We study a nonequilibrium interface growth model that includes the nonlocal shadowing effect in three spatial dimensions. The model is represented by a stochastic partial differential equation for the local growth rate of an interface. The nonlocal effect is modeled by a term in the growth rate that is proportional to the local exposure angle. This leads to a shadowing instability, and the interface develops into a mountain landscape which coarsens in time. The structure factor of the interface shape shows a dynamic scaling form. The scaling exponents are computed.

The differential condition of self-consistency relating the thermodynamic functions and their derivatives locally at a studied point of the phase diagram has been suggested as a closure for the Ornstein-Zernike (OZ) equation. This produces an infinite set of OZ-like equations together with functionals—these are conditions to determine exact values of correlation functions and bridge function. To solve the problem an efficient method was developed that allows one to obtain not only 14 virial terms for a hard-sphere fluid (low-density limit) but the equation of state at high density with good accuracy.

The two-dimensional monomer-monomer (AB) surface reaction model without diffusion is considered for infinitesimal, finite, and infinite reaction rates k. For equal reactant adsorption rates, in all cases, simulations reveal the same form of slow poisoning, associated with clustering of reactants. This behavior is also the same as that found in simulations of the two-dimensional voter model studied in interacting-particle systems theory. The voter model can also be obtained from the dimer-dimer or monomer-dimer surface reaction models with infinitesimal reaction rate. We provide a detailed elucidation of the slow poisoning kinetics via an analytic treatment for the k=$0^{+}$ AB reaction and the voter models. This analysis is extended to incorporate the effects of place-exchange diffusion which slows, but does not prevent poisoning. We also show that the k=$0^{+}$ AB reaction with no diffusion is equivalent to the voter model with diffusion at rate 1/2. Identical behavior of the monomer-monomer reaction and the voter model is also found in an ‘‘epidemic’’ analysis, where one considers the evolution of a surface poisoned by one species, except for a small patch. Finally, we apply our findings to elucidate the behavior of the monomer-dimer surface reaction model for small reaction rates.

We report results of small-angle Rayleigh-scattering experiments performed in an equimolar liquid mixture of toluene and n-hexane that is brought out of thermal equilibrium by the imposition of a stationary temperature gradient ∇T perpendicular to the scattering wave vector. The experiments demonstrate the presence of long-range nonequilibrium fluctuations in temperature, concentration, and momentum and confirm that the strength of these nonequilibrium fluctuations varies with (∇T${)}^2$/${\mathit{k}}^4$, where k is the wave number of the fluctuations. It is suggested that nonequilibrium Rayleigh scattering may provide an alternative technique for measuring Soret coefficients of liquid mixtures.

The motion of shallow-water wave trains is studied in the laboratory in one space dimension and one time dimension (1+1). Our focus is on the nonlinear evolution of the wave trains as recorded at five spatially separated probes. Both the linear Fourier transform and the inverse scattering transform (IST) for the periodic Korteweg–de Vries (KdV) equation are exploited in the analysis of the data. IST provides a set of nonlinear basis functions, which are here computed for measured wave data and compared to the sinusoidal basis of the linear Fourier transform. We find that the scattering-transform mode amplitudes are nearly constants of the motion, while the Fourier modes vary substantially in space and time. The results suggest that the KdV equation more nearly describes the nonlinear evolution of the waves than does linear evolution.

I present experimental observations of weakly nonlinear traveling-wave convection in ethanol-water mixtures in a narrow, rectangular cell of variable aspect ratio. Over ranges in aspect ratio separated by approximately unity, the first nonlinear state seen above the onset of convection consists of irregular ‘‘repeated transients,’’ in which small-amplitude traveling waves initially grow with no change in spatial profile, then lose stability, and finally collapse back down to small amplitude. These states differ qualitatively from the ‘‘blinking’’ states seen just above onset at other aspect ratios, in which wave amplitude alternates regularly back and forth across the cell. The collapse in the ‘‘repeated-transient’’ state appears to be caused by a dephasing of the pattern which is due to the nonlinear dependence of wave number on amplitude. This dephasing shifts the pattern off resonance, causing its decay.

This paper shows that the Taylor dispersion flux is a dissipative flux of extended thermodynamics. Every term in the evolution equations for the Taylor flux components is connected to a thermodynamic function and the entropy production is proved to be positive definite. Thermodynamic restrictions on phenomenological coefficients are also satisfied.

The Taylor-Couette system is an extraordinary hydrodynamic system, showing almost all low-dimensional scenarios for routes to chaos for proper boundary conditions. For a period-doubling route to chaos, bifurcation diagrams were experimentally recorded and the dynamic variables such as fractal dimensions, Lyapunov exponents, and entropies are estimated as a function of Reynolds number. The evolution of the correlation dimension ${\mathit{D}}_2$ with Reynolds number Re shows that ${\mathit{D}}_2$∝(Re-${\mathrm{Re}}_{\mathit{c}}$${)}^{1/4}$, which is similar to continuous phase transitions. An investigation of the critical phenomena must be performed as high-precision hydrodynamic experiments because the results show that the kind of scenario depends sensitively on the boundary conditions.

