Fluctuational transitions between stable states of an all-optical lumped-parameter bistable system have been observed. The dependences of the transition probabilities, and of the statistical distribution of the transmitted-light intensity, on the intensities of incident light and noise have been investigated. Two types of stochastic modulation, that of the incident-light intensity and that of the device itself, have been used. They correspond to multiplicative and additive noise for the intracavity-phase gain and give rise to qualitatively different pictures of the fluctuations. In particular, for the latter type of noise the logarithm of the statistical distribution of the transmitted-light intensity is described by a multibranch function, and the peaks of the distribution are strongly asymmetric. The onset of a zero-frequency peak in the power spectrum of the transmitted light in the range of the kinetic phase transition has been observed. The experimental data are in good qualitative and quantitative agreement with the theory.

A double-expansion procedure, i.e., ε expansion followed by a power-series expansion, is suggested in order to compute the stationary probability distribution of the two-dimensional Fokker-Planck equation. In each ε order, the power series is determined uniquely. The solubility conditions for the leading two ε orders are justified. Noise-induced characteristic features, including the noise-induced phase transition, are briefly discussed.

The theory of Burton, Cabrera, and Frank [Philos. Trans. R. Soc. London Ser. A 243, 299 (1951)] for crystal growth on stepped surfaces is extended to include adatom interactions that are responsible for incipient island formation. By using a reaction-diffusion formulation of growth, a system of nonlinear diffusion equations is derived for the concentrations of surface clusters containing up to a prescribed number of atoms. By an appropriate choice of cells in the coarse graining of the lattice model, we show that the ostensibly one-dimensional equations obtained in the continuum limit in fact contain two-dimensional information averaged over the lateral length of the terrace. This allows the evolution equation for the averages of the various species to be decoupled from the higher-order correlation functions and simplifies the specification of the boundary conditions at the step edges. We have previously used this formalism to derive a nonlinear term for the formation of diatomic islands, from which we were able to predict quantitatively the transition to a step propagation mode for growth on stepped surfaces. Here, we extend the applicability of the original model away from growth by step advancement by allowing the surface atoms to form up to ten-atom islands. Furthermore, by including the breakup of atoms from the islands and adatom capture and detachment kinetics at the step edges, the model is capable of describing the relaxation of the surface toward equilibrium upon cessation of growth.

A statistical treatment of the macroscopic equation of motion leads to memory functions if Markovian-like approximations are not admissible. A nonlinear discrete model, which is nonlocal in time, may be obtained from the logistic map by replacing its linear term by a convolution with an exponentially decaying memory function xt+1=a[Σt′=0tγ0εt-t′xt′-xt2]. This one-dimensional discrete map, R1→R1: x0→x1→x2⋯, possesses the same fixed point 1-1/a for all ε, if we choose the normalization γ0=1-ε. It is the goal of this paper to demonstrate the main features of the map induced by the memory term. Due to the complexity of the problem, most of the results have been derived by a numerical treatment. The range of ε lies in the interval -0.1⩽ε<0.3. For fixed a,ε generally two alternative attractors S and S′ appear. For small |ε|≪0.02 only the usual Feigenbaum scenario S(a) exists, slightly modified by ε. For ε≳0.02 the scenario S(a,ε) is shifted, and different windows with the same period coalesce. The ε-induced scenarios S′(a,ε) arise suddenly. In the (a,ε) plane there exist islands of three-, six-, nine-, or tenfold period-doubling scenarios S′(a,ε). The insertion of these S′(a,ε) discontinuously depends on the starting value.

The site-site distribution function and structure factor of deuterium close to the critical point have been calculated by means of quantum path-integral Monte Carlo simulations. The calculations were performed using a spherically symmetric pairwise-additive potential for the distribution of the molecular center of mass and assuming that ${\mathrm{D}}_2$ may be regarded as a classical free rotor. Some of the problems connected with the simulation of a quantum system close to the critical point are analyzed in detail. The results of the simulations have been compared with the neutron-scattering experiment by Zoppi et al. [Phys. Rev. A 39, 4684 (1989)]. The overall agreement is excellent, but some diffuse discrepancies are found. Possible origins of this inconsistency are discussed.

The velocity autocorrelation function (VACF) of lattice-gas cellular-automata fluids has been calculated by mode-coupling (MC) theory for finite systems, including sound modes, and compared with computer simulations on small (N≃${10}^3$) and large (N≃${10}^6$) two- and three-dimensional (3D) systems for reduced densities f ranging from 0.05 to 0.8. For times t up to 6${\mathit{t}}_0$ (mean free times) the simulated VACF agrees with Boltzmann relaxation. In 2D the agreement with MC theory is excellent for t>9${\mathit{t}}_0$ and has been tested over intervals of several acoustic traversal times. In 3D the agreement is still good, but sets in after much larger times (150${\mathit{t}}_0$ at f=0.1 and 60${\mathit{t}}_0$ at f=0.8). However, there are disagreements in the smallest systems at the lowest densities, where the observed VACF at largest times is about 6% (f=0.1) and 9% (f=0.05) larger than the theoretical values.

