A Lagrangian with dissipative (e.g., Onsager’s) potentials is constructed for the field description of irreversible heat-conducting fluids, off local equilibrium. Extremum conditions of action yield Clebsch representations of temperature, chemical potential, velocities, and generalized momenta, including a thermal momentum introduced recently [R. L. Selinger and F. R. S. Whitham, Proc. R. Soc. London, Ser. A 302, 1 (1968); S. Sieniutycz and R. S. Berry, Phys. Rev. A 40, 348 (1989)]. The basic question asked is ‘‘To what extent may irreversibility, represented by a given form of the entropy source, influence the analytical form of the conservation laws for the energy and momentum?’’ Nöther’s energy for a fluid with heat flow is obtained, which leads to a fundamental equation and extended Hamiltonian dynamics obeying the second law of thermodynamics. While in the case of the Onsager potentials this energy coincides numerically with the classical energy E, it contains an extra term (vanishing along the path) still contributing to an irreversible evolution. Components of the energy-momentum tensor preserve all terms regarded standardly as ‘‘irreversible’’ (heat, tangential stresses, etc.) generalized to the case when thermodynamics includes the state gradients and the so-called thermal phase, which we introduce here. This variable, the Lagrange multiplier of the entropy generation balance, is crucial for consistent treatment of irreversible processes via an action formalism. We conclude with the hypothesis that embedding the first and second laws in the context of the extremal behavior of action under irreversible conditions may imply accretion of an additional term to the classical energy.

We apply recently derived Green-Kubo relations for the various elements of the self-diffusion tensor (SDT) of shearing fluids to three different model systems of rodlike molecules: the Tildesley-Madden model for carbon disulfide, the Gay-Berne fluid, and the Ryckaert-Bellemans model for decane. We study how the various elements of the SDT depend on the shear rate. This dependence is explained in greater detail by examining the various velocity autocorrelation functions, the order parameter, and the shear induced rotation rate. We find that two different mechanisms are responsible for the behavior of the diagonal elements of the SDT. The first is the elliptical distortion of the nearest-neighbor shell and enhances the diagonal elements of the SDT. The second is the shear alignment of the molecules. This facilitates diffusion in the alignment direction and suppresses diffusion in the perpendicular direction. We also suggest ‘‘collision’’ sequences that are responsible for the sign of the off-diagonal elements of the SDT.

Exact relations of two types in the statistical theory of fully developed homogeneous isotropic turbulence in an incompressible fluid were found. The relations of the first type connect two-point and three-point objects of the theory which are correlation functions and susceptibilities. The second type of relations are the ‘‘frequency sum rules’’ which express some frequency integrals from ‘‘fully dressed’’ many-point objects (like vertices) via corresponding bare values. Our approach is based on the Navier-Stokes equation in quasi-Lagrangian variables and on the generating functional technique for correlation functions and susceptibilities. The derivation of these relations uses no perturbation expansions and no additional assumptions. This means that the relations are exact in the framework of the statistical theory of turbulence. We showed that ‘‘a many-point scaling’’ gives birth to the ‘‘global scaling.’’ Here ‘‘many-point scaling’’ is the assumption that two-point, three-point, etc. objects of the theory of turbulence are uniform functions in the inertial interval and may be characterized by some scaling exponents. Under this assumption the only global scale-invariant model of fully developed turbulence suggested by Kolmogorov [Dokl. Akad. Nauk SSR 32, 19 (1941)] is consistent with the exact relations deduced.

By means of Burgers’s equation a stochastic description of turbulent fluid flows is explained which is based on a discrete master equation. The latter governs the dynamics of a discrete multivariate stochastic process representing the random velocity field of the fluid. From the characteristic function corresponding to this stochastic process, the Hopf functional equation of turbulence is obtained. This implies that the infinite hierarchy of correlation functions can be derived from the master equation. The master-equation description naturally leads to a simple stochastic simulation algorithm which is well suited for numerical implementation. Stochastic simulations of the Burgers model of turbulence are performed and are shown to yield very accurate results.

A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a nonideal gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many applications in large-scale numerical simulations of various types of fluid flows.

We study the spreading of the foot of a two-dimensional drop via Monte Carlo simulations without conservation law. The profile, or height of the spreading phase as a function of the distance from the initial drop, is described by a solid-on-solid model. For positive spreading coefficients, we find a precursor film extending linearly with time, and thickening as ${\mathit{t}}^{1/4}$ due to entropic repulsion. For a vanishing spreading coefficient, i.e., at the wetting transition, the foot of the profile is found to scale as ${\mathit{t}}^{1/2}$ parallel and perpendicular to the substrate, with no precursor asymptote. For partial wetting, relaxation is checked against exact results including finite-size effects.

