An isobaric-isothermal Monte Carlo simulation method has been used to investigate the approach to wetting in a 12-6/9-3 potential model of fluid Ar and solid ${\mathrm{CO}}_2$. We have studied adsorption from the subcritical vapor at pressures up to saturation along isotherms at several temperatures. At each state the density profile and the adsorption excess were determined. At the lowest temperatures studied, the adsorption isotherms and density profiles exhibit behavior consistent with partial wetting at coexistence, in that the adsorption remains finite all the way up to coexistence. Over an intermediate range of temperatures we have found behavior consistent with the existence of a prewetting line, a locus of first-order phase transitions from thin- to thick-film adsorption. The adsorption excess increases discontinuously at pressures below saturation as thick liquidlike films form. These liquid films grow in thickness until the saturation pressure is reached and the adsorption excess diverges. At a still higher range of temperatures, behavior consistent with complete wetting at saturation is observed but with a continuous growth in the film thickness as the pressure is increased toward saturation. In contrast with earlier work on the same model system using the grand ensemble Monte Carlo method, our observations are in qualitative agreement with the predictions of density-functional and related theories of wetting phenomena. We discuss possible reasons for the failure to observe such phenomena in previous simulation work.

The competition between sine-Gordon-breather and kink-antikink-pair solitons under the influence of damping and both ac and dc driving is investigated. We introduce soliton collective coordinates, and develop equations of motion for this system. Then we analyze the transition by calculating the perturbed separation of the stable and unstable orbits near the homoclinic point of the motion using Melnikov’s method. We find that the threshold for complicated behavior is strongly dependent on the frequency of the ac driving, and that the contribution of the dc driving is to lower this threshold.

It has been shown that many enzymes should be capable of utilizing free energy supplied by external time-dependent perturbations to drive the chemical or transport reactions they catalyze away from equilibrium. This property is analyzed in terms of thermodynamic and kinetic theory. An explicit demonstration using irreversible thermodynamics, through second order, is given for the case of a simple model enzyme in the presence of a periodic external perturbation. Three reasons for an enzyme to drive a reaction in a nonstationary environment may be identified: the average values of the forces, the root mean square of the external time-dependent perturbation, and the frequency-dependent correlation between the applied perturbation and the enzyme response. The extent to which the output reaction responds to any of these is governed by the kinetic constants of the enzyme. Even if the catalyzed reaction (e.g., the transport of an uncharged substance across a membrane) is in and of itself thermodynamically independent of the periodic perturbation (e.g., an ac electric field), the enzyme is competent to mediate free-energy exchange between the two. This originates from the fact that at high frequencies, the enzyme response lags behind the applied perturbation. It is sufficient that the enzyme interact with the applied field, and that the catalytic rate constants display the kinetic asymmetry typical of many, and particularly transport, enzymes. These results highlight the role of enzymes as free-energy converters in addition to that of biological catalysts.

We consider the problem of a mobile trap (B) diffusing in the presence of stationary particles (A’s) which may be caught by the trap. In particular, we calculate the probability density for the distance of the nearest free A from the trap, as a function of time. The mean value of this quantity is found to vary as $t^{1/2}$ in one dimension, in contrast to the case in which the A’s are mobile and B is stationary, where the mean distance is proportional to $t^{1/4}$ for the analogous quantity. In two dimensions we find by simulation that the mean distance increases as lnt, while in three dimensions it is asymptotically constant.

We consider a one-dimensional random chain where the probabilities of taking steps to the right (or left) at any site are identically distributed independent random variables, having the distribution p($p_i$)=0.5δ($p_i$-α) +0.5δ($p_i$-1+α). Furthermore, this chain contains a random distribution of traps. We compute upper and lower bounds for the asymptotic survival probability. We show that this follows a power law and that the bounds agree as far as the exponent of t is concerned.

The properties of the boundary between basins of attraction of the logistic map in 2×2 real matrices are explored. The relationship between the Julia set and the boundary is analyzed. Numerical values for the capacity dimension are given, and a mechanism for the origin of a transient scaling behavior is proposed.