A powerful flow visualization and measurement method has been developed using ultrafast NMR imaging. This technique enables one to measure instantaneous distribution of any velocity component in any cross-sectional plane. This method was applied to the equilibrium turbulent region, or ‘‘puff,’’ which is intermittently created by large disturbances in a circular pipe when the Reynolds number is around 2250. Instantaneous velocity component distributions were visualized and measured for two velocity components. The flow component parallel to the pipe axis clearly demonstrated the gross nature of the equilibrium puff and that perpendicular to the pipe axis visualized the detailed structures of vortices. Longitudinal vortices were clearly observed near the pipe wall at the upstream interface as well as around the pipe axis in the downstream region. The present measurements made for a single puff, in principle, agree with the ensemble-averaged results obtained in hot-wire measurements previously reported, both qualitatively and quantitatively.

We report theoretical results for Taylor-vortex flow subjected to external rotation. The system consists of an incompressible viscous fluid between two concentric cylinders with the inner one rotating about their common axis. The two cylinders also rotate together with a dimensionless angular velocity Ω about an axis orthogonal to their axis. We perturbatively calculated the base flow to second order in Ω and carried out a linear stability analysis of this flow. We found that external rotation stabilizes the base flow and decreases the critical wave number of the tilted vortices that form at the onset of the first instability. Our results for the critical Reynolds number, the critical wave number, and the tilt angle, together with the coefficients of linear terms in the relevant Ginzburg-Landau amplitude equation, are presented to order ${\mathrm{\Omega }}^2$.

We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth d that is heated from below. Most of the experiments were conducted in a cylindrical container of radius r and aspect ratio Γ==r/d=10. The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference ΔT between the bottom and top plates. After initial transients ended, the reduced Rayleigh number ε==ΔT/Δ${\mathit{T}}_{\mathit{c}}$-1, where Δ${\mathit{T}}_{\mathit{c}}$ is the critical temperature difference for the onset of convection, increased linearly with ramp rate β such that ε(t)=βt. When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 0.01≤β≤0.30. When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing. When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry. In the earliest stages the patterns were then composed of irregularly arranged cells and varied randomly between experimental runs. The same random cellular flow was also observed in samples of square horizontal cross section. The results demonstrate the importance of stochastic effects on pattern formation in this system. However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise.

We consider the advance of the interface separating two domains in a random two-dimensional medium. The domains correspond to regions of opposite spin in magnetic systems or different fluid phases in fluid invasion. A driving force normal to the interface, corresponding to an external magnetic field or pressure, causes one domain to grow. Various types of disorder corresponding to random fields or bonds were studied. When disorder in the medium is large, the interface forms a fractal pattern with large-scale structure characteristic of percolation. As the disorder decreases, a transition to compact, faceted growth is observed if the distribution of random fields or bonds is bounded. The critical phenomena associated with this transition and its relation to a transition found in fluid invasion are discussed.

Thermal orientation fluctuations of the director field during electric-field-induced polarization reversal in ferroelectric liquid crystals lead to the nondeterministic formation of a transient domain-wall foam that strongly scatters light. This foam comprises domains of molecules that have reoriented locally in the same sense on the smectic-C tilt cone and are separated from one another by 2π inversion walls. The dynamics of formation and the subsequent annealing of the foam have been probed using laser light scattering. Anisotropic coarsening of the foam, which is accounted for by including electrostatic (space-charge) interactions in the theoretical description of the ferroelectric liquid crystal, results in a striking pattern of elongated stripes. Stroboscopic microscopy reveals that these stripes are in general rotated from the smectic-layer planes in a chiral sense, the sense of the rotation depending on the sign of dE/dt.

Orientational order in the isotropic phase of liquid crystals confined to 0.2-μm-diam cylindrical channels of Anopore membranes is measured by deuterium nuclear magnetic resonance. At temperatures deep in the isotropic phase, the measurements reveal the order of the first molecular layer at the cavity wall, while at temperatures near the isotropic-nematic transition the measurements are primarily sensitive to order penetrating into the cavity in a manner described by the Landau–de Gennes theory. The degree of order ${\mathit{S}}_0$ at the cavity wall is measured and the surface coupling constant determined for various treatments of the cavity wall. Wide variations of ${\mathit{S}}_0$ are found for different surface treatments. Treatments that yield both perpendicular and parallel molecular anchoring are explored. The angular dependence of the surface-induced nematic order is investigated following the ${\mathit{P}}_2$(cosθ) expression independent of molecular anchoring at the surface.

