A missing redshift factor in my paper [Phys. Rev. A 40, 4857 (1989)] brought to my attention by E. Santos is corrected. The correction results in a better match between theory and observation, thereby strengthening the original argument that the zero-point energy fields are dynamically generated by the quantum-fluctuation motion of charged particles distributed over cosmological space.

This Comment points out misleading aspects of a recent paper by Shao and Stezowski [Phys. Rev. A 42, 5767 (1990)].

We thank Jiqiang Chen and M. J. Stott for their helpful remarks [preceding Comment, Phys. Rev. A 44, 3387 (1991)].

Nonisochronism, the dependence of oscillation frequencies on amplitudes, substantially changes the dynamics of two weakly coupled nonlinear oscillators. Using averaged equations, we find that a nonisochronous passive circuit coupled with an active oscillator displays chaotic and two-frequency oscillation regimes, behaviors not found in the corresponding isochronous system. This system also shows hysteresis at the transitions from two- to one-frequency regimes, and from the one-frequency regime to the suppression of oscillations. The transitions to chaos, via period doubling and type-I intermittency, occur as the detuning of the two partial frequencies of the oscillators is varied, and we identify conditions for the onset of chaos in this system.

We discuss the properties of the wave chaos appearing in some quantized systems that are classically not chaotic.

We discuss the existence of a type of interfacial transition which, by analogy with translational preroughening, we name the orientational preroughening transition. A sine-Gordon renormalization-group analysis of the orientational roughening and preroughening transitions for a lattice-interfacial Hamiltonian is presented. Thus we construct an effective Hamiltonian of a tensionless solid-on-solid interface on a triangular lattice and then study its flow using Wilson’s momentum-shell renormalization-group method. By analogy to the case for translational roughening for an interface that possesses a surface tension, we find both roughening and preroughening transitions. We also discuss the present uncertainties associated with that and with other preroughening transitions.

Multibranched crosslike crack patterns formed in concentrically loaded square plates are studied in terms of fractal geometry, where the associated fractal dimension ${\mathit{d}}_{\mathit{f}}$ is calculated for their characterization. We apply the simplest deterministic and stochastic approaches at a phenomenological level in an attempt to find generic features as guidelines for future experimental and theoretical work. The deterministic model for fracture propagation we apply, which is a variant of the discretized Laplace approach for randomly ramified fractal cracks proposed by Takayasu [Phys. Rev. Lett. 54, 1099 (1985)], reproduces the basic ingredients of observed complex fracture patterns. The stochastic model, although not strictly a model for crack propagation, is based on diffusion-limited aggregation (DLA) for fractal growth and produces a slightly more realistic assessment of the crosslike growth of the cracks in asymmetric multibranches. Nevertheless, this simple ad hoc DLA version for modeling the present phenomena as well as the deterministic approach for fracture propagation give fractal dimensionality for the fracture patterns in accord with our estimations made from recent experimental data. It is found that there is a crossover of two fractal dimensions, corresponding to the core (higher ${\mathit{d}}_{\mathit{f}}$) and multibranched crosslike (lower ${\mathit{d}}_{\mathit{f}}$) regions that contains loops, which are interpreted as representing different symmetry regions within the square plates of finite size.

The path-integral approach is adopted to investigate the motion of vortex lines that are pinned to the crystal lattice and creep thermally against the pinning energy barriers. The thermal creeping process of the entire vortex line is correlated by the presence of vortex tension. Our model results are applicable to a vast number of physical phenomena including the magnetic vortices in type-II superconductors and the superfluid vortices in neutron stars.

The anharmonic-oscillator equation with dissipation has been widely used in various areas of science, and surprisingly little has been known about its analytical solutions. In this paper, we survey the known classes of solutions and the methods employed to obtain them including the Painlevé Test and its results. We propose several approaches, one of which is based on compatibility with a Bernoulli equation. Another method investigated explores the many solutions that take the form of a rational fraction of linear combinations of exponentials. In addition to elementary function solutions, those involving elliptic functions are examined. The way the restriction on the parameters of the equation may be relaxed somewhat is demonstrated, leading to an extension of elliptic-type solutions.

It is shown that diffusion, in momentum space, exists for the periodically kicked quantum rotator when dynamic disorder is considered on the external potential v(θ) (the amplitude of the kick). This is opposite to the behavior without disorder (deterministic) where localization exists. Explicitly if v(θ) is stochastic, then the diffusion coefficient is linked to the second derivative of the correlation function 〈${\mathit{e}}^{\mathit{i}\mathit{v}(\mathrm{\theta }+\mathit{c}\mathit{p}\mathit{h}\mathit{i})}$${\mathit{e}}^{\mathrm{-}\mathit{i}\mathit{v}\left(\mathrm{\theta }\right)}$〉 at cphi=0. Two examples are considered, the Gaussian process and the random linear case v(θ)=ηθ (with η a random parameter). In both cases, the diffusion coefficient was evaluated exactly. Finally, we conjecture that this diffusive behavior may be found in a great variety of kicked systems with static disorder.

A formalism for the global polynomial function approximation for the prediction of chaotic time series is introduced. It takes into account the ergodic invariant measure of the dynamical system. The method presented is based on the generalized Fourier expansion with respect to the polynomial system Π orthonormal to the invariant measure. The expansion coefficients, which are optimal in the ${\mathit{L}}_2$ sense with respect to the natural metrics ${\mathrm{\rho }}_{\mathit{I}}$, are expressed in terms of the hierarchy of moments scrM and the hierarchy of functional moments Γ. In this way, any kind of multivariable parameter optimization becomes unnecessary. The presented approach to reconstruction furnishes good results in the global reconstruction and prediction of time series arising from both discrete and continuous dynamical systems.

