A full study of parity-broken states in the directional solidification of lamellar eutectics is performed within the boundary-integral formulation. Symmetric states cease to exist at a wavelength λ, which is approximately twice that corresponding to their minimum undercooling, whereas solutions with a broken parity, drifting transversely to the growth front, appear as a forward bifurcation. Our results suggest that if one effectively doubles the wavelength of the initially symmetric state—a situation that can be achieved via a sudden jump of the velocity V by a factor of about 4, since ${\lambda }^2$V≃const—then tilted lamellae should appear as extended states and not as ‘‘solitons.’’ We find here that parity-broken states exist for hypereutectic as well as for hypoeutectic and eutectic compositions. We have extended the derivation of the similarity equation derived previously [K. Kassner and C. Misbah, Phys. Rev. Lett. 66, 445 (1991)] to the present situation. This case involves additional subtleties, due to the loss of reflection symmetry about the growth axis. Among other results, we find that the tilt angle φ should depend on σ=${\mathit{d}}_0$l/${\lambda }^2$ and χ=l/${\mathit{l}}_{\mathit{T}}$ only, where ${\mathit{d}}_0$, l, and ${\mathit{l}}_{\mathit{T}}$ are the capillary, diffusion, and thermal lengths, respectively, and λ is the wavelength of the pattern. At large enough growth velocities V, φ≃φ(σ), while at small V the dependence on χ is strong. These predictions can be tested experimentally.

We analyze the long-time behavior of the modified porous-medium equation ${\mathrm{\partial }}_{\mathit{t}}$u=DΔ${\mathit{u}}^{1+\mathit{n}}$ in d dimensions, where n is arbitrary and D=1 for ${\mathrm{\partial }}_{\mathit{t}}$u>0 and D=1+ε for ${\mathrm{\partial }}_{\mathit{t}}$u<0. This equation describes inter alia the height of a groundwater mound during gravity-driven flow in porous media (d=2, n=1) and the propagation of strong thermal waves following an intense explosion (d=3, n=5). Using general renormalization-group (RG) arguments, we show that a radially symmetric mound exists of the form u(r,t)∼${\mathit{t}}^{\mathrm{-}(\mathit{d}\mathrm{\theta }+\mathrm{\alpha })}$f(${\mathit{rt}}^{\mathrm{-}(\mathrm{\theta }+\mathrm{\beta })}$, ε), where θ==1/(2+nd) and α and β are ε-dependent anomalous dimensions, obeying the scaling law nθα+(1-ndθ)β=0. We calculate α and β to O(ε), for general d and n, using a perturbative RG scheme. In the case of groundwater spreading, our results to O(${\mathrm{\epsilon }}^2$) are in good agreement with numerical calculations, with a relative error in the anomalous dimension α of about 3% when ε is 0.5.

We study the time-dependent self-diffusion coefficient for a suspension of interacting, spherical Brownian particles. Guided by an exact result for a dilute suspension of hard spheres, we conjecture that the Fourier transform of the memory function may be represented as a meromorphic function of the square root of the frequency. We show that a two-pole approximation provides a suitable framework for the analysis of experimental data.

The dynamic structure factor S(k,ω) of dense helium at 39.3 K (≃8${\mathit{T}}_{\mathit{c}}$) and 114 bar is measured by inelastic neutron scattering for wave numbers 3≤k≤24 ${\mathrm{nm}}^{\mathrm{-}1}$. In contrast to dense noble-gas fluids at T<2${\mathit{T}}_{\mathit{c}}$, the present S(k,ω) can be described completely by the viscoelastic model, in which S(k,ω) is determined for each k by its zeroth, second, and fourth frequency moment and by one decay rate (that of the microscopic momentum flux).

Immiscible two-fluid displacement was studied experimentally and numerically in inhomogeneous porous models. Square-lattice models were designed using bond percolation. A fraction f of the bonds was randomly given a high permeability, set equal to 1. The rest (1-f) have a low permeability (κ=0.004). The patterns formed by the displacement of glycerol by air injected at the center of the model network were studied and compared with the results of diffusion-limited-aggregation (DLA) simulations on model bond networks that correspond precisely to the experimental models. We studied models with fractions of good bonds close to the threshold value for bond percolation ${\mathit{f}}_{\mathit{c}}$=0.50. Experimental results are well represented by simulations and can be characterized by the same effective fractal dimension ${\mathit{D}}_{\mathit{c}}$≃1.5. We find that the model geometry strongly influences formation of the displacement pattern, and that the results are independent of f. Unlike usual DLA aggregates, which grow mainly at the tips, the geometry of our models causes growth in the interior, yielding a gradual increase of the effective fractal dimension as the aggregate grows.

