Using the Green-Kubo relations it is shown that the generalized Onsager matrix for cellular automaton fluids is positive semidefinite. This implies linear stability of the hydrodynamic modes about equilibrium. The result applies to all lattice-gas automata admitting a stationary equilibrium state that is invariant under translations of the lattice.

The two-layer fluid is considered in the shallow-water approximation. Vertical integration of the spatially three-dimensional, scaled Euler equations yields a spatially two-dimensional, Galilei-invariant system. Diagnostic relations appear formally as the thermodynamics of a two-component, nonideal gas. Certain aspects of the theory are reminiscent of the hydrodynamics of superfluid helium. Nonlinear wave dynamics can be studied analytically: simple waves and shocks are discussed in detail.

The expression for the sixth-frequency sum rule of the velocity autocorrelation function for a two-dimensional classical electron fluid interacting via a 1/r potential has been derived. This as well as lower-order sum rules and a secant hyperbolic form of the memory function have been used to calculate the time evolution of the velocity autocorrelation function. Without introducing any adjustable parameter the model gives results that are in good agreement with the molecular-dynamics data.

The stability of thin shells under arbitrary radial motions can be described by the evolution of two independent surface modes for the inside and outside shell boundaries. The evolution equations can be consistently decoupled for all mode numbers, and specific solutions for ballistic and accelerated shell motions are discussed. They show strong dependences on initial conditions and can explain significant amplification for low mode numbers by interference effects. The theory is applied to the excitation of cavity modes in accelerated high-aspect-ratio shells. By comparison with numerical solutions for the full shell equations, the validity of the analytic predictions is confirmed and the saturated oscillation amplitudes after acceleration can be estimated. The further amplification of these modes by convergence and deceleration effects is discussed and potential inertial confinement fusion applications are illustrated by a simple implosion model.

Ellipsometry and light-scattering measurements are presented for the critical region near the two-dimensional XY-like smectic-C to smectic-A phase transition in thin, freely suspended films of the liquid crystal p-decyloxybenzylidene p-aminocinnamaic acid 2-methylbutyl ester. The macro- scopically observed smectic-C tilt order parameter was found to obey a scaling relation as a function of temperature and film thickness, indicating that only the surface layers order over a wide range of temperatures. Deep within the smectic-C phase, the tilt order parameters for all thickness films measured converged upon a unique value at which the smectic-C to smectic-I transition took place. The light-scattering intensities and decay times above the smectic-C to smectic-A transition were found to scale with the Kosterlitz-Thouless correlation length, as predicted by dynamical theories of the transition. Measurements of the predicted Nelson-Kosterlitz universal jump in θ concurred with estimates for the bulk material parameters and with the light-scattering results.

The observation of a new critical point in liquid-crystal phase transitions is reported. Detailed tilt-angle, polarization, and susceptibility measurements of a ferroelectric liquid-crystal compound in the presence of an applied dc electric field show that a first-order phase transition between the polarized smectic-A phase and the ferroelectric-smectic-C phase terminates at a critical point in the temperature field plane. A liquid-crystal sample exhibiting a second-order smectic-A–ferroelectric-smectic-C transition is studied by similar measurements demonstrating a clearly different behavior to the first-order compound. A simple Landau description of the new critical point is given.

We construct a simple coarse-grained model and use it to study global phase behavior of ensembles of fluid membranes. This model is an improvement over previous phenomenological models of Talmon and Prager, de Gennes and co-workers, Widom, and more recently of Safran and co-workers. We show here that there is necessarily an entropic contribution, missing in all previous theories, to the coarse-grained free energy whose physical origin is the same as that of Helfrich’s entropic repulsion stabilizing lamellar multimembrane phases. The inclusion of this steric entropy in the previous phenomenological studies is essential if they are to be used in the study of periodic phases in microemulsions and analogous surfactant systems. Thus the model enables us to obtain, in a unified way, phase diagrams containing both uniform and periodic phases in microemulsions and in binary systems of nonionic surfactant bilayers in a single solvent. Mean-field theory for this model yields rich phase diagrams containing dilute, random bicontinuous, lamellar, columnar, and an antiferromagnetic phase that may correspond to a droplet crystal or to a ‘‘plumber’s nightmare.’’ The model depends on two phenomenological parameters related to strengths of steric entropy and softening of membrane rigidity. We discuss the sensitivity of phase diagrams (in particular the existence of the middle-phase microemulsion) to values of these parameters. We find that the existence of a realistic middle phase (with structural length scale much larger than the molecular length scale) crucially depends on the presence of steric entropy. The model reproduces the experimentally observed four-phase equilibria among uniform phases in microemulsions.