The theory of thermal radiation forces is extended to the local interactions occurring among phonons and the material particles of a liquid, also in the absence of an external temperature gradient. In a solution, energy and momentum can be transferred by an impinging phonon to a particle, or the latter may perform work on the first, shifting it to a higher frequency. Upon time reversal, each of these elementary interactions commutes into the other. Isothermal diffusion, thermomechanical and mechanothermal effects in solutions can be interpreted within this unifying frame of reference. The density of the ‘‘gas’’ of thermal excitations, and the average of energy exchanged per interaction can be calculated from experimental data for common liquids. Nonequilibrium statistical mechanics and irreversible thermodynamics might be fruitfully revisited on the basis of the notion of phonon-particle interactions, since these are processes that occur at a more elementary level than the regression of fluctuations. Accordingly, the statistical approach proposed here may lead to a microscopic interpretation of Onsager’s reciprocity relations.

An investigation is made of the coupling between Soret-driven convection, at positive separation ratio, and a solid-liquid interface. This phase boundary forms upon the solidification of an upper portion of a thin layer of a dilute binary mixture that is confined between highly conducting and nearly impermeable horizontal plates. Using a long-wavelength expansion, a nonlinear evolution equation is derived that includes the coupled effects of solidification and thermosolutal convection due to the Soret effect. The validity of the derivation is found to be limited to regions, in the parameter space, that are determined as functions of the separation ratio, the Lewis number, and the thickness of the solid layer. The numerical solutions of the evolution equation show that the formation of the solid layer affects the leading-order concentration profile, and that the deviation of the interface from its planar state is weakly affected by the convective currents in the liquid. The interface morphology, however, has the same form as the convective pattern in the fluid mixture. The consideration of boundaries that are poor conductors of heat leads to a problem that is characterized by a heat-transfer Biot number γ and a mass-transfer Biot number β. The threshold values for the onset of convection are determined, and their dependence on β and γ is discussed.

An examination of the scaling structure along with some extensive simulations on viscous fingering in circular geometry strongly suggest that the asymptotic patterns are compact. Experiments and simulations are in a transient regime that may exhibit a reasonable range where apparent fractal growth may be found. Arguments to connect the case of viscous fingering with that of vanishing surface tension are made.

The magnetic-field-induced biaxiality of the originally uniaxial antiferroelectric chiral smectic (Sm-${\mathit{C}}_{\mathit{A}}^{\mathrm{*}}$) phase of 4-(1-methyl-heptyloxycarbonylphenyl) 4’-octylbiphenyl-4-carboxylate (MHPOBC) has been studied in a magnetic field applied perpendicular to the helical axis. The observed distortions of the central part of the conoscopic figures are explained on the basis of a perturbative approach to light propagation in spatially modulated birefringent phases. The critical magnetic field for the unwinding of the helical structure of the Sm-${\mathit{C}}_{\mathit{A}}^{\mathrm{*}}$ phase of MHPOBC is 13 T at 89 °C and is strongly temperature dependent.

We report on light-scattering experiments in the smectic-C phase of a two-dimensional, freely suspended liquid-crystal film at wave vectors intermediate between pure bend and splay director fluctuations. The dynamic signal reveals the presence of two diffusive modes, one of which is the usual hydrodynamic mode for in-plane director fluctuations and one of which has not been previously reported. The wave-vector dependence of the scattered intensity for the new mode is well described by the selection rules for out-of-plane fluctuations (undulations) of the film. However, the overdamped dynamics reveal a nonhydrodynamic and extremely slow decay, in contrast to the usual picture for smectic layer undulations. Near the smectic-C to smectic-I (hexatic) transition, the elastic moduli and decay constants associated with the two modes show a remarkably similar temperature dependence.

A self-consistent mean-field theory of the glass transition is presented for the model of a high-density isotropic melt of rodlike molecules, which was originally proposed by Edwards and Evans [J. Chem. Soc. Faraday Trans. 2 78, 113 (1982)]. In this model, translation along the rod axis is the only mode available, but the diffusional motion of a given rod (hereafter called the test rod) is hindered by end-on collisions with the lateral surfaces of other rods that lie in its diffusion path. The basis of this treatment is the mean-field Green-function theory developed in our previous contribution for one-dimensional diffusion in the presence of many reflecting barriers [Phys. Rev. A 45, 5426 (1992)]. A self-consistency requirement for the dynamics of the test rod and of the barrier rods leads to an asymptotic decrease to zero in the long-time diffusion constant, i.e., a glass transition, as the density of the barrier rods exceeds a critical value. The glass transition is manifested in a divergence of the lifetime τ of the barrier in a power-law (T-${\mathit{T}}_1$${)}^{\mathrm{-}2}$ relation as the temperature T approaches a glass-transition temperature ${\mathit{T}}_1$ from above if a linear thermal contraction is assumed in the mobile phase. At a higher temperature, τ follows Arrhenius behavior. A relaxation is observed in the dynamic-mobility spectrum of rod translation with a change in the profile between the mobile and the glassy phases. We also investigate the complex modulus of the melt and find a spectral distribution similar to that for the shear modulus obtained by reptation theory for entangled linear-chain polymers.