For the elementary diffusion-limited reaction A+B→0 on a one-dimensional system of hard-core particles, we show theoretically that the nature of the source term is a fundamental element in the building of the steady state. We also illustrate the importance of the strict conservation of an equal number of A and B at any time, in contrast to a simple conservation on the average. We show how the spatial correlation between members of incoming A-B pairs affects the steady-state distribution. Also, in the case where either first-order decays, such as spontaneous desorption, or vertical annihilation of asymmetric species, are incorporated, the physics is drastically changed. Furthermore, we derive for each case the macroscopic reaction law, and also obtain information on the spatial distribution of the species. The latter shows, in some cases, a macroscopic or mesoscopic segregation phenomenon. We also specify the likely conditions for observing segregation experimentally.

In this article we study the elementary diffusion-limited reaction A+B→0, for a system of particles with hard-core interactions. We extend a theoretical investigation carried out for dimension d=1 to higher Euclidean dimensions. We show that a source or a first-order decay mechanism can control the steady-state distribution of particles. We derive in dimensions d=2 and 3 the explicit correlation functions and macroscopic reaction laws. We calculate a segregation length, measuring the extent of the clustering for particles of the same type, and we derive its dependence on the Euclidean dimension, the detailed source term structure, and a possible internal decay mechanism.

For diffusion-limited reactions of the type A+A→0, we present a theory for the pair correlation function and the macroscopic reaction law for the Euclidean dimensions d=1, 2, 3 and for self-similar fractal structures with spectral dimension such that 1≤$d_s$≤2. In any dimension we define a length Λ, which is the typical size of the depletion zone around each particle. Λ is expressed as a function of a fundamental size ξ= √ρD/R , where ρ is the steady-state density, R the external source rate, and D the microscopic diffusion constant. For $d_s$≤2, we obtain the ‘‘fractal’’ reaction order X=1+2/$d_s$ and a mesoscopic, density-dependent depletion zone around each particle. We give an interpretation of the particle self-ordering and anomalous rate laws in terms of the random-walk topological properties.

The evolution of the density matrix is calculated in the Wigner representation for the periodically kicked particle [H=(1/2${\mathit{p}}^2$+1/2) ${\mathit{Kx}}^2$${\mathrm{\Sigma }}_{\mathit{n}}$δ(t-nT)] in the presence of dissipation. The dissipation is introduced via a linear coupling to a bath of harmonic oscillators. The behavior in various regions of the parameter space for the problem is analyzed in detail and compared with the Markovian approximation. The degree of agreement with the Markovian approximation is classified. In various regions in parameter space the model reduces to various examples that were studied in the past (damped particle, harmonic oscillator). Most regions of the parameter space were not explored in the past and are of potential interest. One of these regions exhibits a limit cycle.

We analyze the effect of finite memory on the Lyapunov exponent of products of random matrices by considering Markov trials. We study three different cases of physical interest: the one-dimensional Anderson model with correlated random potentials, light propagation in media with correlated random optical indices, and a mimic of the deterministic chaos appearing in dynamical systems with few degrees of freedom. In general the Lyapunov exponent is found to have the same qualitative shape as the inverse of the correlation length of the Markov process. We, however, observe that this rough proportionality fails in some relevant situations. We explain this unexpected behavior in the localization problem by using simple arguments.

The orientational freezing of a system of hard ellipses, as a first approximation for a nematogen adsorbed on a smooth substrate, is studied with the aid of an approximate density-functional theory used previously for the study of hard ellipsoids. The isotropic-nematic transition, which was first order for the ellipsoids, is shown to proceed via a continuous transition in the case of the ellipses. We also show that when reducing the dimensionality of the angular space of ellipsoids, the width of the transition shrinks continuously and reaches zero only for a strictly two-dimensional angular space.

The structure of few-body Hamiltonian matrices is studied in the semiclassical regime. Given (A${^}_1$(q^,p^),A${^}_2$ (q^,p^)), a pair of operators, it can be shown that, under quite general conditions, A${^}_2$ takes the form of a banded matrix in the ordered eigenrepresentation of A${^}_1$. Moreover, the bandwidth depends only on ħ and certain generalized microcanonical averages. In particular, if H=$H_0$+εV, this implies that the perturbed Hamiltonian is banded in the appropriately ordered unperturbed basis.

