We present a simple model for Rayleigh-Bénard convection with an imposed horizontal flow of Reynolds number R in a container of finite width and near threshold. The model consists of two coupled envelope equations representing longitudinal and transverse traveling convection rolls. Each equation is for a wave traveling in the direction of the imposed flow. For small R, transverse rolls are stable at the convective onset. For R>${\mathit{R}}^{\mathrm{*}}$, longitudinal rolls bifurcate from the conduction state. For a range of cross-coupling strengths and for R>${\mathit{R}}^{\mathrm{*}}$, we obtain a transition from longitudinal to transverse rolls as the Rayleigh number is increased. This transition occurs via states for which part of the system is occupied by longitudinal, and another by transverse rolls. The behavior is strongly influenced by the presence of noise since the system first becomes convectively unstable, and therefore noise-sustained structures can play an important role. We also show that for a range of parameters in the model, a mixed state (for which both envelopes assume a nonzero value at the same location) is possible over part of the cell in a finite geometry.

Several groups have recently reported a robust localized state of traveling waves in experiments on convection in binary fluid mixtures. These states resemble the ‘‘pulse’’ solutions of complex Ginzburg-Landau equations with subcritical bifurcations. We study the stability of these pulses experimentally by observing their interaction with high-frequency wave packets, which we inject into our annular convection cell by creating localized disturbances. We find that the spatial phase structure of pulses is central to their stability. An incident wave packet of sufficient amplitude can perturb the phase of the pulse so much that it loses stability and disappears, leading to a transition to a new state. Phase perturbations also determine the interactions between nearby pulses and the role of random fluctuations in the transition from a pulse state to a state in which slow traveling rolls fill the cell.

We present here the natural algebraic-geometrical generalization of the Da Rios–Betchov intrinsic equations governing curvature and torsion of an isolated vortex string moving in an unbounded, perfect fluid flow. The filament is embedded in a manifold that can be assumed to be homeomorphic to an odd-dimensional Euclidean space, and whose connection we do not assume to be torsion-free. We suggest how to account for fluid compressibility in the ambient space by its geometrization, and we discuss some special cases of physical interest such as the torsion-free affine connection case and the Riemannian connection case. Finally, we point out the role our results might have in the context of soliton studies.

To date, the calculation of shear viscosity for soft-core fluids via equilibrium molecular dynamics has been done almost exclusively using the Green-Kubo formalism. The alternative mean-squared displacement approach has not been used, except for hard-sphere fluids, in which case the expression proposed by Helfand [Phys. Rev. 119, 1 (1960)] has invariably been selected. When written in the form given by McQuarrie [Statistical Mechanics (Harper & Row, New York, 1976), Chap. 21], however, the mean-squared displacement approach offers significant computational advantages over both its Green-Kubo and Helfand counterparts. In order to achieve comparable statistical significance, the number of experiments needed when using the Green-Kubo or Helfand formalisms is more than an order of magnitude higher than for the McQuarrie expression. For pairwise-additive systems with zero linear momentum, the McQuarrie method yields frame-independent shear viscosities. The hitherto unexplored McQuarrie implementation of the mean-squared displacement approach to shear-viscosity calculation thus appears superior to alternative methods currently in use.

The change in viscosity of polymeric silicone fluids due to γ irradiation has been studied below the gel point using a sensitive differential viscometer. Using the correspondences between resistivity and viscosity of fluids, the random resistance network has been used to explain the increase in viscosity due to irradiation, and fairly good agreement with experiment has been obtained.

We have measured the diffusion coefficient of strongly interacting ‘‘colloidal liquids’’ near the ‘‘liquid’’-‘‘solid’’ phase transition using nondegenerate two-wave mixing. We self-consistently calculate the diffusion coefficient as the product of the elastic modulus and a relaxation time that is identified as the time taken for a particle to diffuse one-tenth of the average interparticle distance. This procedure also predicts an electrolyte concentration where the diffusion coefficient vanishes, which is identified with the melting point of the colloidal crystal. This is shown to be essentially identical to the Lindemann criterion. In addition, we find that the colloidal liquid-solid transition as a function of ionic concentration gives a critical exponent γ=0.08±0.003.