The dynamics of front propagation in a diblock copolymer melt are described. Systems in which stable ordered phases invade unstable and metastable disordered phases are considered. Employing a model equation deduced by Oono and Shiwa [Mod. Phys. Lett. B 1, 49 (1987)] from a cell-dynamical scheme, these systems are studied in the weak-segregation limit. In this limit, a bifurcation parameter whose magnitude quantifies the distance from the spinodal naturally arises. Exploiting the smallness of this parameter, stationary solutions to the equation of motion are perturbatively constructed for the cases of lamellar, triangular (often referred to as IhexagonalR), and bcc ordered structures. Generalizing this technique, equations of motion describing the invasion processes are derived, and from these, traveling-wave solutions are found numerically. Propagation velocities and front-envelope profiles are determined, and a number of qualitative features of the various invasion processes are described. Experimental observability of the invasion processes and experimental identification of the phenomenological parameters appearing in the equation of motion are discussed. Using existing experimental data, estimates are made of the propagation velocity which would be observed in a particular physical system and the range of temperatures, in degrees Centigrade, over which our perturbative calculation is applicable. It is found that this range includes temperatures well into the mean-field regime.

A first-principles theory for the description of critical phenomena in mixtures is presented. This is a natural extension of the hierarchical reference theory of fluids, which has proven useful and accurate in the treatment of the critical region of one-component fluids. The case of a binary mixture is studied in detail. Near the critical point, the theory develops a renormalization-group structure that allows the identification of several possible critical behaviors corresponding to different fixed points. For a generic binary mixture, the most stable fixed point gives rise to the same critical exponents as are predicted by the well-known phenomenological approach, providing a microscopic mechanism for such behavior. The competition between two fixed points is identified as the mechanism leading to the strong corrections to scaling seen experimentally. Explicit expressions for the most interesting universal quantities are evaluated to O(4-d). This theory is then applied to a few simple models of mixtures in three dimensions. As a first step, the mean-field phase diagram is reproduced and the stability of this solution is determined. The physical nature of the relevant order parameter and the one-loop correction to mean-field results are also calculated within our approach.

The colloidal-crystal–container-wall interface was studied by evanescent-wave scattering. Total internal reflection of incident laser light at the container-suspension interface produced an evanescent wave that probed only the first few colloidal crystal layers. The scattered light intensity was measured as a function of scattering angle and evanescent-wave penetration depth. Positions of four Bragg-like scattering peaks showed that the crystal structure at this interface was body-centered cubic with (110) planes parallel to the container wall. Surface reconstruction was not observed. Evidence for a smaller crystal-lattice parameter near the surface was found from the scattering peak positions. The observed dependence of Bragg-peak scattering intensity on penetration depth compared well with theory.

The electroclinic effect is studied in a compound that presents a chiral nematic–smectic-A phase sequence. The induced tilt angles are measured as a function of the applied electric fields in both phases. A strong deviation from the linear relationship between the tilt and the applied field is observed, especially in the case of the smectic-A phase. In addition, detailed measurements of the critical behavior of the electroclinic effect at the nematic–smectic-A phase transition are presented. The results are analyzed in the framework of the available theoretical models. Other possible alternatives that could account for the behavior observed at the transition are discussed qualitatively.

We report investigations on fast individual molecular reorientations in isotropic, nematic (N), and smectic-A (Sm-A) phases of chiral, achiral, and racemic liquid crystals. These motions, in the ${10}^{\mathrm{-}11}$-${10}^{\mathrm{-}10}$ s range, are probed by the degenerate four-waves-mixing technique and compared to results obtained by other techniques. In homeotropic N and Sm-A phases of achiral compounds and racemic mixture, the individual reorientation time about the long molecular axis is found to be unchanged down to the Sm-A→Sm-C transition, but increases by a factor of about 3 with a chiral compound. A quantitative comparison between theoretical prediction and experiment is presented. This result is in agreement with our previous work [Phys. Rev. Lett. 62, 3049 (1989)] and does not support the recent theoretical work by Brand et al. [Phys. Rev. Lett. 64, 1309 (1990)] as well as the results of the dielectric spectroscopy experiments of Kremer et al. [Phys. Rev. A 42, 3667 (1990)] performed at inappropriately low frequencies.

The roles of steric repulsions and dispersional attractions in determining the behavior of solute molecules in liquid crystals are investigated by computer simulations of simple model systems. These systems involve a hydrogen molecule (${\mathrm{H}}_2$) dissolved in a rigid lattice consisting of parallel, infinitely long cylinders, which interact pairwise additively with the H atoms of the solute. The thermal motion of the ${\mathrm{H}}_2$ molecule (at 300 K) is simulated by Monte Carlo and molecular-dynamics methods, which are shown to lead to identical results for all the studied properties, including the centrifugal distortion. The resulting orientational order parameters S are invariably positive at all densities and structures of the lattice, irrespective of the details of the functional form of the interaction potential. The main role of the attractive forces is to pull the solute against the hard cores of the solvent molecules, thus enhancing the effects of the repulsions (increasing S). The implication is that the negative experimental S values observed in several liquid crystals cannot be attributed to the effects of repulsion and dispersion forces; the presence of other interactions, such as electrostatic forces, appears to be essential. The repulsive forces lead to slight orientation-dependent compression of ${\mathrm{H}}_2$, with the result that the nuclear dipolar and quadrupolar couplings ${\mathit{D}}_{\mathrm{HH}}$ and ${\mathit{B}}_{\mathit{D}}$ are changed by -0.7% and -1.1%, respectively (regardless of the lattice structure and the detailed form of the interaction potential). This points to the inference that the stretching-mode contributions to the orientation-dependent molecular deformations in liquid crystals are generally small, and gives support to the frequently made assumption that NMR spectral parameters of partially oriented molecules can normally be analyzed in terms of a model that includes only the bending-mode deformations.

We have studied the shear viscosity in a water-butoxyethanol (${\mathrm{C}}_4$Et) mixture as a function of temperature and concentration. The critical and off-critical mixtures have been studied over a very large T range, and the results are compared with recent light-scattering data confirming the amphiphilic character of the ethoxylated alcohol molecule that originates micellar structures. On this basis the data are discussed, considering the system as a colloidal dispersion of interacting micellar particles, where the attractive interaction plays the main role. In these terms the data near and below the lower critical solution temperature ${\mathit{T}}_{\mathit{c}}$ are well accounted for by the current mode-coupling theory of critical binary fluids. For low temperatures (T≤20 °C) where large clusters are present, the η data are explained by considering the fundamental role of the attractive interaction effects among the dispersed micelles and using in this respect a two-fluid model, a micelle system plus an inert background.

In this paper the transport of charge in time-dependent finite-amplitude electroconvection, due to unipolar injection, is examined. It is shown that a chaotic mixing of charge occurs, although the fluid flow is laminar. The charge density, which is an active scalar, affects the fluid dynamics through the Coulomb force. Thus we conjecture that this laminar chaotic mixing is at the origin of electrohydrodynamic chaos, with hydrodynamic turbulence playing no role.

Raman spectra of 15 and 30 mol % aqueous LiCl solutions were studied in the frequency range 3–350 ${\mathrm{cm}}^{\mathrm{-}1}$, from room temperature to 78 K. At high temperatures, the spectra are very similar to the Raman spectrum of pure water. As the temperature is lowered through the glass transition, the broad central peak that is typical of liquids evolves continuously into a narrow central peak plus a broad band centered near 60 ${\mathrm{cm}}^{\mathrm{-}1}$, both with a depolarization ratio of ∼0.8. This evolution suggests a common origin for these two features, which are typical of glasses. Comparison of our results with the disorder-induced-scattering model of Martin and Brenig [Phys. Status Solidi B 64, 163 (1974)], which is often used for glasses, produced poor agreement for both the intensity and depolarization ratio. In an alternative approach, we combined Stephen’s [Phys. Rev. 187, 279 (1969)] second-order Raman-scattering theory for fluids with generalized hydrodynamics and mode-coupling concepts. This approach gave predictions for the depolarization ratio in excellent agreement with our experimental results. It also produced a qualitatively correct description of the low-frequency Raman spectral shape in both the glass and liquid phases.

The reduction of the diffusion coefficient of latex spheres near glass surfaces was measured by photon correlation spectroscopy. Theory and experiment are not in agreement; possible causes for the discrepancy are discussed. In addition, the diffusion coefficient of sedimented latex spheres on a glass surface decreases with decreasing Debye length of the solution. This shows that the mean particle-surface separation distance decreases as the strength of the double-layer repulsion between the latex spheres and the glass surface is weakened. The utility of photon correlation spectroscopy for studies of interactions between colloidal particles and surfaces is discussed.