The effect of a small air bubble attached to the nose of a much larger air bubble in a viscous liquid in a Hele-Shaw cell has been studied. The Hele-Shaw cell was tilted to an angle α, measured from the horizontal, so that the buoyancy force allowed the bubbles to rise. The larger bubble became elongated to a nearly elliptical shape and its velocity increased above the value for a circular bubble of the same area. For a given size of main bubble, as the size of the nose bubble decreased, the aspect ratio and velocity of the larger bubble increased. The velocity for a given size bubble could be approximated by the theory presented by Maxworthy [J. Fluid Mech. 173, 95 (1986)] for small values of the bubble ellipticity and large values of α. At small values of α, modification of the bubble drag by gravitational distortion could partially explain the deviation from the simpler theory.

The thermodynamics of the equilibrium polymerization model (grand-canonical ensemble of self-avoiding walks) in two dimensions is worked out by means of the Migdal-Kadanoff renormalization-group technique. This method involves renormalization-group flows in an eight-dimensional parameter space. At the critical point the number of relevant fields (positive exponents) is four. The leading exponent value differs by less than 1% from the (presumed) exact value. The results are exact for the polymerization problem defined on the diamond hierarchical lattice. Some results are peculiar to this lattice and are not expected to hold for Bravais lattices. For instance, the polymerized phase (infinite polymerization index) is dilute (zero density of chemical bonds).

The aggregation kinetics of colloidal silica is highly dependent on conditions such as the pH and salt concentration. In this paper we investigate the aggregation of colloidal silica under conditions that promote rapid growth, contrasting our findings with earlier investigations of the slow growth of silica. A number of interesting effects are observed, including power-law growth of the mean aggregate radius, dependence of the aggregation rate on concentration and the chemical nature of the salt used, a reduced aggregate fractal dimension, fragmentation of the fast aggregates under changing solution conditions, and shear-induced restructuring of aggregates. Finally, we present evidence that the fractal dimension of aggregates is not strongly universal, but depends weakly on such factors as the solution concentration. We conclude that although the diffusion-limited cluster-cluster aggregation model gives a good first-order description of rapid aggregation, real systems exhibit richer behavior that is not given to such a facile interpretation.

We generalize the Chen-Lubensky model for the point where the nematic, smectic-A, and smectic-C liquid-crystalline phases meet (the NAC point) to include the effects of molecular chirality. We calculate the phase diagram for this model when the possibility of a twist-grain-boundary (TGB) phase is included and when it is not. In the latter case, we find that the NAC multicritical point becomes a critical end point where first-order cholesteric to smectic-A and cholesteric to chiral-smectic-C phase boundaries meet a second-order smectic-A to chiral-smectic-C phase boundary. In the former case, we find that the TGB phase always intervenes between the cholesteric and smectic-A phases near the NAC multicritical point of the nonchiral system. The connection between these results and the recent observations of a chiral smectic phase near the NAC point by Goodby and co-workers [Nature 337, 449 (1988); J. Am. Chem. Soc. 111, 8119 (1989)] is discussed briefly.

The stability of twist configurations in cholesteric liquid-crystal films in the presence of an external field applied parallel to the twist axis is considered. First, a general method for finding, in the absence of pretilt at the cell boundaries, the point on the instability line at which the character of the instability mode changes from uniform in the film plane to one with in-plane ripple is developed. The locus of these points (in parameter space) forms a phase boundary with multicritical behavior of the Lifshitz type. Some typical results are presented. Next, pretilt angles are allowed. In this case a uniform instability mode threshold no longer exists; however, a transition to a ripple state is still possible. Methods of analyzing such transitions are presented, along with typical results. The connection between the methods and results presented here and the development of modern liquid-crystal displays is noted.

We discuss the renormalization of the stress, gyration, and diffusion tensors for polymers in dilute solution in the presence of steady shear flow. For all finite values of the reduced shear rate, the first-order perturbation theory of hydrodynamic-interaction and excluded-volume effects yields regular functions of the renormalized model parameters. In the high-shear-rate limit, the power-law dependence of various quantities on the reduced shear rate can be evaluated explicitly.

Profiles of deep solidification cells are computed numerically in the framework of the one-sided model of directional solidification. Previous results obtained for a constant miscibility gap (K=1) are confirmed and extended to arbitrary K values for small Péclet numbers (P≪1). Various approximate relations between experimentally measurable quantities are deduced from a viscous finger analogy and tested numerically. We point out an effective parameter that should prove useful in comparing the miscellaneous experimental results.