The effects of correlated internal rotations in an alkyl chain on the spectral densities of motion in liquid crystals are examined using the master-equation method. It is assumed that the overall reorientation of molecules is decoupled from the internal motions in their alkyl end chains. The pentyl chain that is attached to a cylindrical biphenyl core in 4-n-pentyl-4’-cyanobiphenyl (5CB) is studied as a specific example. The reorientation of a symmetric top in an anisotropic potential is described by the small-step rotational diffusion model. The equilibrium probability of each conformer, which is required to construct the transition-rate matrix for the master equation, is obtained using the Emsley-Luckhurst theory. The effects of the nematic mean field on the chain dynamics are discussed. Both ${\mathit{J}}_1$(ω) and ${\mathit{J}}_2$(2ω) in 5CB are found to be frequency dependent, with ${\mathit{J}}_2$(2ω) being weaker.

We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.

The renormalized-density-functional theory (RDFT) proposed by Groot and Van der Eerden [Phys. Rev. A 36, 4356 (1987)] and the modified renormalized-density-functional theory (MRDFT), which is based upon a global average of the density, are considered. In the MRDFT theory, as in the RDFT theory, the weighting function and the weighted density are determined by the extremal condition of the free-energy functional with respect to the ‘‘coarse-grained’’ densities as free variables. Using an identity due to Percus [in The Equilibrium Theory of Classical Fluids, edited by H. L. Frish and J. L. Lebowitz (Benjamin, New York, 1964)], it is possible to investigate the properties of homogeneous systems in the RDFT, and in the MRDFT. The results are obtained for the RDFT theory and the MRDFT theory and are compared with each other and with those of other theories. In the RDFT theory the low-density expansion is used to calculate the fourth virial coefficient and the second-order pair-correlation function for systems with repulsive potential, in which it disagrees with the exact virial expansion of the system. The results of the RDFT theory show that the RDFT theory is less accurate than the weighted-density-approximation theory [Tarazona, Phys. Rev. A 31, 2672 (1985)] which was based upon an ad hoc form of the weighted density. The MRDFT theory leads to the usual hypernetted-chain equation of state for homogeneous systems, as does the modified weighted-density-approximation theory [Denton and Ashcroft, Phys. Rev. A 39, 4701 (1989)].

We report a computer-simulation study of the stability of the columnar phase in a system of parallel spherocylinders with aspect ratios L/D=5 and ∞. It is found that the range of stability of the columnar phase is strongly dependent upon the system size. In particular, for particles with an aspect ratio L/D=5, the columnar phase that is observed in small systems (N=90) disappears for a system of N=1080 particles. In its place, a simple hexagonal crystal (‘‘AAA stacking’’) appears. On the basis of our present simulations, we cannot tell whether the latter phase is truly crystalline or possibly a smectic-B phase. For particles with an aspect ratio L/D=∞, similar behavior is observed, although in this case a stable columnar ‘‘pocket’’ remains, even for the largest systems we studied. We have computed the locations of all phase transitions involving the new hexagonal phase.

We study the conformation of thin liquid films on rough or heterogeneous solid substrates. The liquid-substrate interaction dominates for sufficiently thin films, and heterogeneity roughens the liquid interface. As the film thickens, surface tension becomes increasingly important, and the liquid interface flattens. A general equation for the equilibrium interface shape is derived. Analytic results are obtained in the limit of weak disorder for rough or self-affine surfaces as well as chemically heterogeneous solids. The effect of disorder depends strongly on the wave vector. Fluctuations at scales smaller than the film thickness or a ‘‘healing length’’ ξ produce little roughness. At larger wavelengths, the film conforms to the local fluctuations. Exact numerical solutions of the general equation are presented for surfaces with square grooves. These confirm the qualitative predictions of the analytic theory, and are in quantitative agreement when the depth of the grooves is small. The variation of roughness with film thickness, as well as the calculated adsorption isotherms, are compared to recent experimental results. We show that previously measured isotherms can be reproduced by corrugated surfaces with a single characteristic length scale, and do not necessarily imply that the surfaces studied were self-similar.

We formulate a density-functional theory that is capable of describing simultaneously the solid, liquid, and gas phases of a simple classical material. The formalism can be reduced to the Ebner-Saam-Stroud theory for the liquid-gas case and to a generalized version of the Ramakrishnan-Youssouff theory for the liquid-solid case. The theory requires as input the direct correlation functions of a uniform fluid. As an example we apply the formalism to the calculation of the phase diagram of a system with Lennard-Jones intermolecular interactions. We obtain the correlation functions from a closure scheme proposed by Zerah and Hansen [J. Chem. Phys. 84, 2336 (1986)]. The calculated density-temperature phase diagram compares favorably with those obtained from numerical simulations of the same model system. We also compute the equations of state in the solid and fluid phases.