We investigate the supercooling of a nematic liquid crystal using fluctuating nonlinear hydrodynamic equations. The Martin-Siggia-Rose formalism [Phys. Rev. A 8, 423 (1973)] is used to calculate renormalized transport coefficients to one-loop order. Similar theories for isotropic liquids have shown substantial increases of the viscosities as the liquid is supercooled or compressed due to feedback from the density fluctuations which are freezing. We find similar results here for the longitudinal and various shear viscosities of the nematic phase. However, the two viscosities associated with the nematic-director motion do not grow in any dramatic way; i.e., there is no apparent freezing of the director modes within this hydrodynamic formalism. Instead a glassy state of the nematic phase may arise from a ‘‘random-anisotropy’’ coupling of the director to the frozen density.

Using the microscopic density-functional theory for inhomogeneous simple fluids, we derive a nonlocal and non-Gaussian expression for the effective Hamiltonian of a fluctuating liquid-vapor interface. If a gradient expansion is applied to this Hamiltonian, one obtains—after a partial resummation—as the leading term the standard effective interface Hamiltonian which is proportional to the increase of the area of the interface relative to that of the flat configuration. The next to leading terms are proportional to the Gaussian and to the mean curvature of the interface, respectively. Microscopic expressions for the coefficients in this expansion are derived. If the interparticle interactions in the fluid decay according to power laws, the gradient expansion breaks down. This is reflected in the nonanalytic behavior of the wave-vector-dependent surface tension which can be expressed in terms of the Fourier transform of the interaction potential between the fluid particles. Various approximations of the nonlocal Hamiltonian are compared quantitatively. The relevance of this Hamiltonian for interpreting scattering experiments is discussed.

The critical behavior of a ternary microemulsion consisting of water, benzene, and benzyldimethyl-n-hexadecylammonium chloride is studied by light-scattering techniques, controlling temperature to approach the critical point. This microemulsion is chosen since it is very stable. Great care was taken to ensure the measurements were performed at the critical concentration, and a wide range of temperature was covered. According to theory, one expects Fisher renormalized Ising critical exponents in a ternary mixture when temperature is the controlled variable. Contrary to this expectation, we find values of the exponents γ=1.18±0.03 and ν=0.60±0.02, indicating rather unrenormalized Ising-like behavior of ternary microemulsions.

We classify the interfacial wetting behavior of binary liquid mixtures at their liquid-vapor interface. The criteria with respect to the atomic interactions between the two species are whether the Hamaker constant of that interface fulfills either sufficient conditions for the absence of a wetting transition, or the necessary conditions for critical wetting, or the necessary conditions either for being wet already at low temperatures or for undergoing a first-order wetting transition upon approaching the critical end point along the triple line. Based on the Blume-Emery-Griffiths model and on the Percus-Yevick theory we scan the parameter space that determines the structure of the bulk phase diagrams. By analyzing the absolute values of the Hamaker constant we pay particular attention to interfacial wetting induced by tricritical points. In addition, we compare the predictions of the Percus-Yevick theory for the bulk phase diagrams and the number densities of the fluid bulk phases with experimental and simulation data as well as with different theoretical approaches.

Optical-activity measurements in the smectic-A phase of various chiral-racemic mixtures of S-4-(2’-methylbutyl)phenyl-4’-n-octylbiphenyl-4-carboxylate (CE8) demonstrate that contributions from fluctuations in more than one chiral structural mode are important near the transition to the smectic-${\mathit{C}}^{\mathrm{*}}$ phase. Although these results are similar to earlier measurements in the isotropic phase of highly chiral liquid crystals, previous theoretical work points out that the nature of these fluctuations and the reason for the importance of the second structural mode are very different. Because the present measurements are reported on mixtures of varying chirality, they provide a stringent test of the theory. Agreement between theory and experiment is good.

We consider the effect of the divergence ${\mathit{K}}_{24}$ term ∇[n(∇n)+n×∇×n] in the nematic free energy, which has been ignored for a long time. The ${\mathit{K}}_{24}$ term is shown to be able to cause spontaneous twist deformations. This mechanism is irrespective of the bulk Frank constant anisotropy in contrast to the well-known mechanism associated with the smallness of the twist elastic constant ${\mathit{K}}_{22}$. For geometries with sufficiently large surface-to-volume ratios, it can also be effective in other condensed media described by similar free-energy functionals, but with considerably less anisotropic constants than liquid crystals (e.g., the B phase of liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ferromagnets). As a specific model we consider the formation of long-wavelength stripe domains in a usual but rather thin hybrid nematic layer. Degenerate boundary conditions are imposed on the surfaces of the latter. Recent experiments show the existence of such domains in a hybrid nematic layer whose state had always been regarded as homogeneous in the layer plane. The theory worked out in the paper allows one to incorporate all the harmonics of the periodic domain structure in the vicinity of the critical point. The dependence of the domain period on the layer thickness, obtained in the paper, makes it possible to find the value of the elastic constant ${\mathit{K}}_{24}$ from the experimental data.