A viscous fingering of non-Newtonian fluids at a finite viscosity ratio is considered in order to study the effect of non-Newtonian fluid on crossover phenomena. The crossover from the fractal pattern to the dense structure is investigated by using a two-parameter position-space renormalization-group method. The global flow diagrams in two-parameter space are obtained. It is found that there are two nontrivial fixed points: the fractal point and the Eden point. When the viscosity ratio is finite, the pattern must eventually cross over to the dense structure. The dependences of the crossover phenomena on the parameter k, which describes the different non-Newtonian fluids, are shown. It is found that the non-Newtonian fluids have important effects on the fractal point and the crossover line but the crossover exponent is independent of the non-Newtonian property.

We report two-dimensional contour dynamics simulations of cluster growth by diffusive transport with a finite surface resistance, relating the observed morphologies to terms in the interfacial boundary condition. Both surface tension and finite kinetics are stabilizing influences, at least for short times. For slow kinetics, surface features ‘‘heal,’’ but form deep narrow indentations or invaginations in the process. We note conditions under which tip splitting appears to be anomalous, yielding three rather than two new tips. The evolution of interfacial structure is presented in terms of a local scaling exponent, which varies approximately periodically with the logarithm of the cluster size.

A self-consistent fluid model of radio-frequency glow discharges has been used to analyze the existence of two different discharge regimes and the transition between them. The existence of these regimes had been previously established by Levitskii [Sov. Phys. Tech. Phys. 2, 887 (1958)]. The self-sustaining and power-deposition mechanisms that characterize each of these regimes are drastically different. In the first regime, termed as the ‘‘wave-riding regime’’ corresponding to low discharge power, most of the power deposition is due to bulk plasma electrons heated by the sheath expansions. In the second regime termed as the ‘‘secondary electron regime’’ corresponding to higher discharge power, the discharge is sustained mainly by electrons emitted by the electrodes under ion bombardment and avalanching in the sheath regions. The numerical results are in good agreement with previous experimental measurements by Godyak and Kanneh [IEEE Trans. Plasma Sci. PS-14, 112 (1986)]. The results presented in this paper form the first self-consistent description of these different regimes and of the transition between them. The validity domain of the model is restricted to pressure higher than a fraction of Torr and frequency less than a few tens of MHz. The gas being considered is helium and the discharge power varies between 0 and 700 mW ${\mathrm{cm}}^{\mathrm{-}2}$. The model is based on solutions of electron and ion fluid equations describing charged particle transport coupled with Poisson’s equation for the electric field. A realistic description of the electron kinetics has been obtained by considering separately two electron groups representing, respectively, the tail and the bulk of the electron distribution function. The validity of the two-electron group fluid model has been checked with Monte Carlo simulations.

A nonlocal heat-transport formula is derived by including the electrostatic potential and then solving the reduced Fokker-Planck equation for strongly inhomogeneous laser-produced plasmas. Our typical result shows a further reduction of the streaming heat-flow value, which corresponds to a flux-limiting factor scrf∼0.04.

A nonlinear one-dimensional theory is developed that describes some important aspects of intense laser-plasma interactions. The self-consistent laser-plasma analysis includes nonlinear plasma wake-field generation, relativistic optical guiding, coherent harmonic radiation production, as well as other related phenomena. Relativistic optical guiding is found to be most effective for long laser pulses having slow rise times. Short laser pulses are shown to be weakly guided. Coherent harmonic generation using a linearly polarized laser is found to be most efficient for short laser pulses and can be enhanced by the presence of large amplitude plasma wake fields. Aspects of particle acceleration by laser pulses as well as possible methods for upshifting the frequency of laser pulses are also discussed.

The space charge and the electrical current in a weakly ionized radioactive gas is theoretically evaluated. The results are compared with experimental data for a deuterium gas at room temperature containing 0.1 mol % of tritium. The dc electrical conductivity has been measured for gas densities from 0.1 to 10 mol/I and applied voltages over the range 0.1 to 400 V. The resulting current density increases with increasing gas density and the decreases at higher densities. The theoretical results show that the charge-density profiles in the gas as well as the space-charge potential change dramatically with the applied voltage. Varying the electronic recombination coefficients until theoretical predictions agree with the measured results provides a means to determine them. From this comparison it is found that the three-body recombination coefficients is 6.2×${10}^{\mathrm{-}26}$ ${\mathrm{cm}}^6$ ${\mathrm{s}}^{\mathrm{-}1}$, whereas the two-body recombination coefficient is indeterminate and of little influence on the quality of the fit as long as its value is below ${10}^{\mathrm{-}5}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$. .AE