A two-dimensional lattice is considered with a linear charge-density gradient produced by a charge source at one end and a sink at the opposite end. A fraction p of the lattice sites are occupied by mobile particles that interact only with neighboring particles and empty sites (the substrate) and carry charges from source to sink; the charge neutrality of the whole lattice is maintained. The root-mean-square (rms) displacement of the particles (i.e., the tracers) and their effective conductivity for the charge transport are studied as a function of temperature and concentration p. The rms displacement shows a crossover from diffusion (at short time) to driftlike behavior (in the long-time regime). The effective conductivity depends nonmonotonically on the carriers’ concentration, in which two maxima peaks are observed; the peak at the higher concentration seems to characterize the onset of static percolation. At a fixed concentration, the conductivity remains almost constant at low temperatures and increases before it saturates to a higher value in the high-temperature regime. In the intermediate-temperature range, an Arrhenius dependence seems valid at high concentrations; however, a deviation on varying the concentration cannot be ruled out at low concentration. We find that the activation energy depends on carrier concentration and temperature.

In this paper we propose to estimate the role of chain conformations in bringing about reentrant polymorphism in a nonpolar sample of mesogens. To this end we also show that the reentrant phenomenon is built in the McMillan model, if one explicitly incorporates the effect of tail-chain conformations in the molecular potential instead of treating the chains as an extension of the rigid part. The model is next utilized to predict the single reentrance I-N-Sm-${\mathit{N}}_{\mathrm{re}}$ with lowering of temperature in a nonpolar system.

The liquid-glass transition of a binary system of neutral hard spheres is investigated in terms of the matrix of nonergodicity parameters, which are closely related to the Debye-Waller factors (DWF’s) of the two species. By using the mode-coupling approximation, the nonergodicity parameters are calculated, and their dependence on size ratio, total packing fraction, and concentration is examined in detail. It is demonstrated that all DWF’s will be nonzero in the glass phase, irrespective of possible high mobilities of small particles. When approaching the glass transition, the DWF’s critically decrease with exponent 1/2 to a finite limit.

The wave-number-dependent Lamb-Mössbauer factors (LMF’s) of big and small particles in a glass of neutral hard spheres are investigated within mode-coupling theory by varying size ratio δ, total packing fraction η, and concentration ${\mathit{c}}_1$. It is possible to form a glass by the big particles only, while the small particles retain their mobility. Diffusion blocking of small particles is achieved by increasing either η or δ. The wave-number dependence of the small particles’ LMF shows characteristic deviations from a Gaussian in contrast to big particles’ LMF, which is almost Gaussian.

We present a statistical-thermodynamic theory that associates fracture of a solid with the approach of a spinodal upon increasing stress. This formulation is illustrated by a one-dimensional model, and the temperature dependence of the nonlinear stress-strain relation and fracture stress is obtained. A two-dimensional network model is treated by both effective-medium theory and Monte Carlo simulations, showing metastability and the nucleation of microcracks.

An extension of previous work on the ballistic annihilation reaction A+A→0 to the coagulation reaction A+A→A is presented. Three possible velocities c (with probability p), -c (with probability q), and zero are considered. While the long-time behavior is controlled by moving particles when p=q, it is controlled by the stationary particles when p≠q. The comparison of the coagulation reaction with the annihilation reaction shows that the long-time results are essentially the same except for a rescaling of the time. In addition, the time dependences of the decay in the ballistic coagulation reaction when p=q and the diffusion-limited coagulation reaction are also identical, but for different physical reasons. The reason for this becomes transparent by rederiving the ballistic coagulation results using a random-walk formalism, which can perhaps be generalized to more complicated ballistic reactions.

Diffusion-limited aggregation on Sierpinski carpets is studied by computer simulation. We propose a fractal-cell generation method to form an infinite fractal lattice with the structure of Sierpinski carpets. The simulated results indicate that the exponent D, associated with the power-law behavior N∼${\mathit{R}}^{\mathit{D}}$, is dependent on the fractal dimension of Sierpinski carpet ${\mathit{d}}_{\mathit{f}}$.

Numerical and analytical solutions of the electron Boltzmann equation in two-temperature steady-state helium plasma are studied in a broad range of conditions (5000 K≤${\mathit{T}}_{\mathit{a}}$≤20 000 K, 10 000 K≤${\mathit{T}}_{\mathit{e}}$≤20 000 K; ${10}^{10}$ ${\mathrm{cm}}^{\mathrm{-}3}$≤${\mathit{N}}_{\mathit{a}}$≤${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$). The WKB analytical solution is found to be satisfactory in most situations. The deviation of the electron distribution from Maxwellian and a possibility of raising of the tail of the distribution is also discussed.