A detailed numerical bifurcation analysis of the forced Brusselator is performed, exposing local and global bifurcation curves that constitute the internal structure of the dominant Arnol’d tongues. The results of our analyses are presented as phase diagrams and one-parameter bifurcation diagrams. Two theorems concerning the existence of global bifurcations near generic codimension-2 bifurcation points are stated and proved. It is argued that the results are generic to a class of periodically forced self-oscillating systems.

Tethered vesicles at various constant pressure differences Δp are investigated by Monte Carlo simulations. Flaccid vesicles (Δp=0) exhibit uncrumpled configurations with a mean-square radius of gyration 〈${\mathit{R}}^2$${\mathrm{〉}}_0$∼${\mathit{N}}^{\nu }$, where ν≊1.0 and N is proportional to the surface area. The roughness of their surfaces is characterized by an exponent ζ=0.65. The crossover to inflated vesicles (Δp>0) and to deflated vesicles (Δp<0) are analyzed by means of finite-size crossover scaling assumptions. The crossover to inflated vesicles (ν=1.0) is governed by the reduction of the corrugation due to the pressure, i.e., from ζ=0.65 to 0, which is characterized by a crossover exponent cphi=1.88. The crossover to deflated vesicles is ruled by the change of their sizes, i.e., from ν=1.0 to 0.66, which is characterized by cphi’=4.4.

We have developed a combined theoretical and numerical method for constructing analytic solutions to a class of stochastic (random-walk) problems set in lattices of arbitrary (integral) dimension. The method is illustrated for the case of a particle diffusing in a finite d-dimensional space defined by a hypercube with N=$3^{\mathit{d}}$ lattice sites and subject to periodic boundary conditions. Using results generated for d≤10, it is shown how analytic expressions can be obtained for the mean number 〈n〉 of steps before trapping at a centrosymmetric site in a hyperspace of high dimension, with explicit results given for d≤5. The results obtained cast light on certain geometrical aspects of the (strictly ergodic) flow of a phase point in a high-dimensional space, on an invariance relation first proved by Montroll [J. Math. Phys. 6, 165 (1965)], and on some consequences of compactification.

The effect of quenched random internal disorder on tethered membranes is studied by modifying treatments of pure systems to allow for small local fluctuations in the metric due to defects. To lowest order in ε=4-D, where D is the internal membrane dimensionality, we find that the flat pure phase is stable to disorder at finite temperatures, but unstable at low temperatures to a phase that lies outside the range of the ε expansion. For D<4 the instability is triggered by any finite amount of disorder, while for D>4 there is a threshold value of disorder below which the flat phase is stable at all temperatures. We speculate on the nature of the new phase. We argue that the low-temperature instability persists in the presence of random spontaneous curvature, and show that the flat phase is always unstable when unbound disclinations are included in the disorder.

We study the general problem of small-signal amplification by globally coupled oscillator arrays. The analysis is relevant, for example, to series-array Josephson-junction parametric amplifiers and to certain multimode laser systems. Maximum amplification is achieved near symmetry-preserving bifurcations; the response near symmetry-breaking bifurcations is substantially worse. In the presence of noise, we find a seemingly paradoxical phenomenon wherein individual array elements suffer large-scale random fluctuations, yet the total array response remains steady.

The notion of lacunarity makes it possible to distinguish sets that have the same fractal dimension but different textures. In this paper we define the lacunarity of a set from the fluctuations of the mass distribution function, which is found using an algorithm we call the gliding-box method. We apply this definition to characterize the geometry of random and deterministic fractal sets. In the case of self-similar sets, lacunarity follows particular scaling properties that are established and discussed in relation to other geometrical analyses.

The evolution of a spinlike variable in a double potential well that depends upon both angular coordinates is investigated as the system is subjected to both deterministic damping and stochastic noise linked by the fluctuation-dissipation relationship. A variational procedure appropriate for large barrier-to-noise ratio is adopted, and it can be seen that the resulting Euler-Lagrange equation introduces an angle-dependent field conjugate to the leading Fokker-Planck eigenfunction. In this way the spectral problem of the Fokker-Planck operator is approximated by two coupled first-order partial-differential equations, whose solutions allow the determination of the relaxing probability distribution and the equilibration current in almost all phase-space regions. A detailed application to the Lipkin model of many-body theory is presented.

We investigate numerically and analytically the dynamics of a rigid rotator under the action of ‘‘kicks’’ with slowly varying strength and period. We derive a discrete map for this model and use the map to study three effects. The first of them is the dynamic autoresonance, which can lead to a significant regular acceleration or deceleration of the rotator. We find conditions for which the effect occurs, including the condition for an unlimited acceleration. The second effect is the transition to global chaos that arises due to the increase of the stochasticity parameter with time. We find that this transition occurs through bifurcation of the main island (the bifurcation parameter being simply time) and the development of a complicated separatrix structure. Also, slowly evolving global chaos is studied numerically, and a time-dependent analog of the ‘‘quasilinear’’ diffusion equation is shown to describe quite accurately the numerical simulations.