Using scanning tunneling microscopy, we directly observe monolayers of smectic liquid crystal, 4’-n-octyl-4-cyanophenyl (8CB), on oriented polyimide Langmuir-Blodgett (LB) films. We find that the monolayers form a two-dimensional crystalline structure and 8CB molecules are always aligned along the chain direction of polyimide. The results demonstrate that the anchoring structure of 8CB monolayers is an epitaxial alignment growth on the oriented polyimide LB films.

Macroscopic fluid motion can have dramatic consequences near the isotropic-nematic transition in fluids of nematogens. We explore some of these consequences using both deterministic and stochastic descriptions involving coupled hydrodynamic equations of motion for the nematic order parameter and fluid velocity fields. By analyzing the deterministic equations of motion we identify the locally stable states of homogeneous nematic order and strain rate, thus determining the homogeneous nonequilibrium steady states which the fluid may adopt. By examining inhomogeneous steady states we construct the analog of a first-order phase boundary, i.e., a line in the nonequilibrium phase diagram spanned by temperature and applied stress, at which nonequilibrium states may coexist, and which terminates in a nonequilibrium analog of a critical point. From an analysis of the nematic order-parameter discontinuity across the coexistence line, along with properties of the interface between homogeneous states, we extract the analog of classical equilibrium critical behavior near the nonequilibrium critical point. We develop a theory of fluctuations about biaxial nonequilibrium steady states by augmenting the deterministic description with noise terms, to simulate the effect of thermal fluctuations. We use this description to discuss the scattering of polarized light by order-parameter fluctuations near the nonequilibrium critical point and also in weak shear flow near the equilibrium phase transition. We find that fluids of nematogens near an appropriate temperature and strain rate exhibit the analog of critical opalescence, the intensity of which is sensitive to the polarizations of the incident and scattered light, and to the precise form of the critical mode.

Wetting in a (‘‘concave’’) wedge, or corner, is considered from a macroscopic point of view. Combination with basic thermodynamics of the classic equations due to Laplace and Young yields, surprisingly, a number of interesting results in this context. The wetting transition is shifted to lower temperatures and is no longer confined to the coexistence line, but extends a finite distance into the gas phase. Regardless of the nature of the wetting transition on a flat substrate, the wetting transition in a wedge is continuous, sharpening to a first-order transition as coexistence is reached. The extent of the region in which macroscopic arguments apply is discussed, and is found to depend on the detailed nature of the wetting transition on a flat substrate. Finally, we speculate that wedge wetting might open up new possibilities for observing phenomena connected with the prewetting line.

We present an alternative approach to the calculation of long-time diffusion coefficients of dense suspensions. The main idea is to approximate friction coefficients rather than the diffusion coefficients. Within this scheme we derive a very simple yet accurate theory of dynamic properties of a hard-sphere suspension: to calculate friction coefficients we keep only the two-particle dynamics while taking the higher-density effects into account via a renormalization of the frequency of the binary encounters by the contact value of the pair-correlation function. Using this theory we calculate the long-time self-friction and self-diffusion coefficients, the time-dependent self-diffusion kernel, and the wave-number-dependent long-time friction coefficients. The explicit results compare reasonably well with Brownian-dynamics simulations.

We present a theory for calculation of the long-time self-diffusion coefficient of suspensions of interacting colloidal particles without hydrodynamic interactions. The theory follows the idea put forward in the preceding paper [Jan A. Leegwater and Grzegorz Szamel, Phys. Rev. A 46, 4999 (1992)]: The self-friction coefficient is calculated approximately and the self-diffusion coefficient can be obtained using the Einstein relation. To calculate the friction coefficient, we retain the part of the three-particle dynamical correlations that can be expressed in terms of the two-particle dynamical correlations. In this way we renormalize the two-particle dynamics. To get explicit results for hard spheres, we introduce a decoupling approximation for the long-time contributions to the friction coefficient. For intermediate densities the predictions of our theory agree very well with Brownian-dynamics simulation.