The director-field configuration of a nematic liquid crystal confined to cylindrical cavities of polycarbonate Nuclepore membranes ranging from 0.3 to 0.05 μm in radius is determined using deuterium nuclear magnetic resonance ${(}^2$H NMR). Spectral patterns from cavities of radius 0.3 μm reveal the escaped-radial configuration with singular point defects, but as the cylinder size is decreased, the elastic energy imposed by the curvature of the confining walls competes with the anchoring energy to tilt the directors away from their preferred perpendicular anchoring direction, preventing the expected transition to the planar-radial configuration. A surface fitting parameter is directly determined by simulating ${}_{}{}^2{}_{}{}^{}\mathrm{NMR}$ line shapes, and by studying a series of samples with different radii, the molecular-anchoring strength ${\mathit{W}}_0$ and surface elastic constant ${\mathit{K}}_{24}$ are extracted.

By means of ultrasonic and Brillouin light-scattering techniques, we have performed extensive measurements of the attenuation coefficient and sound velocity in 2-butoxyethanol aqueous solutions over a large temperature range. In the more concentrated solutions, the frequency dependence of these properties is well accounted for by a double relaxation time equation thus excluding contributions from concentration fluctuations. This finding, as well as the overall behavior as a function of concentration and temperature, suggests the presence of alcohol aggregates beyond a characteristic concentration-temperature line resembling a critical micelle concentration curve in micellar systems. The similarity between the ultrasonic behavior and the type observed in nonionic surfactant aqueous solutions, as well as indications from other experimental sources, strongly supports the possibility that butoxyethanol aggregates are micellelike structures.

Under shear, nematic liquid crystals can exhibit localized excitations that propagate much faster than simple one-dimensional analysis can predict. We describe a two-dimensional theory in which the excitations are fronts between distinct solutions of the steady-state Ericksen-Leslie equations. We find that a front’s speed is proportional to its width and also to the difference in an effective free energy that we also define. We consider the effects of shear in Hele-Shaw cells on the director field of a nematic liquid crystal, and find distinct classes of multiple steady-state director-field configurations. The front between two solutions always moves in the direction that decreases the total effective free energy. Although the speed cannot be calculated explicitly without knowing the details of the front region, it can be estimated self-consistently using experimentally determined values for the observed front width. In this way we can obtain values for the front speed in reasonable agreement with observation.

We use numerical methods to study the simplest Langevin model applicable to the description of dense fluids. We find in qualitative agreement with theory and experiment that there is a ‘‘stretching’’ of the dynamics for low temperatures and short wavelengths.

Effects of an intense laser field on liquid water are investigated by using classical molecular-dynamics computer simulations and a water model SPC-FP, which for the first time includes both flexible intramolecular bonds and instantaneous electronic polarization effects. Comparisons with the field-off system are made throughout. Under the influence of the strong external torque, both the liquid structure and the intramolecular geometry are distorted. These effects significantly change the dynamical behavior of the liquid compared with the field-off system. The presence of the intense electric field furthermore gives rise to a nonlinear response of the medium. We estimate the nonlinear index of refraction and give a brief discussion of self-focusing and supercontinuum generation.

Homogeneous nucleation with arbitrary preexisting nuclei distribution is studied in the limit of a high nucleation barrier. An asymptotically exact expression for the time-dependent nuclei flux at the critical size is obtained.

The dynamics of electric fields at a neutral or charged point in a one-component plasma is considered. The equilibrium joint probability density for electric-field values at two different times is defined, and several formally exact limits are described in some detail. The asymptotic short-time behavior for both neutral and charged-point cases is shown to be Gaussian with respect to the field differences, but with a half-width depending on their sum. In the strong-coupling limit, the joint probability density is dominated by weak fields (charged-point case), leading to a Gaussian distribution with time dependence entirely determined from the electric-field time-correlation function. The limit of large fields is shown to be determined by the time-dependent autocorrelation function for the density of ions around the field point; for the special case of fields at a neutral point, this result implies that the joint distribution at large fields is determined entirely by the dynamic structure factor. Finally, the full distribution (all field values and times) is studied in the weak-coupling limit.

We present the basic equations for modeling a plasma column produced and sustained by a traveling electromagnetic wave in the presence of a constant external magnetic field. The model consists of two equations—a local-dispersion relationship and a wave-energy-balance equation—and a relation between the absorbed wave power per unit length averaged across the column (proportional to the squared-wave electric field) and the local electron number density. The dispersion relation and the balance equation are derived in explicit forms and depend on two numerical parameters σ=ωR/c (ω being the wave angular frequency, R the plasma column radius, c speed of light) and Ω=${\mathrm{\omega }}_{\mathit{c}}$/ω (${\mathrm{\omega }}_{\mathit{c}}$ is the electron cyclotron frequency). The limit of an infinite external magnetic field (Ω→∞) is also considered. The influence of the two parameters Ω and σ on the dimensionless axial profiles of the wave characteristics and plasma column density, obtained by numerical solution of the basic equations, has been studied for two different gas-discharge regimes. A three-dimensional wave structure has been obtained, and it is shown that the wave can be a generalized surface mode, a pure surface, or a pseudosurface one. The results obtained are in agreement with the available experimental data.