A phase-field model for isothermal solidification of a binary alloy is developed that includes gradient energy contributions for the phase field and for the composition field. When the gradient energy coefficient for the phase field is smaller than that for the solute field, planar steady-state solutions exhibit a reduction in the segregation predicted in the liquid phase ahead of an advancing front (solute trapping), and, in the limit of high solidification speeds, predict an alloy solidification with no redistribution of composition. Such situations are commonly observed experimentally.

High-resolution x-ray scattering and ac-calorimetric measurements have been carried out near the nematic–smectic-${\mathit{A}}_1$ phase transition of the pure liquid-crystal compound octyloxyphenylnitrobenzoyl- oxy benzoate (${\mathrm{DB}}_8$${\mathrm{ONO}}_2$). Several forms of the structure factor S(q) for fitting the x-ray line shape have been tested. The critical temperature dependences of the resulting longitudinal and transverse correlation lengths ${\xi }_{\mathrm{\parallel }}$ and ${\xi }_{\mathrm{\perp }}$ and the smectic susceptibility σ are insensitive to the detailed form of reasonable choices for S(q). The behaviors of ${\xi }_{\mathrm{\parallel }}$, ${\xi }_{\mathrm{\perp }}$, and σ are analyzed here in terms of pure power laws; the effective critical exponents for the reduced temperature range 2×${10}^{\mathrm{-}5}$–1.2×${10}^{\mathrm{-}2}$ are ${\nu }_{\mathrm{\parallel }}$=0.69±0.03, ${\nu }_{\mathrm{\perp }}$=0.59±0.03, and γ=1.28±0.05. Although ${\nu }_{\mathrm{\parallel }}$ and γ are quite close to three-dimensional (3D) XY values, the system is anisotropic with ${\nu }_{\mathrm{\parallel }}$-${\nu }_{\mathrm{\perp }}$=0.10±0.03. The heat-capacity data are analyzed using a nonasymptotic power-law expression with first- and second-order corrections-to-scaling terms. This analysis yields a critical exponent α which agrees with 3D XY theory: α=-0.007±0.003. Thus, anisotropic hyperscaling (α+${\nu }_{\mathrm{\parallel }}$+2${\nu }_{\mathrm{\perp }}$=2) appears to be violated if effective exponents based on pure power-law fits to x-ray data are used. However, hyperscaling can be recovered by a preasymptotic XY analysis of the x-ray data, as shown in paper II [Phys. Rev. E 47, 1918 (1993)].

X-ray data are reported for the nematic phase near the nematic (N)–smectic-${\mathit{A}}_1$(Sm-${\mathit{A}}_1$) transition in a binary mixture of pentylphenylcyanobenzoyloxy benzoate (${\mathrm{DB}}_5$CN)+cyanobenzoyloxypentylstilbene (${\mathrm{C}}_5$ stilbene). These data and x-ray data from four other N–Sm-${\mathit{A}}_1$ systems, plus the corresponding high-resolution ${\mathit{C}}_{\mathit{p}}$ data, are analyzed using the exact solutions of preasymptotic three-dimensional (3D) XY theory. The correlation volume ${\xi }_{\mathrm{\parallel }}$${\xi }_{\mathrm{\perp }}^2$, smectic susceptibility σ, and heat capacity ${\mathit{C}}_{\mathit{p}}$ are in good agreement with preasymptotic theoretical predictions. First-order corrections-to-scaling terms were known previously to be important for describing ${\mathit{C}}_{\mathit{p}}$; their importance for ${\xi }_{\mathrm{\parallel }}$${\xi }_{\mathrm{\perp }}^2$ and σ is demonstrated here. Many universal features of the 3D XY model are confirmed by the present self-consistent analysis, but the critical anisotropy of the individual lengths ${\xi }_{\mathrm{\parallel }}$ and ${\xi }_{\mathrm{\perp }}$ and the fact that ${\mathit{C}}_{\mathit{p}}$ exhibits a normal XY amplitude ratio rather than the theoretically predicted inverted ratio are still unresolved issues.