A model for the generic reaction of the type A+B→AB on a fractal surface, in the square lattice of size L×L (L≤300), is simulated by means of the Monte Carlo technique. The employed model, based on the Langmuir-Hinshelwood reaction mechanism, has a single parameter, namely the mole fraction of B in the gas phase (${\mathit{p}}_{\mathit{B}}$). In the absence of B desorption, there is no reactive steady state with AB production, but an irreversible phase transition (IPT) from A- to B-poisoned states at ${\mathit{p}}_{\mathit{B}}$=1/2. Nevertheless, assuming B desorption, an IPT occurs at the critical point ${\mathit{p}}_{\mathit{c}\mathit{B}}$≃0.5562 (L=∞), so that for ${\mathit{p}}_{\mathit{B}}$≤${\mathit{p}}_{\mathit{c}\mathit{B}}$ the fractal becomes poisoned by A species while for ${\mathit{p}}_{\mathit{B}}$>${\mathit{p}}_{\mathit{c}\mathit{B}}$ a stationary state with AB production is found. The critical behavior of the coverages with the reactants and the rate of production are studied and the corresponding critical exponents are determined. Also the correlation length exponent is evaluated.

Recently a general phase equation has been derived from the boundary integral equation, and preliminary results on the Eckhaus instability were given [K. Brattkus and C. Misbah, Phys. Rev. Lett. 64, 1935 (1990)]. The first focus of the present study is devoted to an extensive analysis of both the derivation of the phase equation and the computation of the Eckhaus boundaries from the low-velocity regime until the planar-front restabilization. We pay a special attention to the experiments on liquid crystals [J. M. Flesselles, A. J. Simon, and A. J. Libchaber, Adv. Phys. 40, 1 (1991)]. The special shape of the Eckhaus boundaries in the present situation provides a simple hint for experimental investigations. The second line of this paper is motivated by a strong wish to go further towards the understanding of the diverse variety of dynamical manifestations observed in experiments, such as oscillatory modes and ‘‘chaotic’’ motions. The study of these phenomena is greatly facilitated by focusing on the large-velocity regime where the front dynamics turns out to be described by a local equation. We outline here the derivation of that equation appropriate for liquid-crystal experiments. A full study on this equation, going from order to chaos, is presented elsewhere [K. Kassner, C. Misbah, and H. Müller-Krumbhaar, Phys. Rev. Lett. 67, 1551 (1991)]. Among other results presented here we show that the wavelength of the pattern λ scales with the growth velocity V and the thermal gradient as λ∼${\mathit{V}}^{\mathrm{-}1}$f(G/V). At the fold singularity for steady symmetric solutions, we find that λ∼${\mathit{V}}^{\mathrm{-}1}$, which is in agreement with experiments on liquid crystals. This scaling is to be contrasted to the one obtained in the small-Péclet-number limit λ∼${\mathit{V}}^{\mathrm{-}1/2}$f(G/V) [K. Kassner and C. Misbah, Phys. Rev. Lett. 66, 445 (1991)].

We use the real-space renormalization-group approach to calculate the fractal dimension of diffusion-limited aggregation for a lattice with an arbitrary Euclidean dimension d. The results obtained are in good agreement with numerical results. We prove that D→d-1 as d→∞.

We consider the effect of a periodic oscillation on the growth velocity of a liquid-solid interface during the directional solidification of a binary mixture. By using a different formalism for the description of the interface motion, we confirm the eventual stabilizing properties of the oscillation found in the analysis of Wheeler [J. Cryst. Growth 67, 8 (1984)] in the same configuration. In addition, we determine, in the small-forcing-parameter limit, the regions in the stability diagram where the oscillation has a stabilizing or a destabilizing effect. A stabilizing effect is found in an intermediate range of wave numbers and for a frequency larger than unity. The stabilizing effect is increased for larger partition coefficient and larger forcing frequencies. The magnitude of the capillary length is relatively neutral concerning this stabilization.

A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.

