A modified set of equations is given for the simulation of a canonical ensemble based on the method introduced by Nosé. The equations produce trajectories that are sufficiently chaotic to calculate average properties of a canonical ensemble, even for a small number of degrees of freedom. This important fact is demonstrated by presenting results for a single one-dimensional harmonic oscillator. It is shown that the extended system is chaotic and that the trajectories cover the whole energy surface in phase space.

A method for the calculation of first-passage times for non-Markovian processes driven by continuous noise is presented. The input noise is identical to that of phase fluctuations in laser fields in the jump models. Both linear and nonlinear random processes are studied. In addition to the general formalism, some examples are worked out in detail.

We study the kinetics of nucleation and growth in systems with an arbitrary number of distinct stable phases for both homogeneous and heterogeneous nucleation. Exact solutions for the phase transformation kinetics in one dimension are obtained and compared with the mean-field results. We have observed anomalous power-law asymptotics for both homogeneous and heterogeneous nucleation in one dimension, while the mean-field theory predicts exponential asymptotic behavior for large times. Numerical simulations for 2d systems show that the mean-field theory is surprisingly accurate. Some properties of the spatial patterns at the final stage of nucleation and growth are elucidated.

A bivariate interaction scheme is introduced based on single-humped functions f(x) and g(y), which generate the length scales and their measures, respectively, according to a multifractal distribution. The largest eigenvalue of this procedure is connected with the Gibbs potential G(β,q), from which dimensions, entropies, and Lyapunov exponents can be extracted. The mechanisms leading to phase transitions in the Gibbs potential and in multifractal spectra are analyzed. The method provides us with a general scheme for classifying possible phase transitions in multifractals. As a novel phenomenon in the field of dynamical systems, we study phase transitions in spectra belonging to the natural measure of nonhyperbolic repellers of one-dimensional maps.

We evaluate the time evolution of ${\mathrm{\sigma }}_{\mathit{x}}$, the transverse component of a spin-1/2 dipole coupled to an Ohmic bath, using a theory balancing the quantum-mechanical fluctuations of the bath, as depicted by the noninteracting-blip approximation, with the nonlinear dynamics of the discrete nonlinear Schrödinger equation. As a relevant effect of the joint action of these two ingredients, we find that the time evolution of the system does not lead to the localization predicted by some equilibrium analyses. More precisely, starting from an eigenstate of ${\mathrm{\sigma }}_{\mathit{x}}$, the spin system will never asymptotically reach a broken-symmetry state.

The quantum kinetic equation of a Bose gas is derived by means of the Bogoliubov approach and the Wigner distribution function from the Liouville–von Neumann equation. It is an improved Boltzmann-Uehling-Uhlenbeck equation including the correctional binary collision with many-body effects.

The transport coefficients of shear viscosity, thermal conductivity, thermal diffusion, and mutual diffusion are estimated for a binary, equimolar mixture of hard spheres having a diameter ratio of 0.4 and a mass ratio of 0.03 at volumes of 5${\mathit{V}}_0$, 10${\mathit{V}}_0$, and 20${\mathit{V}}_0$ (where ${\mathit{V}}_0$=1/2 √2 N ${\mathit{tsum}}_{\mathit{a}}$ ${\mathrm{x}}_{\mathit{a}}$${\mathrm{\sigma }}_{\mathit{a}}^3$, ${\mathit{x}}_{\mathit{a}}$ are mole fractions, ${\mathrm{\sigma }}_{\mathit{a}}$ are diameters, and N is the number of particles) through Monte Carlo, molecular-dynamics calculations using the Green-Kubo formulas. Calculations are reported for as few as 108 and as many as 4000 particles, but not for each value of the volume. Both finite-system and long-time-tail corrections are applied to obtain estimates of the transport coefficients in the thermodynamic limit; corrections of both types are found to be small. The results are compared with the predictions of the revised Enskog theory and the linear density corrections to that theory are reported. The mean free time is also computed as a function of density and the linear and quadratic corrections to the Boltzmann theory are estimated. The mean free time is also compared with the expression from the Mansoori-Carnahan-Starling-Leland equation of state.

Extensive molecular-dynamics simulations have been carried out for a model tracer-solvent system made up of 100 solvent molecules and 8 tracer molecules interacting through truncated Lennard-Jones potentials. The influence of the size ratio between solute and solvent, of their mass ratio, and of the solvent viscosity on the diffusivity of a small tracer was investigated. Positive deviations from a Stokes-Einstein behavior are observed, in qualitative agreement with experimental observations. It was also observed that as tracer and solvent become increasingly dissimilar, their respective dynamics become decoupled. We suggest that such decouplings can be interpreted by writing the mobility of the tracer as the sum of two terms, the first one arising from a coupling between tracer dynamics and hydrodynamic modes of the solvent, and the second one describing jump motion in a locally nearly frozen environment.

We investigate the motion of a random walker that is driven by a ‘‘random-walk’’ shear flow. This unidirectional two-dimensional flow is defined by a velocity field in the x direction, which depends only on the transverse position y, and whose magnitude v=${\mathit{v}}_{\mathit{x}}$(y) is given by the displacement of a random walk of y steps. For this model, the root-mean-square longitudinal displacement of a diffusing particle that is passively carried by the flow increases as ${\mathit{t}}^{5/4}$. In a single configuration of the random shear, the probability distribution of displacements is bimodal, while the distribution function averaged over many configurations has a single cusped peak at the origin. As a consequence, the configuration-averaged probability that a walk is at x=0 decays more slowly than the ${\mathit{t}}^{\mathrm{-}5/4}$ dependence that would be expected on the basis of single-parameter scaling. The large-distance decay of the average probability distribution is also found to be anomalously slow. These unusual features can be explained on the basis of a scaling argument together with an effective-medium-type approximation. Our results are confirmed by numerical simulations.

The linear stability of exothermic autocatalytic reaction fronts is considered using the viscous thermohydrodynamic equations for a fluid with finite thermal diffusivity. For upward front propagation and a thin front, the vertical thermal gradient near the front is reminiscent of the Rayleigh-Bénard problem of a fluid layer heated from below. The problem is also similar to flame propagation, except that here the front propagation speed is limited by catalyst diffusion rather than by activation kinetics. For small density changes in a laterally unbounded system, the curvature dependence of the front propagation speed stabilizes perturbations with short wavelengths λ<${\lambda }_{\mathit{c}}$, whereas long wavelengths are unstable to convection. The critical wavelengths ${\lambda }_{\mathit{c}}$ are calculated and compared with experiments and with theoretical results for a similar problem that is driven by a Rayleigh-Taylor instability arising from a discontinuous density difference at the reaction front.

We construct a statistical-mechanical treatment of equilibrium flows in the two-dimensional Euler fluid which respects all conservation laws. The vorticity field is fundamental, and its long-range Coulomb interactions lead to an exact set of nonlinear mean-field equations for the equilibrium state. The equations depend on an infinite set of parameters, in one-to-one correspondence with the infinite set of conserved variables. We illustrate the equations by solving them numerically in simple cases. In more complicated cases we use Monte Carlo techniques, with the eventual aim of detailed comparison with the Red Spot dynamical simulations of Marcus: Preliminary efforts show good agreement. We review previous literature on two-dimensional (2D) Euler flow in light of our theory. In particular, we derive the Kraichnan energy-enstrophy theory and the Lundgren and Pointin point-vortex mean-field theory as special cases of our own. Our techniques may be generalized to a number of other Coulomb-like Hamiltonian systems with an infinite number of conservation laws, including some in higher dimensions. For example, we rederive Lynden-Bell’s theory of stellar-cluster formation, as well as the Debye-Hückel theory of electrolytes. Our results may also be applicable to cylindrically bound guiding-center plasmas, which under idealized conditions provide another realization of 2D Euler flow.

We introduce a one-dimensional model of a turbulent velocity field. It consists of a superposition of successively smaller eddies, forming a Cayley-tree-like structure. The randomness of the eddy decay is modeled by a multiplier distribution p(s), whose parameters can be determined from experiment. In contrast to other cascade models, which are not stated in terms of the velocity field, every other quantity of the turbulent flow can now be calculated consistently. Scaling relations between the statistics of the velocity and the dissipation fields are shown to depend greatly on physical assumptions about the cascade. Specifically, we study the influence of the spatial coherence of eddies, and of the action of the viscous cutoff.

We have applied the Evans-Cummings (EC) nonequilibrium molecular-dynamics (NEMD) heat-flow algorithm for liquid mixtures to an equimolar Lennard-Jones (LJ) mixture where the potential parameters and the state point have been chosen to model an argon-krypton mixture at its triple point. We have calculated the thermal conductivity and the Soret coefficient for one 108-particle system and one 1024-particle system. In order to check the results we have used the color conductivity algorithm to obtain the mutual diffusion and the Dufour coefficients. According to the Onsager reciprocity relations the Dufour and the Soret coefficients should be equal, and this has also been found to be the case within the statistical uncertainty. The thermal conductivity and the diffusion coefficient increase slightly with the system size, but the statistical error makes it impossible to discern any size dependence of the cross-coupling coefficients. We also computed the Soret coefficient for three hypothetical types of LJ mixtures. A consistency control was done by evaluating the Green-Kubo (GK) relations for the different transport coefficients by performing an equilibrium molecular-dynamics simulation. The GK thermal conductivity and the diffusion coefficient agree very well with the NEMD results but GK cross-coupling coefficients are very noisy and the error is probably about 15%. The EC algorithm is a NEMD algorithm that violates adiabatic incompressibility of phase space, but this does not cause any difficulties.

An anomaly in the refractive index is observed in the cubic liquid-crystalline blue phases (BP’s) I and II of several cholesteric-nematic mixtures in the vicinity of optical Bragg reflection. Because the reflection wavelength is of the order of the BP lattice constant, this phenomenon can be explained by spatial dispersion of the dielectric tensor.

