Harmonic generation is investigated at an intensity range of ${10}^{15}$–${10}^{18}$ W/${\mathrm{cm}}^2$ by using a 280-fsec KrF laser. The highest-order harmonic observed with Ne as a nonlinear medium is the 25th (9.9 nm), which gives the shortest-wavelength coherent radiation ever obtained. The inversions or anomalous peaks of harmonic intensity are first found at the 19–21st in Ne, the 17–19th in He, and the 11–13th in Ar. The intensity dependence of the harmonics is measured over a range of ${10}^{15}$–${10}^{18}$ W/${\mathrm{cm}}^2$. The observed distribution of harmonics is discussed and compared with the previous reports.

A general enhancement mechanism is reported for nonlinear optical processes originating from real population of electronic excited states. The calculated nonresonant third-order optical susceptibility ${\gamma }_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}\mathit{n}}^{\mathit{S}}$(-${\mathrm{\omega }}_4$;${\mathrm{\omega }}_1$,${\mathrm{\omega }}_2$,${\mathrm{\omega }}_3$) of quasi-one-dimensional conjugated linear chains can be enhanced by orders of magnitude, or even change sign, when the first (${\mathit{S}}_1$) or second (${\mathit{S}}_2$) electronic excited state is optically pumped and then populated for times suitably long to perform nonresonant measurements of ${\gamma }_{\mathit{i}\mathit{j}\mathit{k}\mathit{l}\mathit{n}}^{\mathit{S}}$(-${\mathrm{\omega }}_4$;${\mathrm{\omega }}_1$,${\mathrm{\omega }}_2$,${\mathrm{\omega }}_3$) at frequencies different from the resonant pump frequency.

We analyze the nonlinear dynamics in the normal-dispersion regime near the zero-dispersion point of a single-mode optical fiber using a connection between the nonlinear Schrödinger and Korteweg–de Vries equations. We predict a new type of optical soliton in this region and demonstrate a possibility of transformation of one type of soliton to another.

We report a general method for evaluating the partial chemical potentials of a dense neutral multicomponent system of charged particles. The results of this analysis can be directly applied to the evaluation of chemical potentials and partial chemical potentials for the electron gas, for a neutral two-component charged system such as the metallic phase of hydrogen, and even for a three-component system such as a metal hydride.

The spectral density of the fluctuations of an underdamped, single-well, nonlinear oscillator driven by a random force has been investigated. Electronic analog experiments have demonstrated the existence of a narrow spectral peak at zero frequency; such a peak only appears, however, in those cases where the potential is non-centro-symmetric. The evolution of the peak with variation of a parameter characterizing the asymmetry of the potential, and with noise intensity, has been investigated both experimentally and theoretically. It is found that the half-width of the peak remains relatively small (of the order of the reciprocal relaxation time) over a broad range of noise intensities. The theory of the peak shape is shown to be in close agreement with experiment. The relationships of the peak to the (apparently similar) zero-frequency peaks observed previously in double-well oscillators, where they are responsible for stochastic resonance, and to the supernarrow spectral peaks found near kinetic phase transitions in periodically driven systems, are discussed.

A quantitative method for the treatment of large-scale intrinsic fluctuations amplified by chaotic trajectories in macrovariable physical systems is presented. Paradigmatic results for the Rossler model and preliminary computational results for chaotic Josephson junctions and for chaotic multimode Nd:YAG (yttrium aluminum garnet) lasers are described. These studies are directed towards identification of a real physical system in which experimental confirmation may be realized. The probability distribution on the intrinsic-noise-modified, chaotic attractor is identified as a likely candidate for comparison of experiment and theory.

We study the eigenvalue spectrum of the hopping transition matrix for percolation clusters on square, simple cubic, and body-centered-cubic lattices and show that certain scaling laws are satisfied. As a result, velocity and acceleration autocorrelations attain asymptotic power-law decays as were previously seen by Monte Carlo and by numerical summation of Brownian paths for long times.