A series of experiments has been performed on a horizontally oriented, rectangular Hele-Shaw cell. Air was injected in the middle of one of the short sides of the cell into the silicon oil contained between the glass plates of the cell. The resulting unstable, immiscible interface resulted in a series of fingering patterns that were photographed and digitized. A variety of analytical techniques was applied to the images in order to quantify the observed phenomena. These included (i) calculating pattern densities, as a function of distance from the injection port, which help to identify growth regions, (ii) determining power-law relations between several of the patterns’ growth parameters (e.g., interface length, gyration radius, and flow area), and (iii) obtaining time series of two fractal measures, thus illustrating temporal variability in the geometrical properties of the images. In addition, an extensive study of the distributions of length scales and their temporal evolution was done using histograms with two bin regimes and scatter plots of percent population within given bins. The temporal evolution of dominant scales and a modal distribution of length scales conforming to the predictions of linear stability has been witnessed.

Certain kinds of nonlinear instabilities are related to the existence of negative-energy perturbations. In this paper, an exact energy expression for linear quasineutral electrostatic perturbations is derived within the framework of dissipationless multifluid theory that is valid for any geometry. Taking the mass formally as a tensor with, in general, different masses parallel and perpendicular to an ambient magnetic field allows one to treat in a convenient way different approximations such as the full dynamics and restriction to parallel dynamics or the completely adiabatic case. Application to slab configurations yields the result that the adiabatic approximation does not allow negative energy for perturbations which are perfectly localized at a mode resonant surface, whereas inclusion of the parallel dynamics does. This is in agreement with a recent numerical study of drift-wave turbulence within the framework of collisional two-fluid theory by B. Scott [Phys. Rev. Lett. 65, 3289 (1990); Phys. Fluids B 4, 2468 (1992)]. A dissipationless theory can be formulated in terms of a Lagrangian, from which the energy is immediately obtained. We start with the nonlinear theory. The theory is formulated via a Lagrangian which is written in terms of displacement vectors ${\xi }_{\nu }$(x,t) such that all constraints are taken into account. The nonlinear energy is obtained from the Lagrangian by standard methods. The procedure used is the same as that developed in a forthcoming paper by Pfirsch and Sudan [Phys. Fluids B (to be published)] for ideal nonlinear magnetohydrodynamics theory. From the exact Lagrangian one obtains the Lagrangian of the linearized theory by simple expansion to second order in ${\xi }_{\nu }$. This Lagrangian then yields the energy of the linearized theory. People working in this field have hitherto considered only (positive semidefinite) expressions for the nonlinear energy which do not immediately allow one to investigate the existence of linear negative-energy perturbations relating to nonlinear instability.

An experimental analysis of the focusing of a continuous electron beam, induced by the mutual interaction with charges produced by electron impact, is presented. The phenomenon has been observed by measuring the beam current on two different detector active areas as a function of the gas pressure in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$. The stationary solutions of a three-fluid model, already developed, allow us to measure the maximum beam density. Moreover, we carry out information about the main processes responsible for ionization and their cross sections in the case of a three-component quasiequilibrium plasma.

Results from the standard quasilinear theory of ion-acoustic and Langmuir plasma microturbulence are incorporated into the kinetic theory of the electron distribution function. The theory is then applied to high current discharges and laser-produced plasmas, where either the current flow or the nonlinear laser-light absorption acts, respectively, as the energy source for the microturbulence. More specifically, the theory is applied to a selenium plasma, whose charge state is determined under conditions of collisional-radiative equilibrium, and plasma conditions are found under which microturbulence strongly influences the electron kinetics. In selenium, we show that this influence extends over a wide range of plasma conditions. For ion-acoustic turbulence, a criterion is derived, analogous to one previously obtained for laser heated plasmas, that predicts when Ohmic heating dominates over electron-electron collisions. This dominance leads to the generation of electron distributions with reduced high-energy tails relative to a Maxwellian distribution of the same temperature. Ion-acoustic turbulence lowers the current requirements needed to generate these distributions. When the laser heating criterion is rederived with ion-acoustic turbulence included in the theory, a similar reduction in the laser intensity needed to produce non-Maxwellian distributions is found. Thus we show that ion-acoustic turbulence uniformly (i.e., by the same numerical factor) reduces the electrical and heat conductivities, as well as the current (squared) and laser intensity levels needed to drive the plasma into non-Maxwellian states.

These effects are large over a wide range of plasma temperatures and densities such as found in Z-pinch, laser-produced, or opening switch plasmas. The reduction in laser intensity thresholds for generating non-Maxwellian states is a result of microturbulence enhanced laser absorption, which can be observed at any laser intensity. Thus, if microturbulence is the cause of the heat flux inhibition, then the magnitude of the inhibition might be directly observed through the use of probe-laser beams. Finally, we calculate the laser intensities and the current densities needed to change the electron distributions in the presence of ion-acoustic turbulence. These calculations are carried out by assuming that the electrostatic fluctuations scale as the square root of the electron plasma parameter in a weakly microturbulent selenium plasma. The laser intensities calculated in this example are found to be only slightly in excess of those used in recently conducted experiments.

The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schrödinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations.