition from ‘‘soft’’ to ‘‘hard’’ turbulence at Rayleigh number (Ra) of about ${10}^8$, which is seen as a qualitative change in the statistics of temperature fluctuations; (ii) a transition at Ra of about ${10}^{11}$, seen in the power spectra of temperature fluctuations measured at the center of the experimental cell; and (iii) a change, at Ra of about ${10}^{13}$, in the power spectra of a probe placed 0.2 cm from the bottom boundary. In this paper we present experimental evidence for the last two changes and offer a unified mechanism for all these transitions. The main ingredient of our theoretical analysis is a calculation suggesting that isothermal surfaces wrinkle, or appear fractal, above an inner scale. This inner scale and the Hausdorff dimension of the isothermal surfaces are estimated theoretically. This scale diminishes upon increasing Rayleigh number. We argue that as it diminishes it goes through the relevant scales of this experiment, i.e., the height of the central probe, the size of the mixing zone, and the height of the bottom probe. Thus it is suggested that all these transitions may be but different manifestations of the very same physics.

We study universal scaling properties of quasiperiodic Rayleigh-Bénard convection in a ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixture. The critical line is located in a parameter space of Rayleigh and Prandtl numbers using a transient-Poincaré-section technique to identify transitions from nodal periodic points to spiral periodic points within resonance horns. We measure the radial and angular contraction rates and extract the linear-stability eigenvalues (Flouquet multipliers) of the periodic point. At the crossings of the critical line with the lines of fixed golden-mean-tail winding number we determine the universality class of our experimental dynamics using f(α) and trajectory-scaling-function analyses. A technique is used to obtain a robust five-scale approximation to the universal trajectory scaling function. Different methods of multifractal analysis are employed and an understanding of statistical and systematic errors in these procedures is developed. The power law of the inflection point of the map, determined for three golden-mean-tail winding numbers, is 2.9±0.3, corresponding to the universality class of the sine-circle map.

It is shown that, in an imploding spherical shell, the surface instabilities are of two different types. The first, which occurs at the outer surface, is the well-known Rayleigh-Taylor instability. The second instability occurs at the inner surface. The characteristics of this instability are similar to those of amplified sound waves in an imploding plasma shell. It is suggested that this instability is driven by the amplified sound waves.

We study the interaction of disclinations in the presence of an applied magnetic or extensional flow field, which tends to align the director. Disclinations and inversion walls in the director field of nematic thermotropic liquid-crystal polymers are imaged at high resolution using the lamellar decoration technique of Wood and Thomas [Nature 324, 655 (1986)]. At intermediate field strengths, where the disclination separation is comparable to the characteristic length for director-field distortions, pairwise interaction no longer dominates, but clusters of disclinations having zero net topological dipole moment are observed to form. The applied field tends to minimize the long-range distortional energy, which is proportional to the square of the dipole moment. As a result, quadrupolar (Lehmann) clusters of disclinations are commonly observed in either magnetically or extensionally flow-aligned samples. These clusters are stabilized at intermediate field strengths, but at high fields, a second-order symmetry-breaking transition occurs that is analogous to the ferromagnetic transition of an Ising magnet. The transition is of the same class as Fréedericksz transition, but it has dimensionality of two instead of one.

The effects of solid structure and interatomic potential are investigated for density-functional theories based on the definition of a weighted or effective density for approximating the solid phase in terms of the uniform liquid. The introduction of solidlike structure to the modified-weighted-density-approximation (MWDA) theory of Denton and Ashcroft [Phys. Rev. A 39, 4701 (1989)] leads to loss of existence of the weighted density for a system of hard spheres. This behavior is more pronounced for loose crystalline structures, such as the diamond lattice. By contrast, the generalized-effective-liquid-approximation theory (GELA) of Lutsko and Baus [Phys. Rev. A 41, 6647 (1990)] always predicts single-valued weighted densities in the cases studied here. The thermodynamic mapping, which is the core of both of the MWDA and GELA approximations, is ineffective for Lennard-Jones fluids, according to a criterion for the relative stability of the solid phase evaluated using liquid-state information.

We have studied electrically driven convective flow in thin, freely suspended films of smectic-A liquid crystal. Here we report measurements of the two-dimensional velocity field of this flow as the driving voltage is varied. Our results are well described by the first few terms of an appropriate mode expansion over a range of the experimental control parameter, from the onset of convection to the appearance of unsteady flow substantially above onset. The behavior of the mode amplitudes near onset indicates that the bifurcation to convection is forward. We also present measurements of the current through the film, which show an enhanced charge transport due to convection, and measurements of the pattern wavelength at and above onset. We argue that a reduction in the onset wavelength observed above a cutoff frequency is related to the relaxation time of the charge distribution in the film.