We study the dynamics of an interface driven far from equilibrium in three dimensions. First we derive the Kardar-Parisi-Zhang equation from the Langevin equation for a system with a nonconserved scalar order parameter, for the cases where an external field is present, and where an asymmetric coupling to a conserved variable exists. The relationship of the phenomena to self-organized critical phenomena is discussed. Numerical results are then obtained for three models that simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We first make a study of crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. We then estimate the dynamical scaling exponents. Within the precision of our study, the Kardar-Parisi-Zhang equation and the solid-on-solid model have the same asymptotic behavior, indicating that the models share a dynamical universality class. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this by monitoring the surface step energy, which shows a dramatic jump at a finite temperature for a given driving force. At the same temperature, a finite-size-scaling analysis of the bond-energy fluctuation shows a diverging peak.

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

We consider the influence of random noise on low-dimensional, nonlinear dynamical systems with parameters near values leading to a crisis in the absence of noise. In a crisis, one of several characteristic changes in a chaotic attractor takes place as a system parameter p passes through its crisis value ${\mathit{p}}_{\mathit{c}}$. For each type of change, there is a characteristic temporal behavior of orbits after the crisis (p>${\mathit{p}}_{\mathit{c}}$ by convention), with a characteristic time scale τ. For an important class of deterministic systems, the dependence of τ on p is τ∼(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{-}\gamma }$ for p slightly greater than ${\mathit{p}}_{\mathit{c}}$. When noise is added to a system with p<${\mathit{p}}_{\mathit{c}}$, orbits can exhibit the same sorts of characteristic temporal behavior as in the deterministic case for p>${\mathit{p}}_{\mathit{c}}$ (a noise-induced crisis). Our main result is that for systems whose characteristic times scale as above in the zero-noise limit, the characteristic time in the noisy case scales as τ∼${\mathrm{\sigma }}^{\mathrm{-}\gamma }$g((${\mathit{p}}_{\mathit{c}}$-p)/σ), where σ is the characteristic strength of the noise, g(⋅) is a nonuniversal function depending on the system and noise, and γ is the critical exponent of the corresponding deterministic crisis. A previous analysis of the noisy logistic map [F. T. Arecchi, R. Badii, and A. Politi, Phys. Lett. 103A, 3 (1984)] is shown to be consistent with our general result. Illustrative numerical examples are given for two-dimensional maps and a three-dimensional flow. In addition, the relevance of the noise scaling law to experimental situations is discussed.

It is well established that anisotropy does not affect the critical behavior of a system in thermodynamic equilibrium that undergoes a second-order phase transition. We study here an anisotropic kinetic model for heterogeneous catalysis that mimics the oxidation of CO on the (110) surface of a transition metal like Pd. We have mapped out the phase diagram of possible steady states for various anisotropic reaction and absorption processes as a function of the ${\mathrm{O}}_2$/CO adsorption rate and the CO diffusion rate. The phase diagram depends upon the amount of anisotropy and exhibits both a first-order and a second-order phase transition for a reactive to an unreactive steady state. We have examined the critical behavior at the second-order phase transition with finite-size scaling and have found that this model belongs to the directed percolation universality class irrespective of the anisotropy.

We have studied the ground-state energy of the single-impurity Kondo model. Results using a strict 4×4 Lanczos truncation are shown to be equivalent to a relaxed 26×26 Lanczos basis. An application of the connected-moments expansion to obtain the ground-state energy of this model many-body Hamiltonian is shown to be limited to certain regions of parameter space.

The chaotic dynamics in a separatrix layer are investigated using the ‘‘separatrix map.’’ Quantizing this map we show that localization effects inhibit the quantum transport across the separatrix layer. Depending on the size of the nonintegrability parameter, the mechanism of localization is connected with either the remnants of the barely broken separatrix, or with barely broken Kolmogorov-Arnold-Moser tori (‘‘cantori’’) inside the separatrix layer, or with dynamical localization due to destructive interference of random transition amplitudes.

