We consider a system of classical particles equipped with internal degrees of freedom grouped together into a Potts-like spin object. We assume that in addition to hard-core repulsion the mechanical part of particle-particle interaction is of the van der Waals type, that is, it is attractive, long-ranged, and weak. Furthermore, we assume that the Potts spin interaction is also present and that it is also of the van der Waals type. This kind of interaction makes use of the mean-field analysis more plausibly than usual. Following this analysis we derive the phase diagram for our system and we discuss its main properties.

The classical dynamics and the quantal spectrum of a two-parameter Barbanis Hamiltonian is studied. Regions of almost regular and of weakly chaotic motion are found. The dipole strength function is found to be independent of the underlying classical motion.

We determine exactly the numbers C(N,m) of self-avoiding rings of N steps and m nearest-neighbor pairs, for N up to 28, on the square lattice, as well as the average squared radius of gyration for such rings. From these data we locate the θ point and determine its exponents as ν=0.58±0.01, φ=0.90±0.02. We also calculate a universal quantity for the rings, which was recently determined for the θ’ point. Our results are inconsistent with the θ and θ’ points being in the same universality class.

We define a simple hierarchical model in two dimensions incorporating two independent and nonsimultaneous rescaling procedures in orthogonal directions. The multifractal framework and corresponding thermodynamic formalism necessary for analyzing models of this type are set up using the concept of partial dimensions, and the model is then analyzed. We define an evolution space such that distinct paths in the evolution space correspond to distinct ways of constructing the hierarchy. If we utilize four scale Cantor sets in the construction of our hierarchy the equivalent Hamiltonian corresponds to that due to nearest-neighbor interactions between spins at the sites of a one-dimensional path on a two-dimensional lattice and is path dependent.

Fluctuations of a nonlinear oscillator driven by an intense resonant field with fluctuating phase are considered in the region of bistability. The general expression for the probability of a fluctuational transition between stable states is found to logarithmic accuracy. In the weak-damping limit the probabilities are obtained in the explicit form including both the argument of the exponential and the preexponential factor. A simple general method of determining the latter for underdamped systems is suggested. The probability of an escape from a metastable state near the bifurcation point where this state disappears is analyzed. The low-frequency susceptibility of the oscillator is shown to have a peculiar structure in the region of parameters where the stationary populations of the stable states are of the same order of magnitude. The stochastic modulation of the phase of an oscillator due to coupling to a bath is considered and its consequences are compared to those of randomness of the phase of a driving field.

We apply a recently developed generalization of the Feynman-Vernon approach to the case of a quantum-mechanical damped oscillator. We develop a variational method to treat the path integral that controls the dynamics of the reduced density operator of the system once it is subject to an arbitrary initial condition. The method is completely independent of the specific symmetries involved in the problem. Although we have applied it particularly to the harmonic oscillator, we believe it could be extended to more complex systems.

There have been a number of recent investigations of statistical properties of the nearest-neighbor distance of the closest diffusing particle in the presence of a trap. These have been shown to be useful characterizations of self-organizing properties of simple binary reactions of the form A+A→A or A+A→0. In this paper we extend our results to diffusion in the presence of an imperfect trap in one and three dimensions. The imperfect trap is modeled in terms of a radiation boundary condition. Our exact solution permits one to follow the transition in the shape of the probability density for the nearest-neighbor distance from the exponential in one dimension corresponding to total reflection, to the skewed Gaussian form for perfect reaction. Similar results are given for the case of a reactive sphere in the presence of mobile particles in three dimensions.

An equation of state is proposed for an isotropic fluid of hard convex bodies in any number of dimensions. In general, only knowledge of the first three virial coefficients is required. In three dimensions an approximation can be used that involves a single nonsphericity parameter. The result appears to be very accurate as far as it can be tested against available computer simulations.

We study the evolution of long shallow waves in a convecting fluid when the critical Rayleigh number slightly exceeds its critical value. The surface displacement is found to obey a perturbed Korteweg–de Vries equation that includes diffusion and instability effects.

The renormalization-group (RG) method applied to homogeneous and isotropic turbulence is built up as an expansion around the particular dimension where the energy cascade reverses. As usual, the expansion parameter is related to the turbulent expression of the Reynolds number (λ¯∼${\mathrm{\epsilon }}^{1/2}$). The eddy-damped quasinormal Markovian approximation, which has been found to be consistent with RG at order ${\mathrm{\epsilon }}^1$ by Dannevick, Yakhot, and Orszag [Phys. Fluids 30, 2021 (1987)], is used to obtain a constraint on the Kolmogorov constant in such a way that no adjustable parameters are needed. Furthermore, several constants appearing in theories widely used in turbulence modeling are estimated and compared with their experimental values.