An analysis is given of the various contributions to the x-ray diffraction in smectic-A liquid crystals, where several effects due to the real structure are superimposed upon the algebraic decay of the correlations due to thermal fluctuations. The finite size of either the sample or intrinsic domains is shown not only to determine the half-width of the Bragg peak but also to contribute to the wings of the diffraction curve, thus overlapping with the algebraic decay. The asymmetry of the peak-intensity distribution observed for nonoriented (powder) samples is also explained. For samples with a small mosaicity, the transition from the limit of powder diffraction to that of a perfectly oriented sample is calculated as a function of the wave-vector magnitude. Finally the possible broadening of the x-ray peak due to dislocations is analyzed. Results of various high-resolution experiments on monomeric, polymeric, and lyotropic smectic liquid crystals are analyzed and the possible sources of observed real-structure effects are discussed.

In the framework of a discrete two-sublattice soliton model the dynamics of the ionic defects in a thermalized hydrogen-bonded chain has been numerically studied. For these defects the Peierls potential relief has been calculated, which appears essentially to depend on their polarity. The mobilities of the positive and negative ionic defects have been evaluated and are in good agreement with the experimental data. The thermally activated formation of ionic defect pairs has also been considered, and the evaluation of their density in the chain is given in comparison with the well-known data from ice physics. The role of the cooperativity of the proton dynamics is shown to be crucial under the processes of the defect creation. The dynamics of two-component nontopological supersonic solitons and their interaction with the ionic defects is also investigated.

We study a lattice model for a three-component system of water, oil, and surfactants in two dimensions. Large-scale Monte Carlo simulations were performed to obtain the phase equilibria for a wide range of temperatures and surfactant concentrations. We show that this model has a rich phase behavior, and both microemulsion and liquid crystalline phases were found. The phase behavior is consisent with that of a real system, and is in qualitative agreement with the model of Gompper and Schick [Phys. Rev. Lett. 62, 1647 (1989)], which is based on three-body interactions.

A generalization of the Landau–de Gennes phenomenological theory of smectic-A liquid crystals is described. The theory is based on a Landau-Ginzburg free energy that includes local and nonlocal parts. The local part consists of the isotropic-Ising-model free energy and de Gennes’s phenomenological free energy of the nematic phase. The nonlocal part is derived from the form of two-body contributions to the free energy in molecular density-functional theories, expanded in gradients of the number density and orientational order parameter. A mean-field approximation to the theory is analyzed by both Landau expansion and by a full numerical solution, involving Fourier-series representations of the number density and an orientational order parameter with an appropriately large number of Fourier coefficients. The main purpose of the analysis is to show that the smectic phase results from the instability of a uniform phase induced by the gradient terms in the free energy, particularly those that couple modulations in the density and orientational order parameter.

The phase diagram of a large-pitch cholesteric liquid crystal sandwiched between two parallel glass plates with homeotropic anchoring is determined both experimentally and theoretically. Contrary to previous experiments [P. Ribière and P. Oswald, J. Phys. (Paris) 51, 1703 (1990)], the materials chosen have a negative dielectric anisotropy so that experiments are performed at smaller thickness than the critical value ${\mathit{d}}_{\mathit{c}}$ that is necessary to unwind the helical structure completely at vanishing electric field. The two control parameters are the frustration ratio d/p of the thickness over the quiescent pitch of the cholesteric liquid crystal and the applied voltage V. The main difference with previous experiments is that the cholesteric-nematic phase transition can be second order or first order depending on the sample thickness. There is thus a Landau tricritical point in the phase diagram. Furthermore, we have found a triple point where the nematic phase coexists with both a translationally invariant configuration and a periodic structure. A theoretical model, including two order parameters, allows us to calculate the coordinates of these two particular points as a function of the Frank elastic constants as well as the general aspect of the phase diagram. The agreement between theory and experiment is satisfactory.

Previous simple theories for the binding energy of excess electrons in liquid Ar, Kr, and Xe, which corresponds to the electron affinity, could not get good agreement with experimental results for the whole range of liquid densities. Here, we present an improvement of these theories yielding results for the electron affinity of liquid rare gases, which agree well with experiments at all densities, including the solid phase. This theory is quite universal and can also be directly applied to the electron affinity of liquids of nonpolar molecules.

