We examine the growth of a faceted crystal in the cellular regime of directional solidification. We prove, both by a model and by a complete numerical solution, the existence of faceted cusplike cells and the possibility of maintaining a Saffman-Taylor picture at least for the tip. Faceting does not modify the usual selection mechanism and the wavelength of the pattern remains unpredicted.

An integral equation for the dynamic pair-correlation function is derived from the nonequilibrium Kirkwood hierarchy of integral equations for simple fluids subject to shear. The shear effect appears as an additional contribution to the intermolecular potential. The integral equation reduces to the Percus-Yevick equation for the equilibrium pair-correlation function as the shear rate vanishes. To show the utility of the theory an approximate dynamic pair-correlation function is calculated by treating the shear part of the nonequilibrium potential as a perturbation. The basic features of the shear-induced distortions of the pair-correlation function and structure factor are reproduced by the approximate dynamic pair-correlation functions thus calculated.

We report extensive measurements of hypersonic sound velocity in sodium-di-2-ethylhexyl-sulfosuccinate–water–decane system in the one-phase region where it forms water-in-oil microemulsions. The experiments were performed as a function of the droplets volume fraction φ in the range 0 to 0.75 and for several temperatures. A comparison of these results with ultrasonic data shows the presence of dispersion effects strongly dependent on the temperature at φ≥0.3. The overall analysis of the data in terms of a static effective-medium approach indicates that the observed effects are related to the dynamics of the aggregation process near the percolation threshold.

In homogeneous systems, symmetry is found to exist between the hierarchies of kinetic equations of multipoint joint probability density functions of two diffusion-limited reactions A+A→A (coagulation) and A+A→inert (annihilation) by rescaling their multipoint joint density functions. Given one set of the joint density functions, this symmetry allows the solution of the others. A general class of diffusion-limited reactions, which are incomplete reactions between coagulation (with probability p) and annihilation (with probability 1-p), are found to share the same scaling symmetry.

Motivated by some recent remarks on the ‘‘removability’’ of Berry’s phase [Ph. De Sousa Gerbert, Ann. Phys. (N.Y.) 189, 155 (1989)] or its classical counterpart, the Hannay angle, we present here a fresh analysis of Berry’s-phase calculations for some coherent states of general theoretical interest. Our reasoning, though semiclassical, lends itself easily for comparison with the exact results. Unlike spin-coherent states, both the (ordinary) harmonic-oscillator and squeezed coherent states are contained in Hamiltonians for which Berry’s phase can be removed globally by a canonical transformation.

Analytic expressions of the mean error and of the error probability versus time are derived for chaotic attractors. The expressions are studied for the logistic and Bernoulli maps and for the Rössler flow. In all cases mean error growth follows a logisticlike curve, the characteristics of which are related to the intrinsic properties of the attractor.

Analytical self-similar profiles of the Saffman-Taylor experiment in a sector of a disk are determined by conformal mapping, in the absence of surface tension. I show the existence of a continuous set of symmetric solutions either in the convergent or divergent fluid flow case.

We present an experimental study of the Eckhaus instability and the spatial-temporal evolution of the roll structure in two-dimensional (2D) anisotropic systems. In spite of the fact that the instability in 2D systems is manifested via the nucleation of topological defects, contrary to the case of 1D systems, we find no differences in the basic instability mechanism. Longitudinal, long-wavelength modulation is reponsible for the instability, exactly as in 1D systems, and thus the stability boundary and the spatial-temporal evolution dynamics are identical for 1D and 2D roll patterns.

The dynamical behavior of the diblock copolymer polystyrene-poly(methylmethacrylate) (PS-PMMA) in toluene has been investigated by quasielastic light scattering. Two distinct modes have been observed in the autocorrelation function of the scattered light. In the semidilute range, at one polymer concentration c>${\mathit{c}}^{\mathrm{*}}$ (where ${\mathit{c}}^{\mathrm{*}}$ is the overlap concentration) and far from the microphase separation, the variation of the two relaxation processes characterized by their frequencies Γ,Γ’ and their amplitudes A,A’ has been examined as a function of the scattering vector ‖q‖. The experimental results are in good agreement with the theoretical predictions.

We describe two types of curvature-related interfacial transitions occuring in soluble amphiphile monolayers under compression. The first type corresponds to the buckling of areas with sizes up to the monolayer’s de Genres–Taupin persistence length squared, and starts to occur when the interfacial tension is about one-half its bare value. The second type corresponds to the transformation of the simply connected monolayer into either a dispersion of droplets or an interconnected bicontinuous structure. The resulting type of volume-spanning state is determined by the sign of the saddle-splay bending constant

Optical second-harmonic generation has been used to determine the average molecular orientation of liquid-crystal (LC) molecules adsorbed on various silane-covered substrates. With the use of different preparation methods for the silane layers, considerable changes in molecular orientation of the polar-ordered part of the first LC monolayer were observed. Concomitantly, the number of polar-ordered LC molecules changed.

