A rigorous three-dimensional linear and weakly nonlinear analysis of Rayleigh-Bénard convection in planarly aligned nematic liquid crystals is presented. We use realistic boundary conditions and allow for a stabilizing magnetic field. The analysis includes a determination of all parameters of the amplitude equation in different regimes of the magnetic field where normal, oblique, and parallel rolls occur. It turns out that there exists a range at intermediate fields were the primary transition is subcritical for the standard material (4-methoxybenzylidene-4’-n-butylaniline). The (‘‘nonlinear’’) stability of rolls is determined to second order in the amplitude so that nonpotential effects (especially mean flow) are included. In the low-field supercritical range the roll solutions are destabilized at a secondary threshold via a skewed-varicose instability leading presumably to spatiotemporal chaos. In the high-field supercritical normal-roll range a secondary transition can lead to oblique rolls that are ultimately destabilized by a short-wavelength instability.

The dynamic slowing down of the first cumulant and the stretched exponential decay of the droplet density-time correlation function at long time, previously observed for the one-phase sodium-di-2-ethylhexylsulfosuccinate (AOT)–water–decane microemulsion system, are attributed to the approach to a percolation threshold as the volume fraction of the microemulsion is increased at constant temperature. A model for dynamic light scattering, formulated along the line of the scattering from a system of transient polydispersed fractal clusters, quantitatively accounts for all the light-scattering data reported so far and also for some additional results.

Exact traveling-wave solutions of the nonlinear Klein-Gordon equation with dissipation are found. The solutions are discussed in the context of propagating nonlinear mechanical waves as well as domain walls (solutions interpolating between two local minima in the potential) and relaxation modes (solutions interpolating between a local minimum and a local maximum in the potential) in systems undergoing second-order phase transitions. Using the Lyapunov method the stability of traveling waves is analyzed. Explicit solutions for domain walls are found and shown to be asymptotically stable. While domain walls propagate with a velocity uniquely determined by the parameters of the model, relaxation modes can move with arbitrary velocities. Among those solutions only one solution propagating with a characteristic velocity ${\mathit{v}}_{\mathit{c}}$ is asymptotically stable. Other solutions are demonstrated to be Lyapunov unstable. It is found that relative values of the mass density and the damping coefficient are crucial for the dynamic critical behavior, which changes from ${\mathit{v}}_{\mathit{c}}$∼(${\mathit{T}}_{\mathit{c}}$-T${)}^{1/2}$ for small densities to ${\mathit{v}}_{\mathit{c}}$ that is temperature independent for large densities.

Uncertainties in the anisotropic surface tension, as determined by experiment, may generate additional singularities, which under conditions of slow growth may influence or determine the velocity selection in the region of the stability constant σ≤${\mathrm{\sigma }}^{\mathrm{*}}$. Model calculations of this effect are presented for the geometric model and the symmetric model of dendritic growth, together with a detailed comparison with experiment. The five known experiments were performed in the region σ>${\mathrm{\sigma }}^{\mathrm{*}}$, where noise influence is small. To test the microscopic-solvability theory one needs to investigate smaller σ. This would be difficult or impossible to do because dendrites do not exist at σ≤${\mathrm{\sigma }}^{\mathrm{*}}$.

The dielectric properties of a high-tilt-angle chiral-nematic–smectic-${\mathit{C}}^{\mathrm{*}}$ phase ferroelectric liquid crystal are studied in the frequency range of 30 Hz to 1 MHz. Measurements of electric permittivity at different temperatures and biasing fields were taken in thin homogeneously aligned samples with the electric measuring field being parallel to the layer planes. In the smectic-${\mathit{C}}^{\mathrm{*}}$ phase two relaxation mechanisms have been found, viz., the Goldstone mode originating due to the phase fluctuations of the director and 180° flip of the molecular relaxation connected with the reorientation of the liquid-crystal molecule around its short axis. Temperature and bias-field dependence of the dielectric permittivity and the critical relaxation frequency of the molecular mode in the smectic-${\mathit{C}}^{\mathrm{*}}$ phase are studied and discussed.

An equation for the time evolution of the density of directed polymers is derived in the limit of a high rate of cutting. The equilibrium solution is found to be equivalent to that obtained from the transfer-matrix approach for a single directed polymer. For potentials that depend only on the transverse coordinates, the logarithm of the mobility is found to behave as ∼(-${\mathit{U}}^{1/2}$), or barrier height U. Application to the motion of flux lines in superconductors is briefly discussed.

The lineal-path function L(z) for two-phase heterogeneous media gives the probability of finding a line segment of length z wholly in one of the phases, say phase 1, when randomly thrown into the sample. The function L(z) is equivalent to the area fraction of phase 1 measured from the projected image of a slab of the material of thickness z onto a plane. The lineal-path function is of interest in stereology and is an important morphological descriptor in determining the transport properties of heterogeneous media. We develop a means to represent and compute L(z) for distributions of D-dimensional spheres with a polydispersivity in size, thereby extending an earlier analysis by us for monodispersed-sphere systems. Exact analytical expressions for L(z) in the case of fully penetrable polydispersed spheres for arbitrary dimensionality are obtained. In the instance of totally impenetrable polydispersed spheres, we develop accurate approximations for the lineal-path function that apply over a wide range of volume fractions. The lineal-path function was found to be quite sensitive to polydispersivity for D≥2. We demonstrate how the measurement of the lineal-path function can yield the particle-size distribution of the particulate system, thus establishing a method to obtain the latter quantity.

The baroeffect is analyzed to include a gas that aggregates into higher-order polymers or oligomers. The resulting pressure change is found to vary independently of the molecular weight of the gas components and to depend only on the aggregation or oligomeric order of the gas. With increasing aggregation, diffusive slip velocities are found to increase. The calculations are extnded to include general counterdiffusion of two distinct aggregation states (k-, j-mer) for the gas, and the pressure change is derived as a function that is independent of both molecular weight and the absolute aggregation. The only parameter that determines the baroeffect is the ratio of aggregated states, β=k/j. For gases that reversibly aggregate, possible oscillatory behavior and complex dynamics for pressure are discussed. Gas aggregation may play a role for low-temperature crystal-growth conditions in which vapor concentrations of one (or more) species are high.

We study the effects of fluctuations on the mean-field phase diagram of a Landau-Ginzburg-Wilson (LGW) action of the form H=1/2${\mathcal{F}}_{\mathbf{q}}$‖${\mathit{cphi}}_{\mathbf{q}}$${\mathrm{\Vert }}^2$(${\mathbf{q}}^4$+b${\mathbf{q}}^2$+c)dRdq +λ/4!${\mathcal{F}}_{\mathbf{q}}$${\mathrm{\Phi }}_{{\mathbf{q}}_1}$ ${\mathrm{\Phi }}_{{\mathbf{q}}_2}$ ${\mathrm{\Phi }}_{{\mathbf{q}}_3}$${\mathrm{\Phi }}_{{\mathbf{q}}_4}$δ (${\mathbf{q}}_1$+${\mathbf{q}}_2$+${\mathbf{q}}_3$+${\mathbf{q}}_4$), where b may be positive or negative. In the latter case the inclusion of fluctuations may produce large quantitative and qualitative effects in the phases and the transitions between them. The renormalization is accomplished by resummation to all orders of two classes of diagrams and is reminiscent of a calculation earlier described by Brazovskii (Zh. Eksp. Teor. Fiz. 68, 175 (1975) [Sov. Phys.—JETP 41, 85 (1975)]). Since the LGW theory (with b<0) may be extracted from an isotropic frustrated-lattice model of microemulsion it is possible to compare the predictions of the present study with earlier Monte Carlo simulations of the Ising model. It is therefore also possible to describe the correlation functions in the disordered phase, which had earlier been identified as the bicontinuous phase of the microemulsion model. In particular, strong renormalizations of the two length scales d and ξ originally introduced by Teubner and Strey [J. Chem. Phys. 87, 3195 (1987)] to describe the bicontinuous-microemulsion phase are derived. In addition renormalizations of the surface energies are derived and discussed in the context of bicontinuous microemulsion.

In thin-film directional solidification of the ${\mathrm{CBr}}_4$-${\mathrm{C}}_2$${\mathrm{Cl}}_6$ eutectic alloy, we observe a quasi-instantaneous transition from symmetric states to drifting parity-broken (‘‘tilted’’) states as a result of a sudden increase of the pulling velocity. We show that (i) the observed transition is essentially the forward-tilt bifurcation that Kassner and Misbah [Phys. Rev. Lett. 65, 1458 (1990); 66, 522 (1991)] have recently found, numerically, in a model without anisotropy of the solid phases; (ii) crystal anisotropy, in the eutectic system, makes the bifurcation slightly imperfect. In lamellar eutectics, phase diffusion is extremely slow, and permanent spatial modulations of the pattern wavelength are always present, generated at eutectic grain boundaries. We show that the tilt angle, i.e., the degree of parity breaking of the pattern, adjusts itself locally to the wavelength in a very short time, in contrast with the slow phase diffusion.

Based on a suitable density-functional theory for inhomogeneous fluids we investigate both the liquid-vapor coexistence curve of the bulk phase diagram and interfacial structures of molecular fluids in general and Stockmayer fluids in particular. We derive a scheme which allows us to analyze one-component fluids composed of molecules with strong permanent dipole moments which are shown to affect significantly the bulk phase diagram. The critical temperature increases as a function of the strength of the dipole moments, whereas the critical density remains unchanged if the repulsive interaction of the molecules at short distances is modeled by a constant hard-core potential. A temperature-dependent diameter of the hard-core potential that mimics the actual soft repulsive potential is also considered. It results in an additional enhancement of the critical temperature and a slight increase of the critical density at larger dipole strengths and higher temperatures. Our analytic results turn out to be in good agreement with published Monte Carlo data. The density profile and the orientational ordering at interfaces are shown to be determined by a system of coupled integral equations that are applicable for dipole moments of arbitrary strength. Its corresponding numerical solution will be presented in a subsequent paper.

We use quasielastic light scattering to investigate bond-orientational order in freely suspended, tilted smectic films of the liquid-crystal 4-(2-methylbutyl)-phenyl-4’-(octyloxy)-(l, ’)-biphenyl-4-carboxylate (8OSI). We find that the scattering for bend and splay in-plane fluctuations of the magnetically aligned smectic-C director in thin (2–4-layer) and thick (≊1000-layer) samples is well described by a simple elastic free energy coupling the bond-orientational to the molecular-tilt order parameter, combined with the form factor for a tilted smectic film. We discuss results for the elasticity and overdamped dynamics of the coupled fluctuations in light of the theory of defect-mediated melting in two dimensions. In addition, we draw an interesting comparison with results obtained on the closely related compound 4-(2’-methylbutyl)-phenyl-4-octylbiphenyl-4-carboxylate (${8\mathrm{S}\mathrm{I}}^{\mathrm{*}}$), which suggests that the magnitude of the intrinsic bond-tilt coupling is surprisingly different in the two materials and that the melting of the two-dimensional (2D) solid phase may involve different dislocation unbinding processes. Finally, orientational scans of the in-plane wave vector in the lower hexatic phase of 2D 8OSI films reveal evidence of pronounced temperature-dependent changes in the liquid-crystal director alignment, which we account for with a simple phenomenological model for the effect on the light scattering of textural defects in the 2D director field.

Recently, we demonstrated that the liquid-solid interface of the isotropic model of lamellar eutectic growth may undergo a parity-breaking transition from a symmetric to a tilted state. We found that the bifurcation to the asymmetric state is supercritical. Now we have solved the full boundary integral equation of the system assuming anisotropic surface tension. We observe that generically the supercritical bifurcation becomes imperfect, as could be expected from a simple phenomenological picture. In order to study whether finite domains of tilted states can exist under these circumstances, we consider a simple model for the coupling between tilt angle and phase dynamics that exhibits an imperfect bifurcation. We find that if the anisotropy is not too strong, the coupling leads to a picture that retains many of the qualitative features of the phenomenological approach given by Coullet, Goldstein, and Gunaratne [Phys. Rev. Lett. 63, 1954 (1989)] for subcritical bifurcations. Furthermore, we offer a natural explanation for the experimental finding that on creation of a tilted state lamellae of a given grain preferentially tilt in one direction, not in the opposite one.

The spinodal decomposition in a critical mixture of polydimethylsiloxane–diethyl carbonate was investigated by a time-resolved light-scattering technique, focusing especially on the early and the intermediate stages of phase separation. The most essential characteristics of this system are that both the refractive index and the density of the solvent and of the polymer are almost the same, and the effects of multiple scattering and sedimentation are mostly eliminated. The exponential growth of the scattered light intensity without changing of its wave number was clearly observed, in good agreement with Cahn-Hillard theory. The second peak, adding to the main (most dominant) peak, was found in the higher-scattering-angle region in the spectrum, characteristic of the intermediate stage. The scaled time dependences of the wave numbers of both peaks are well represented, respectively, by a master curve for various quenching depths by use of the characteristic wave number and time determined from the time dependence of the scattered light intensity at the early stage of spinodal decomposition. The quench depth dependence of the interdiffusion coefficient and of the wave number, where the most dominant fluctuation grows first in the unstable region, are in good agreement with three-dimensional Ising-model values, indicating the validity of the symmetric law of critical-point universality.