A few-mode Lorenz-like model for convection in a rotating binary mixture confined between stress-free, impermeable boundaries is presented. It describes for positive separation ratios standing patterns of convective rolls in mutually perpendicular directions and the superposition of these rolls with the same wave number. The model is used to investigate the effect of slow rotation on convective patterns. In ideal systems squares are unstable, and the dynamical behavior immediately in the Rayleigh regime is chaotic. Side-wall forcing is incorporated by introducing a small inhomogeneity into the model. In the presence of side walls the chaotic behavior disappears, squares are stabilized close to onset, and rolls are stable in the Rayleigh regime with oscillations occurring in between. For Taylor numbers above a critical value, oscillations disappear and stable stationary patterns are possible over the whole range of Rayleigh numbers.

We consider the nonlinear processes of interaction between a random field of short deep gravity waves and a deep long gravity wave, as well as the effects of nonlinear interactions among the driven short waves. The interactions are characterized by two types of invariants. First, the short waves possess an adiabatic invariant as regards their interaction with the long waves. Second, a collision between short waves conserves frequency and wave vector. As a consequence of these invariants, extra degrees of freedom appear. This results in a two-fluid description at the surface of the liquid for the mean flow of the long wave plus a distribution of waves. The two-fluid theory implies a spectrum of oscillations of the surface where, besides the usual gravity waves, there exists a surface mode with longitudinal oscillations. The regimes of validity of this hydrodynamic description are discussed, and the solutions for the dispersion relation are also presented. The power spectrum of a stormy sea is derived within the framework of nonlinear wave interactions. Finally, we comment on the relevance of the results to phase-velocity measurements in a wind-wave laboratory experiment, as well as possible experiments to observe the theoretically predicted new mode.

We show how both the contact structure and the metric structure of the thermodynamic phase space arise in a natural way from a generalized canonical probability distribution ρ. In particular, the metric form and the contact form are found to be derived from the microscopic entropy s=-lnρ. Thus the first law and the second law of thermodynamics can be given the geometric interpretation that a thermodynamic system must possess both a contact and a compatible metric structure. We proceed to construct explicitly a new nondegenerate bilinear form on the thermodynamic phase space, whose restriction to state space yields the Weinhold-Ruppeiner metric, and whose restriction to Gibbs space can serve as an alternative to the metric proposed by Gilmore.

A procedure is presented for constructing a thermodynamic free energy for fluids in the critical region that incorporates the crossover from Ising-like singular behavior near the critical point to regular classical behavior far away from the critical point. The procedure is based on an approximation of the solution of the renormalization-group theory of critical phenomena, modified to include effects from a cutoff wave number for the crossover to the classical limit. As an illustration we show how the procedure can be applied to a truncated classical Landau expansion. The results are compared with experimental thermodynamic-property data for carbon dioxide, steam, and ethylene in the critical region.

We report experimental results of Rayleigh-Brillouin light-scattering studies of fluids with chemical reaction processes. An adapted hydrodynamic model allows the description of the coupling between the chemical relaxation process and hydrodynamic sound and thermal modes.

When a nematic liquid crystal is spread on a crystalline substrate, the latter can orient the nematic molecules on top. Recently, it was shown that if water vapor is adsorbed onto the nematic-substrate interface, a discontinuous jump in the orientation can be observed. In this article we report a systematic study of the conditions under which this anchoring transition takes place. We find that, in addition to water, alcohols and diols cause a transition. Further, the nematic orientation depends only on relative humidity and not directly on temperature.

The smectic-A (Sm-A) to chiral-smectic-C transition has been studied by high-resolution ac calorimetry in seven mixtures of two chiral esters of 2,5-diphenyl pyrimidine (2f+3f) over the range 38.72≤${\mathit{X}}_{2\mathit{f}}$≤65.30, where ${\mathit{X}}_{2\mathit{f}}$ is the mole percent of 2f. The heat-capacity results have been fit below the transition temperature using an extended mean-field model and show that the transition is quite close to a tricritical point over the entire range of composition. In all seven mixtures, the excess heat capacity above the transition temperature is observed to scale in the same manner as the Landau contribution does below the transition. This behavior is consistent with the presence of thermal fluctuations in the Sm-A phase.

We formulate the problem of finding the stability spectrum of the cellular pattern seen in directional solidification. This leads to a nonlinear eigenvalue problem for an integro-differential operator. We solve this problem numerically and compare our results to those obtained by linearizing the eigenvalue problem by employing the quasistatic approximation. Contrary to some recent claims, we find no evidence for a Hopf bifurcation to a dendritic pattern.

We have studied the aggregation of colloidal gold particles with finite interparticle attraction energies with static light scattering and the combination of conventional transmission electron microscopy (TEM) and high-resolution TEM. The finite interparticle attraction energies are achieved by adding a surfactant in the suspension via adsorption. The interparticle interaction can be changed by changing the amount of the surfactant. Using a modified Derjaguin-Landau-Verwey-Overbeek theory to describe the interparticle interaction, we show that (i) the aggregates of colloidal particles can still be fractal objects with a finite interparticle attraction and (ii) the fractal dimension changes with the interparticle attraction energy, in agreement with the computer simulations of Shih, Aksay, and Kikuchi [Phys. Rev. A 36, 5015 (1987)].

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.