A cellular-automaton model is presented for the segregation of a granular flow. The need for such a model arose originally from consideration of a problem related to the ferro-alloy industry. The flow consists of particles of two different sizes, which in this specific industrial application are lumps of ore and coal or coke. It is known from experiments [S. A. Halvorsen, S. E. Remnes, and P. Hyldmo (unpublished)] that these particles show different mobilities under different circumstances. This effect is incorporated in our model via the inclusion of a ‘‘hydrostatic pressure’’ term.

The interfacial profile of the isotropic-nematic interface of a rigid-rod system is solved numerically based on a generalized Onsager model. For long rigid rods, the surface tension has the lowest value at a π/2 tilt angle between the nematic director and the normal to the interface. The density and order parameter are found to have different interfacial widths and interfacial positions. We find a dip in the density profile near the isotropic phase when the nematic director is almost parallel to the interfacial normal. The surface tension obtained here is 50% lower than the best variational calculation.

We investigate the current status of the mode-coupling theory (MCT) of the glass transition by making a comparison with two recent sets of experiments: the scaling data resulting from the dielectric measurements of Dixon et et al. et al. [Phys. Rev. Lett. 65, 1108 (1990)] and the neutron-scattering data. Our main conclusions include the following. (a) Experiments do show the sequence of time scales in the relaxation predicted by MCT. In particular, we believe that the high-frequency tail of the data of Nagel and co-workers is the realization of the so-called von Schweidler relaxation predicted by MCT in the frequency regime. (b) The nature of scaling discovered by Dixon et al. is quite different from and more universal than that predicted by MCT, which is basically a time-temperature superposition. Furthermore, the dielectric measurements show that there exists a universal relation between the exponent b governing von Schweidler relaxation and the exponent β governing a stretched exponential: 1+b=3/4(1+β). (c) Dixon et al. find no evidence for the existence of a special temperature ${\mathit{T}}_0$ (well above the phenomenological glass-transition temperature ${\mathit{T}}_{\mathit{g}}$) above and below which the relaxation dynamics is substantially different. This constitutes a discrepancy between the two sets of experiments since neutron-scattering experiments have been interpreted as confirming the existence of such a temperature well above ${\mathit{T}}_{\mathit{g}}$. A possible reinterpretation of MCT is suggested so as to reconcile these two sets of experiments and MCT.

We simulate one-dimensional crystal growth from an undercooled melt using a phase-field model and find interesting behavior when the liquid is undercooled by L/${\mathit{c}}_{\mathit{p}}$ degrees (‘‘unit undercooling’’). L is the latent heat and ${\mathit{c}}_{\mathit{p}}$ the specific heat. For smaller undercoolings, the diffusion of latent heat limits growth and the velocity of the solid-liquid interface decays with time as ${\mathit{t}}^{\mathrm{-}1/2}$. For larger undercoolings, non- equilibrium interface kinetics limits growth, and the interface velocity is constant. At unit undercooling, there are two scenarios, depending on the ratio of order parameter to thermal diffusivity (p). If p is small, the front-decay velocity is very well described by a power law ${\mathit{t}}^{\mathrm{-}\nu }$, with ν≊0.3. If p is large, the velocity at unit undercooling is finite. The branch of steady-state solutions then extends to smaller undercoolings, where the solid created is superheated. At the end of the branch, the solution jumps to a ${\mathit{t}}^{\mathrm{-}1/2}$ velocity-decay law. Although pure materials have small p’s, impure materials can have large p’s, so that the two scenarios at unit undercooling should be observable experimentally. Although our simulations apply strictly only to one-dimensional fronts, similar behavior is expected in two and three dimensions. The presence of the Mullins-Sekerka instability is unlikely to change our conclusions.

Dynamic-light-scattering experiments on semidilute aqueous solutions of gelatin indicate three relaxation processes: an exponential for times less than ∼50 μsec followed by a power law at intermediate time and then a stretched exponential at long time. The characteristic time of the stretched exponential diverges as the system evolves to a gel. The latter two relaxations can be explained in terms of an anomalous diffusion mechanism where the mean-square displacement behaves as 〈${\mathit{R}}^2$〉∼lnt at intermediate time and 〈${\mathit{R}}^2$〉∼${\mathit{t}}^{\mathrm{\beta }}$ with β<1 at late time. Length scales derivable from these diffusion mechanisms obey scaling, and it is proposed that β is related to the fracton density-of-states exponent and the fractal dimension of the gelatin molecules.

The standard wetting transition consists of the transformation of a microscopically thin two-dimensional interface into a macroscopically thick structure composed of two interfaces separated by a bulk phase. We consider the one-dimensional analog of this phenomenon, when a contact line among three or more phases decomposes into two contact lines separated by an interface. We uncover a wetting transition for the contact line, which occurs at surface two-phase coexistence, as a function of a line or edge field. This is exemplified by means of a lattice mean-field calculation for an Ising model bounded by two surfaces that meet in an edge.