The kinetics of irreversible aggregation are studied using power series in time for general sum and product kernels of the type (${\mathit{i}}^{\mathrm{\alpha }}$+${\mathit{j}}^{\mathrm{\alpha }}$) and (ij${)}^{\mathrm{\alpha }}$. Assuming a power-law form for the asymptotic behavior of the first moment of the cluster distribution, ${\mathit{M}}_0$∼${\mathit{t}}^{\mathrm{-}\gamma }$, we are able to determine the exponent γ by inverting the series to give t as a function of the first moment. Exact solutions are known for α=0 and 1. Our numerical method gives γ as a function of α for α in the range from 0 to 1 for the sum kernel. For the product kernel we are able to determine γ near α=0 and 1, but a power-law form does not seem to fit the series well in the midrange near α=1/2. For the product kernel we clearly detect the onset of the gelation transition at α=1/2.

The size-specific coagulation frequencies of fractal aggregates formed by the simulation of diffusion-limited cluster-cluster aggregation in two and three dimensions are determined from dynamic-scaling spectra by an inverse-problem approach. The four cases considered are two- and three-dimensional aggregation in which the cluster diffusivity is independent and dependent upon the mass of the cluster. The frequencies dervied from this approach describe the transient simulation results very well, the predictions being better than those with the Smoluchowski Brownian-coagulation frequency [Phys. Z. 17, 557 (1916)] modified by scaling arguments in three dimensions. Furthermore, frequencies are obtained for two-dimensional aggregation for which physical models have been evasive. The validity of the mean-field equation with a time-independent homogeneous frequency is examined. It is found that the mean-field approximation is valid in the range of simulation results but progressively deteriorates with time. The power of the inverse-problem approach here lies in its yielding size-specific aggregation rates of particles whether or not physical models are available.

We have studied the dynamics of phase separation in a binary liquid mixture contained between a pair of closely spaced quartz plates. The system behaves very differently from a bulk mixture undergoing spinodal decomposition. For example, the domains do not increase in size as a power of time, and in fact coarsening happens much faster than within a bulk mixture. This is because the process is dominated by the wetting of the plates by one of the two phases. One of the emerging phases, the one that wets the plates, forms an initially thick wetting layer on each quartz plate. Both layers are connected with a few isolated channels. As the time progresses, these layers thin, causing the channel radii to increase. We studied the growth of the channels in detail and found that there was a smallest radius ${\mathit{r}}_{\min }$, such that channels with radius r<${\mathit{r}}_{\min }$ dissolved, while those with r>${\mathit{r}}_{\min }$ grew.

The evolution of density profiles in plasmas produced by ${10}^{14}$-W ${\mathrm{cm}}^{\mathrm{-}2}$, 1-ps, 580-nm-wavelength laser pulses has been determined from spectral shifts imposed on a reflected picosecond probe pulse. The shifts are caused by two mechanisms: hydrodynamic expansion and ionization front motion. Both time-resolved expansion velocities and ionization rates are inferred from the spectral shifts and are compared to one-dimensional hydrodynamic simulations.

Enhanced stopping and effective charges of energetic (${\mathrm{C}}^{4+}$, ${\mathrm{S}}^{7+}$, and ${\mathrm{Br}}^{6+}$) ions in dense plasmas are considered within the framework of the standard stopping model (SSM), the most economical extension to plasmas of the standard cold-matter formalism (Bohr-Bethe-Bloch). The main goal of this work is to check quantitatively the SSM predictions using the setup SPQRII (Stopping Plasma Quantitatively Reinforced) developed at Orsay. It consists of a dense hydrogen discharge inserted in an ion-beam line from a tandem Van de Graaff accelerator. Simultaneous ion spectrometry and plasma diagnostics yield quantitative energy-loss measurements, monitored by target free electrons. Specific aspects of the project such as, ion-beam–plasma interface, synchronization of plasma with beam time structure, and ion transmission in the target, are given due attention. Measured enhanced plasma stopping and projectile effective charge are then quantitatively matched with theoretical predictions, for ions with a kinetic energy between 1 and 2 MeV/amu. Relevance to heavy-ion-driven inertial compression is stressed.