Within a mode-coupling approximation we investigate the influence of the short-time dynamics of colloidal fluids on the glass-transition scenario. We assume Brownian dynamics, neglect hydrodynamic interactions, and follow approximations used to construct a mode-coupling theory (MCT) for structural relaxation in dense atomic fluids with underlying Newtonian dynamics. This approach predicts the same scenario for the kinetic glass transition in colloidal systems as the MCT for atomic systems. We compare this result with recent computer-simulation studies of the glass transition for atomic and colloidal liquids.

The magnetically induced splay Fréedericksz transition is reexamined to look for pattern forming phenomena slightly above or below criticality. By using our traditional scheme of stochastic nematodynamic equations, situations are, respectively, found of transient and permanent predominance of transversal periodicities (wave numbers) along the direction perpendicular to the initial orientation within the sample. The relevance of these predictions in relation with recent observations in the electrically driven splay Fréedericksz transition, and in general with other pattern forming phenomena, is stressed.

The interaction free energy per unit area between planar walls is given as a convolution of wall-solvent pair-correlation functions. This result, derived from the large radius limit of the macrosphere-solvent Ornstein-Zernike equations, and from the hypernetted-chain closure, provides a statistical-mechanical basis for the Derjaguin approximation, and is both generally applicable and computationally tractable. It is found that the interaction between hard walls in a hard-sphere fluid is oscillatory, and in good agreement with simulations. The van der Waals attraction emerges from asymptotic analyses of Lennard-Jones and dipolar fluids, and the full expression allows calculation of this quantity down to molecular separations. This is demonstrated by numerical results for dipolar fluids.

The adsorption of simple electrolytes in narrow planar pores is studied. The validity of the limiting law according to which the density of a classical ionic fluid approaches the fugacity in the pores barely exceeding the diameter of the ions is confirmed using the graphical expansion of the singlet-ion distribution. The same result emerges from the Kirkwood equation for the ion-wall correlation. The analysis is paralleled by the open-ensemble Monte Carlo simulation of the electrolyte in the pore, the periodic boundary conditions being implemented using the two-dimensional Ewald summation. The computations conform with theoretical predictions for extremely narrow slits and provide useful insights into the partitioning of the salt between the slit and the bulk solution at intermediate widths of the pores.

A computationally practical density-functional theory of nonuniform fluid mixtures ‘‘designed primarily for the study of interfacial phenomena’’ is presented and applied to the structure of a binary hard-sphere mixture near a hard wall. The theory is based on a weighted-density approximation for the one-particle direct correlation functions of the nonuniform system, and requires as input only the one- and two-particle direct correlation functions of the corresponding uniform system. Numerical results for density and concentration profiles are presented and compared with available simulation data.

We present the results of a systematic study of the propagation of sound in sodium di-2-ethyl-hexylsulfosuccinate (AOT) micelles and microemulsions. The dispersion in the sound velocity v is determined over three and a half decades in frequency by using both ultrasonic and Brillouin-scattering techniques. The dispersion in the sound velocity is also measured as a function of the volume fraction φ of micelles or microemulsions. In addition, we measure the dependence of the sound velocity dispersion on the linear hydrocarbon chain length of the solvent molecules, and on the size of the microemulsion droplets. A consistent physical picture emerges that accounts for all of the results. The sound velocity in the micelle or microemulsion phases is greater than that in the solvent, leading to the observed increase of v with φ. In addition, due to the overlapping of the surfactant tails, there is a weak, short-range attractive interaction between the droplets, causing them to form short-lived, extended networks. These networks can support shear, leading to a further increase in v at higher φ, provided the frequency of the sound is sufficiently high that the instantaneous networks remain intact over the period of the sound wave. This results in the additional frequency dispersion in v at high φ. The strength of the attractive interaction, and hence the dispersion in the sound velocity, depends on the chain length of the solvent molecule and the diameter of the microemulsion droplet.

The use of an effective-medium model is critical in confirming the validity of the physical picture. The effective-medium model includes the contribution of a shear modulus of one of the phases and can account for the φ dependence of v for all the systems. The shape of the full Rayleigh-Brillouin spectra is shown to be describable by a formalism that includes the relaxation of the extended networks. Finally, since the micelle or microemulsion networks cannot support shear unless they extend across the whole system, we show that the additional shear modulus contributed by the droplet phase exhibits scaling behavior when the volume fraction exceeds a critical value defined by the rigidity percolation threshold. This allows us to measure both the critical volume fraction and the exponent for rigidity percolation. However, since this additional shear modulus only occurs at high frequency, this effect is an example of dynamic rigidity percolation.