A Riemannian metrical structure of the parameter space has been introduced and investigated for magnetic systems described in the framework of quantum statistics. The introduced metric is based on the conception of the relative information. Two contrasting models have been investigated in detail: the one-dimensional Ising model, with short-range interactions, and the mean-field model of Kac, with long-range interactions. In the second case the metric tensor degenerates. The degeneration has been removed by adding the lattice energy to the original magnetic Hamiltonian. It turns out that in both cases the scalar curvature of parameter space tends toward plus infinity while approaching the critical points. The inverse of the scalar curvature, given by the second and third moments of stochastic variables, has been interpreted as a measure of the stability of the considered magnetic systems. The scalar curvature represents a joint part of fluctuations caused by the interactions of spins.

We have studied various one- and two-dimensional models in order to simulate the behavior of avalanches. The models are based on cellular automata and were intended to have the property of ‘‘self-organized criticality’’ proposed by Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 384 (1988)]. By varying the sizes of the systems, we have investigated the scaling properties of these models. In particular, we have addressed the question as to whether simple finite-size scaling or multifractal analysis is more suited to fitting the data on the distribution of avalanche sizes. By varying the underlying microscopic rules that describe how an avalanche is generated, we have also studied whether different models have the same, universal properties. In our one-dimensional models we find that the multifractal analysis is much better than the analysis based on simple finite-size scaling. We also find that there are several different universality classes. Nevertheless, certain models with similar rules appear to belong to the same class. In two dimensions, we find that the simple finite-size scaling works quite well and that the distribution functions can be fit over wide ranges by a simple power law. The multifractal analysis also works well and it is difficult to tell which form is a better fit to the data. Again, as in one dimension, there are several different universality classes and different models with similar rules belong to the same class.

This paper deals with the attractors associated with some volume-nonpreserving generalized Fibonacci trace maps. It is shown that a central role in their behavior is played by certain pseudoinvariants. On the basis of the presence of these attractors, we illustrate the coexistence of regular and Cantor-like excitation spectra.

Using an exact-enumeration approach, we study the multifractal spectrum of diffusion-limited aggregation. The enormous number of possible configurations is reduced by many orders of magnitude using symmetry considerations. The most interesting result is that we find evidence which strongly suggests the existence of a phase transition in the multifractal spectrum: specifically, the ‘‘free energy,’’ ‘‘energy,’’ and ‘‘specific heat’’ develop singularities near a critical ‘‘temperature’’ ${\beta }_c$. Moreover, the energy shows large fluctuations near ${\beta }_c$. We also find that for β<${\beta }_c$, the free energy is dominated by the maximum energy $E_{\max (\mathrm{L}}$), which increases with system size L: $E_{\max \left(\mathrm{L}\right)\mathrm{\sim }{L}^2}$/lnL. The implications of this phase transition are that the free energy is not defined for β<${\beta }_c$, and that the large energy part of the ‘‘entropy’’ function is a straight line of slope ${\beta }_c$. We provide a phenomenological explanation for the origin of this phase transition.

We describe a reptation model applicable to long-chain polyelectrolytes, like DNA in a gel, and derive an exactly solvable master equation for the probability distribution of the chain’s extension in an applied electric field. The effect on the steady-state mobility of reduced charge at the chain’s ends is studied, and differences between the model’s steady-state probability distributions and ones derived from counting chain configurations are noted.

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.

The behavior of the theoretically predicted correlational ‘‘fine’’ energy-loss spectrum of inelastic electron scattering in disordered systems close to single resonance is investigated near the critical point. In extending our earlier work, it is shown that the relation of the statistical expression of the cross section of energy loss to the function which describes the line shape in an ideal gas asymptotically increases near the critical point as a power law. ‘‘Fracton’’ interpretation of display of the localization of a single excitation in disordered systems in the resonance-line shape of the energy-loss spectrum is suggested. The possibility of direct determination of the pair distribution function (without Fourier transformation of the structure factor) using the method of charged-particle scattering is discussed.