We have examined the nonlinear dynamics associated with beat-wave (Δω,Δk) generation of long-wavelength plasma waves (Δk≤${\mathrm{\omega }}_{\mathit{p}}$/c) in the presence of a strong (δn/n-0.15 to 0.75) short-wavelength density ripple [${\mathit{k}}_{\mathit{i}}$-(5 to 130) Δk] using the relativistic Lagrangian-oscillator model. Two cases are considered: time-varying detuning ratio (${\mathrm{\omega }}_{\mathit{p}}$/Δω) and time-varying laser intensity I. In the absence of the plasma ripple, it is found that the Lagrangian-oscillator motion contains half-harmonic components in an Arnold tonguelike parameter space (${\mathrm{\omega }}_{\mathit{p}}$/Δω,${\mathit{v}}_{\mathrm{osc}}$/c) centered around ${\mathrm{\omega }}_{\mathit{p}}$/Δω≊0.5. The effect of the ripple is twofold: (a) It lowers the minimum driver strength needed to access the half-harmonic parameter region around ${\mathrm{\omega }}_{\mathit{p}}$/Δω≊0.5, and (b) it makes a second parameter region available, centered around ${\mathrm{\omega }}_{\mathit{p}}$/Δω≊2.0. Although the Lagrangian model exhibits further period doubling followed by a transition to chaos when a time-varying laser intensity is used, wave breaking sets in after the first bifurcation, thereby limiting the validity of the model. The origin of the first period doubling, however, is found to be linked to the stability of an equivalent Mathieu equation to 1/2 subharmonic resonances. Finally, a particle-in-cell-code simulation shows spatial wave-number peaks displaced by Δk/2 on both sides of the driver frequencies, giving support to the idea that the first bifurcation behavior may be observable in an experiment.

Experiments have shown that a single 10-μm-radius laser spot is not able to produce the 90° side-emitted 3/2 harmonic efficiently in a preformed laser plasma. However, with the help of one or two auxiliary laser spots with a size similar to that of the main spot, the side-emitted 3/2 harmonic can frequently be detected when some positional and angular conditions for the auxiliary spots are met. The origin of these phenomena has been analyzed in terms of a proposed reflected laser photon-coupling model.

A three-dimensional density-functional molecular-dynamics code is developed for the Thomas-Fermi density functional as a prototype for density functionals using only the density. Following Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985)], the electronic density is treated as a dynamical variable. The electronic densities are verified against a multi-ion Thomas-Fermi algorithm due to Parker [Phys. Rev. A 38, 2205 (1988)]. As an initial application, the effect of electronic polarization in enhancing ionic diffusion in strongly coupled plasmas is demonstrated.

The mechanism of the spontaneous emission in a uniform magnetic field with a dielectric medium is being studied. The actual process can be divided into two branches: a vacuum branch and a Čerenkov branch. In the limit of vanishing matter density, a vacuum branch is the only one that remains. For each of these two branches, we derive general expressions for angular energy and power distributions with the corresponding spectra. For the Čerenkov branch, however, we deduce that a new effect, a helical Čerenkov effect, exists in a dielectric medium. This effect, unlike the ordinary Čerenkov effect, depends on the radius of curvature of the electron trajectory, measured in a plane perpendicular to the direction of the electron guiding center. Furthermore, for an index of refraction n that is independent of the radiation angle and also is a slowly varying function of the radiation frequency, the spontaneous emission from spiraling electrons may go into a large number of harmonics for either of the two branches. As compared to a vacuum, the effect of the dielectric medium is to increase the overall energy emission.

The Wigner phase-space formalism has been shown to provide the natural tools to treat charged-beam transport. In this article we show how simple experiments, exploiting electron beams propagating through quadrupole magnets and drift-tube sections, can be designed to measure the Wigner rotation.