We investigate percolation clusters in a d-dimensional hypercube of linear dimension 2. This set can be used to describe the configurational space of an Ising spin-glass system. We derive the perimeter polynomials for general dimensions and expand in powers of 1/η, where η=d-1 and the coordination number is d. The leading term in the series expansion yields the Bethe approximation. In a finite dimension, a crossover occurs from scaling to homogeneous behavior in a finite region above the percolation threshold. In the scaling region, finite-dimensional scaling is considered for the cluster size distribution by applying a phenomenological renormalization-group argument. For the percolation clusters we consider the mean Hamming distance of random walks; this quantity corresponds to the Ising spin-glass order parameter. This configuration-averaged Hamming distance shows (i) a stretched exponential relaxation (p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{-}\mathit{a}}$${\mathit{t}}^{\mathrm{-}\mathit{x}}$exp[-(t/scrT${)}^{\mathrm{\beta }}$] with scrT∼(p-${\mathit{p}}_{\mathit{c}}$${)}^{\mathrm{-}\mathit{z}\nu }$ as p→${\mathit{p}}_{\mathit{c}}^{+}$ with the exponents a∼3/5, x∼1/6, β=2/5, zν=3; and (ii) an extremely slow relaxation at p=${\mathit{p}}_{\mathit{c}}$, in infinite-dimension limit. This result illustrates Ogielski’s numerical simulation data [Phys. Rev. B 32, 7384 (1985)] in an Ising spin-glass system.

In this contribution, we discuss dynamical phase-transition-like behavior in dynamical systems and give evidence for the occurrence of such effects in an experimental, parametrically modulated radio-frequency laser. We elucidate the connection between a generalized scaling behavior that depends on two scaling exponents, i.e., the fractal dimensions and the Lyapunov exponents, and the procedures available for the evaluation of scaling functions of Lyapunov exponents from experimental data.

A hierarchical approximation of a generic chaotic attractor can be formulated in terms of unstable periodic orbits. We demonstrate the possibility of extracting the most dominant unstable periodic orbits from a measurement of a time-continuous flow. Since unstable periodic orbits not only represent the static properties of the system but also dominate the dynamics, they can be used to fit models of the flow and to predict the orbit. We show that predictions for the Roessler system using unstable periodic orbits extracted from a time series of moderate length are significantly better than those from other approaches.

Measurement results on the absorption coefficient, speed of sound, and Raleigh light-scattering intensity in two stratified solutions containing one and two ‘‘double’’ critical points are presented. A model describing the temperature dependence of the sound absorption coefficients and light scattering, considering the superposition of all phase transitions existing in the systems, is proposed.

With three different pair potentials we study the thermal collective transport coefficients of the ${\mathrm{N}}_2$ model liquid by molecular-dynamics calculations. The first two of the considered pair potentials are Lennard-Jones (LJ) one-center and two-center potential functions, while the third represents a two-center LJ function plus a point-quadrupole interaction term. All three potential functions lead to acceptable transport coefficients compared with experiment. However, there appear to be significant differences in the coefficients for certain thermodynamic states. While the quadrupole interaction has only a slight effect on the time correlation functions, the two-center LJ potential influences the time correlation functions appreciably in comparison with the spherically symmetric LJ potential. The latter findings agree well with our previous results obtained for LJ liquids with four or more center potentials. On the whole, the thermal conductivity coefficient is less sensitive to the employed pair potential function than the bulk or the shear viscosity coefficient. Unfortunately there are no experimental data for the bulk viscosity.

We report results of a detailed study by light scattering and a model simulation of spinodal decomposition in a binary liquid mixture under constant uniform shear flow. The effects of flow are found to be important when the growth rate of the phase-separating domains is smaller than the shear rate. The growth of these domains is strongly modified by the shear flow only in certain directions. In the direction perpendicular both to the flow and shear, the flow has little effect on the growth. Some essential features observed in the experiments are reproduced in a computer simulation that incorporates only the deformation produced by the flow. The effect of surface tension must be considered to account for the other observed effects. A new growth mechanism can be induced by the interaction of capillary forces with the shear flow.

The diffusion of gases through foams with nonuniform cell sizes is described using fractal models. These models correspond to the limit of extreme nonuniformity, since essentially all cell sizes are present in fractal-like foams. The calculated diffusion currents in the fractal models are anomalous, and a diffusion current entering a fractal surface, J(t), can exhibit a power-law time dependence [J(t)≊${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$]. The exponent α depends on the structure of the model. In the simplest one-dimensional case, α is determined by the fractal dimension. For the three-dimensional fractal models, α is related to an additional parameter that compares the resistances of large and small cells to the current flow. Qualitatively, we show that diffusion in foams with a large variety of cell sizes can be anomalously large or anomalously small, and the unusual currents depend as much on the distribution of cell-wall thicknesses as they depend on cell-wall sizes.