We present and investigate a lattice model for layered structures. It involves a lattice Laplacian operator and corresponds to a three-dimensional XY model with competing antiferromagnetic nearest- and ferromagnetic next- and third-nearest-neighbor couplings. The model describes the loss of order in a wide variety of layered systems, most notably the layered phases of microemulsions and smectic liquid crystals, where the transition leads to an isotropic or a nematic phase with a residual orientational order. The latter point is demonstrated by integrating out the nematic order fluctuations in a much more general model also proposed in this article, which extends the de Gennes field theory by describing the transitions between isotropic, nematic, and smetic-A phases of liquid crystals. Monte Carlo simulations exhibit a first-order isotropic-layered phase transition, changing to second order in the limit of infinite interlayer distance.

We report an extensive study of electrochemical deposition of copper with growth under galvanostatic conditions and parallel geometry. In such conditions a clear understanding of the origin of the ramified deposit and of its growth speed is possible, at least in the case of dense morphology. We confirm that this morphology belongs to a steady-state regime where growth can be modeled as the displacement of a flat strip of nearly equipotential copper. The growth velocity is exactly the drift velocity of the anions, which is proportional to the current density. We also show that the mass of the deposit does not depend on the speed at which it was grown but only on the concentration of salt in the bulk of the electrolyte. We compute the modifications in concentration profiles and in the electric field due to pH changes during growth.

We study the macroscopic particle concentrations both in a diffusion-limited coagulation (A+A→A) and in a two-species diffusion-limited annihilation reaction (A+B→scrI), where scrI represents an inert result, in spatial dimension d, using a general closure scheme for truncating the hierarchies of the kinetic equations of the joint density functions. In the coagulation reaction, the concentration C(t) goes to zero asymptotically as ${\mathit{t}}^{\mathrm{-}\mathit{d}/2\mathrm{}}$ for d<2, as lnt/t for d=2, and as ${\mathit{t}}^{\mathrm{-}1}$ for d>2, while in the annihilation reaction with equal initial density ${\mathit{C}}_{\mathit{A}}$(0)=${\mathit{C}}_{\mathit{B}}$(0), the density ${\mathit{C}}_{\mathit{A}}$(t)=${\mathit{C}}_{\mathit{B}}$(t) goes to zero as ${\mathit{t}}^{\mathrm{-}\mathit{d}/4\mathrm{}}$ for d≤4 and ${\mathit{t}}^{\mathrm{-}1}$ for d>4. Our approximation reproduces correctly all these asymptotic concentrations. An alternative approximation is also applied to the two-species annihilation reaction in one dimension, and its result is the same as that obtained from the general closure scheme.

A diffusion-limited-aggregation (DLA) model with two immiscible components (A and B atoms) is presented to investigate a phase transition in morphological changes. A segregation occurs where the DLA pattern is constructed by a mixture of trees consisting of only A atoms and trees consisting of only B atoms. Above a critical concentration ${\mathit{p}}_{\mathit{c}}$, trees with only A atoms exceed trees with only B atoms, and the DLA with only A atoms dominates. It is found that a phase transiton between A-DLA and B-DLA occurs at the critical concentration ${\mathit{p}}_{\mathit{c}}$, where A-DLA and B-DLA represent, respectively, DLA with only A atoms and DLA with only B atoms. The phase transition is analyzed by making use of the real-space renormalization-group method. The correlation length ξ scales as ξ≊(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{-}\nu }$, where ${\mathit{p}}_{\mathit{c}}$=0.5 and ν=1.85 on the square lattice.

A complete series of three experiments dedicated to the study of a photopumping and resonance fluorescence scheme is presented. An aluminum plasma is preformed in the heliumlike ground state by a 2-J 1.06-μm laser beam, then this plasma is photopumped by an x-ray source ∼1 ns later. The pump is a spatially distinct laser-produced plasma that emits intense emission of the heliumlike resonance lines in the 4–8-Å region. The pump is line coincident with the transitions to be photopumped. The resulting perturbation is studied by the fluorescence, which is directly observed and absolutely quantified. The separate characterization of each component of this system is discussed in detail, with an emphasis on the experimental quantities that will be compared with numerical calculations.