We use x-ray diffraction on aligned samples of the smectic-A and -${\mathit{C}}^{\mathrm{*}}$ phases to confirm the existence of a chevron-layer structure even within the smectic-A phase. Furthermore, we demonstrate that an ac electric field can be used to eliminate the chevron structure and produce uniform orientation of the smectic-${\mathit{C}}^{\mathrm{*}}$ layers perpendicular to the glass plates. The results of the x-ray study are in agreement with the earlier optical observations. The practical implication of the chevron removal is the significant enhancement of the optical contrast of the cell.

Statistical distribution functions are derived for the polarization of optical waves transmitted through a random medium. Excellent agreement is obtained with experiment. Our most significant result is the distribution function for the ellipticity ε, the ratio between the major and minor axes of the elliptically polarized scattered light. This has a maximum at ε=0 and vanishes for ε=1, indicating that linear polarization is the most probable state and that circular polarization has vanishing probability. The averaged ellipticity is found to be 〈ε〉=1-ln2=0.307.

The critical behavior of two-dimensional vesicles in the deflated regime is studied analytically using a mapping onto a gauge model, scaling arguments, and exact inequalities. In agreement with the results of earlier studies the critical behavior is governed by a branched-polymer fixed point. The shape of the critical line in the gauge model is deduced in the weak and in the inifnitely deflated regime.

The geometric approach to quantum mechanics initiated by Berry’s remarkable discovery [Proc. R. Soc. London Ser. A 392, 45 (1984)] of the anholonomy of the phase of the wave function and subsequent developments leading to a recent reformulation of the geometry of quantum evolution by Anandan and Aharonov [Phys. Rev. Lett. 65, 1697 (1990)] is shown to find an explicit and suggestive realization through the coherent-state representation.

Following a recent revival of interest in the properties of SU(1,1) Hamiltonians, we discuss the properties of classical-limit dynamics for a class of such models. Using a coherent-states technique, we analyze the classical energy function determining the motion and discuss the existence of stable and unstable stationary solutions. Appropriate phase diagrams are also presented. Comparison with previous works on similar models is made.

In a generalized quantum-mechanical framework with fuzzy dynamical variables, there exists a small radical length R<${10}^{\mathrm{-}17}$ cm, which is related to the physical impossibility of unlimited accuracy in measuring a particle’s position. It sheds light on the problem of a detailed and gradual transition, as the mass increases, from the probabilistic behavior of microscopic objects (mcR≪ħ) to the deterministic behavior of macroscopic objects (mcR≫ħ), a problem unaddressable within the framework of ordinary quantum mechanics. A generalized equation of motion for a particle with an arbitrary mass m is postulated. It possesses a new local gauge symmetry and reduces to the Schrödinger and the Hamilton-Jacobi equations in the limits of small m and large m, respectively. For the double-slit experiment, the theory predicts that, as the mass increases with the momentum fixed, the interference pattern will have roughly half the usual intensity and two bright spots when mcR/ħ∼1.

We describe the measurement of a component of the nonadiabatic transition probability in a two-level system that depends only on the path through parameter space followed by the Hamiltonian, and not on how fast the path is traversed [M. V. Berry, Proc. R. Soc. London 430, 405 (1990)]. We performed the measurement by sweeping a radio-frequency field through the Zeeman resonance of carbon-13 in a static magnetic field and measuring the transition probability P at the end of each sweep. We found that, for appropriately chosen radio-frequency sweep forms, a factor of P is independent of the duration of the sweep, in accordance with the theory of Berry.

The improved Hill determinant method with a variational parameter is applied to the general polynomial quantum anharmonic-oscillator and multiwell-oscillator problems. We calculate the eigenvalues and the expectation values 〈${\mathit{x}}^{2\mathit{m}}$〉 of the oscillator, which are in good agreement with the exact values obtained by using supersymmetric quantum mechanics.

We have studied positronium quenching resulting from collisions with the triplet states of benzaldehyde, oxygen, benzophenone, and bromonaphthalene. Positronium pick-off decay rates are presented as functions of triplet populations via uv irradiation of benzaldehyde-ethane, benzaldehyde-helium, and oxgyen-ethane gaseous mixtures and of benzophenone and bromonaphthalene adsorbed porous silicas. Our results show that the cross sections for positronium quenching in collisions with excited triplet states are not as high as reported previously. The oxygen data suggest reactions between ‘‘hot’’ (nonthermal) positronium and oxygen molecules.