Density-functional theory within the effective-liquid approximation is applied to the problem of the isotropic-nematic transition of D-dimensional hard convex bodies. It is shown that the free-energy functional factorizes into its radial and angular contributions. Due to this factorization two different versions of the self-consistent equations can be implemented, and it is shown that in D=3 they coincide with previous theories. In the present work all the formulas are worked out with a particular choice for the angular distribution: the one-order-parameter approximation. The problem of determining the excluded volume of two hard convex bodies is discussed. For hard ellipsoids the Gaussian-overlap approximation is used, whereas an exact formula is given for the excluded volume of two hard spherocylinders. For D=2 the virial coefficients of the isotropic phase as well as the transition are incorrectly predicted, due to the approximation of the direct correlation function involved. For D=3 the results are in very good agreement with simulations. Expression and data for the isotropic-nematic transition for D>3 are also provided. Extensive comparisons with the results of other theories are made throughout. The one-order-parameter approximation is proven not to alter the order of the transition. Finally, it is shown that the present approximation becomes exact in the large-D limit.

The statistical mechanics of melts and blends of polymers with directed bond vectors is studied. We study this bond-vector interaction and the phase behavior of such polymers caused by this interaction. In pure melts a microphase separation due to local ordering of the bonds is predicted. In blends of polymers with directed bond vectors several phase transitions take place.

In this paper we present a phase-field model to describe isothermal phase transitions between ideal binary-alloy liquid and solid phases. Governing equations are developed for the temporal and spatial variation of the phase field, which identifies the local state or phase, and for the composition. An asymptotic analysis as the gradient energy coefficient of the phase field becomes small shows that our model recovers classical sharp-interface models of alloy solidification when the interfacial layers are thin, and we relate the parameters appearing in the phase-field model to material and growth parameters in real systems. We identify three stages of temporal evolution for the governing equations: the first corresponds to interfacial genesis, which occurs very rapidly; the second to interfacial motion controlled by diffusion and the local energy difference across the interface; the last takes place on a long time scale in which curvature effects are important, and corresponds to Ostwald ripening. We also present results of numerical calculations.

The growth of gold deposits on smooth glass from the vapor phase at 30 ${\mathrm{nm}}^{\mathrm{-}1}$ ${\mathrm{s}}^{\mathrm{-}1}$, 298 K, and incident angle near the substrate normal covering the 30–1000 nm average film thickness (h¯) range is investigated through scanning tunneling microscopy (STM) complemented with oxygen-adatom electrosorption measurements. The STM images of the deposits reveal a columnar structure resulting from a mechanism involving shadowing and surface diffusion. Quantitative data are obtained directly from STM images. The height distribution N(h) of the interface obeys an N(h)∝${\mathit{e}}^{\mathrm{-}\mathit{k}\mathit{h}}$ relationship. For h¯<500 nm, the interface thickness (ξ) increases as a power law with h¯, whereas for h¯>500 nm it reaches a steady state. Under the latter condition, ξ depends on the STM scan length (S) as ξ∝${\mathit{S}}^{\mathrm{\alpha }}$ with α close to 1/3. These results indicate that the growth process of the gold deposits results in compact nonfractal structures with self-affine fractal surfaces, as predicted by ballistic deposition models. However, the latter fail to describe some aspects of the morphology and evolution of thin vapor-deposited gold films on this substrate.

We analyze the limits of validity of a previously found distribution function of solitons [S. Ponce Dawson and C. Ferro Fontán, Phys. Rev. A 39, 5289 (1989)] when applied to the derivative nonlinear Schrödinger equation. This function allows an easy determination of the solitons that evolve from a given initial condition. We are particularly interested in weakly unstable cases that generate anomalous solitons. We study this case both analytically and numerically. We conclude that the distribution function describes a subset of the solitons correctly. An additional term obtained by Mjo/lhus (private communication) must be added to take into account the most energetic anomalous solitons. The complete distribution fits the simulations quite accurately, even in situations that do not satisfy the necessary conditions discussed by Dawson and Fontán.

The plasma maser, an interesting nonlinear process in plasma, is an effective means of energy up-conversion in frequency from Langmuir turbulence to the electrostatic Bernstein mode. It is shown here that the primary momentum and energy source of the plasma maser is the external magnetic field, which is not the case for the standard mode-mode coupling processes. For strongly magnetized plasma (${\mathrm{\Omega }}_{\mathit{e}}$≥${\mathrm{\omega }}_{\mathit{p}\mathit{e}}$, where ${\mathrm{\Omega }}_{\mathit{e}}$ and ${\mathrm{\omega }}_{\mathit{p}\mathit{e}}$ are the electron cyclotron frequency and the plasma frequency, respectively), the growth rate of the Bernstein mode arises from the polarization term. The growth rate is large in contrast to the previous ion-sound-turbulence case. These results have potential importance in the interpretation of anomalous radiation phenomena in astrophysical, laboratory, and fusion plasmas.