We examine the possibility of nematic order in systems described by the Brazovskii model [Sov. Phys. JETP 41, 85 (1975)] of the isotropic-lamellar phase transition, including symmetric diblock copolymer melts and bilayer-forming surfactant systems. We introduce a nematic order parameter and look for states that break rotational symmetry–that is, which have a well-defined direction for interfacial normals, but no phase coherence between interfaces. We find an isotropic-nematic phase transition, but it is always precluded by an isotropic-lamellar phase transition occurring at higher temperature. We show that the lamellar phase is stable to dislocation-mediated melting to a nematic phase in the limit of long copolymer chains, even though the isotropic-lamellar phase transition becomes second order in this limit.

The features of hydrothermal waves that appear when a liquid layer is laterally heated are presented. A bifurcation is observed from a steady regime to a regime of a basic flow with superimposed traveling waves. Measured characteristics of waves are shown and compared with some recent theoretical predictions.

The early-to-late stage of spinodal decomposition in a critical mixture of polystyrene and polymethylphenylsiloxane was studied by time-resolved light scattering over 1.8<k<21.1 μ${\mathrm{m}}^{\mathrm{-}1}$ and 0<t<502 h, with k and t being the wave number and the elapsed time after temperature quench into the spinodal region, respectively. The time dependences of the maximum intensity of the scattered light ${\mathit{I}}_{\mathit{m}}$ and of the corresponding wave number ${\mathit{k}}_{\mathit{m}}$ were represented by the power laws; ${\mathit{I}}_{\mathit{m}}$∝${\mathit{t}}^{\mathrm{\beta }}$ and ${\mathit{k}}_{\mathit{m}}$∝${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$ with α=0 in the early stage, α=0.17 in the intermediate stage, and β=1.08 and α=0.36 satisfying β=3α in the late stage. The behavior in the early stage was well expressed by the Cahn-Hillard theory. These exponent values are almost the same as those observed for Fe-Cr alloys. The behavior of the scaled structure factor in the late stage was expressed by a ${\mathit{k}}^{\mathrm{-}6}$ dependence in ${\mathit{k}}_{\mathit{m}}$<k<2${\mathit{k}}_{\mathit{m}}$ and by a ${\mathit{k}}^{\mathrm{-}4}$ dependence in k>2${\mathit{k}}_{\mathit{m}}$, in good agreement with the recent theoretical prediction.

The coupling between the motion of ionic impurities and the bend-type director distortion in a ferroelectric liquid crystal is examined theoretically. We calculate the relaxation rate of the (fast) director mode to lowest order in the ion concentration. Moreover, we calculate the ratio ${\mathit{K}}_{\mathrm{fast}}$(τ=0)/K(τ=0), where K(τ) is the amplitude of the temporal autocorrelation function for director fluctuations, τ is the correlation time, and ${\mathit{K}}_{\mathrm{fast}}$(τ) is the corresponding value for the quickly decaying component of this quantity. The ratio, which can be measured in a light-scattering experiment, yields the inverse Debye-Hückel screening length κ.

We show that smectic-A plates growing from the top of isotropic droplets are subject to an interfacial growth instability. This instability occurs before the static textural instability already known which produces focal conics in order to relax the smectic-A–isotropic surface energy. We study the growth instability and its relation with the tunneling through the barrier of the first-order static instability. We find that the focal conics nucleate on the nonlinearities of the growth instability through a fracture mechanism.

The growth of two-dimensional crystals with and without anisotropy in a channel is analyzed by a Green’s-function method. A one-sided diffusional model is treated in quasistationary approximation. Our numerical results on the steady-state growth of symmetrical fingers are in agreement with approximate analytical predictions (E. Brener, M. Geilikman, and D. Temkin, Zh. Eksp. Teor. Fiz. 94, 241 (1988) [Sov. Phys. JETP 67, 1002 (1988)]). For fixed supercooling the dependence of growth velocity versus channel width is nonmonotonic, passing a maximum. We did not find stationary solutions for supercooling less than 0.5. When the width of the channel exceeds some critical value we observed that the symmetrical finger becomes unstable against tip splitting. In this case we found stable steady-state growth of nonsymmetrical fingers. We have also found an expected instability of two fingers in the common diffusion field caused by competition.