Jolicoeur and Le Guillou have recently proposed [Phys. Rev. A 40, 5815 (1989)] a very interesting derivation of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy using functional techniques. In this paper we generalized their derivation to higher-form distributions in phase space. At the heart of our method there is a path integral for classical mechanics that we put forward some time ago. This path integral describes the dynamics not only of scalar distributions in phase space but also of p-form valued densities [E. Gozzi, M. Reuter, and W. D. Thacker, Phys. Rev. D 40, 3363 (1989)]. The distribution functions entering this infinite set of coupled integro-differential equations (BBGKY hierarchy) carry a double grading now: besides the level in the hierarchy, they are characterized by their degree as differential forms. The higher forms are related to the dynamics of the Jacobi fields and therefore contain information about the behavior of nearby trajectories. This kind of information could be used in the study of turbulence, for instance.

We establish the equivalence between a one-dimensional sandpile model recently introduced by Chhabra et al. [Phys. Rev. A (to be published)], and the diffusion-limited reaction A+A→0 with a point source. The equivalence is used to predict the power-law decay of the avalanche size distribution, P(s)∼${\mathit{s}}^{\mathrm{-}3}$, in agreement with numerical simulations. This result differs from the mean-field treatment of Chhabra et al., demonstrating the importance of fluctuations in this low-dimensional system.

In a recent paper [B. Tadić, U. Nowak, K. D. Usadel, R. Ramaswamy, and S. Padlewski, Phys. Rev. A 45, 8536 (1992)], the directed two-dimensional sandpile is modified to include a concentration p of randomly placed holes. For p>0, they observe a characteristic cutoff size for the duration (and mass) of avalanches. This breaks the formal power-law behavior that is a signature of self-organized criticality. The scaling of these characteristic sizes with the concentration of defects is observed empirically to follow a power law, and the exponents are numerically determined. In this Brief Report, it is shown that a previously described mean-field approximation can account for the observed exponents.

A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.

The nonlinear quantum kinetic equation for the interaction of sound waves is solved via analytic and numerical techniques. In the classical regime energy cascades to higher frequency (ω) according to the steady-state power law ${\mathrm{\omega }}^{\mathrm{-}3/2}$. In the quantum limit, the system prefers a reverse cascade of energy which follows the power law ${\mathrm{\omega }}^{\mathrm{-}6}$. Above a critical flux, a new type of spectrum appears which is neither self-similar nor close to equilibrium. This state of nonlinear quantum wave turbulence represents a flow of energy directly from the classical source to the quantum degrees of freedom.

We expand an accurate, closed-form equation for the reflectivity in a power series around ${\mathit{q}}_2$=0, where ${\mathit{q}}_2$ is the z component of the wave-vector transfer in a film of constant composition. We examine, in particular, the case where ${\mathit{q}}_2$=0 at the critical edge. Such an example might be realized through a neutron-reflectivity experiment on a microemulsion that exhibits surface layering. We find the coefficients of this low-wave-vector expansion to be the moments of the scattering-length density profile. We demonstrate how the first moment of the profile can be obtained from an accurate reflectivity measurement.

The theroretical prediction of the existence of Clifford toroidal vesicles by Ou-Yang [Phys. Rev. A 41, 4517 (1990)] has been confirmed by the experiment of Mutz and Bensimon [Phys. Rev. A 43, 4525 (1991)]. However, the few nonaxisymmetric toroidal vesicles observed by Fourcade, Mutz, and Bensimon [Phys. Rev. Lett. 68, 2551 (1992)] raise the question of why the formation of nonaxisymmetric toroidal vesicles is so rare in comparison with that of axisymmetric ones. In this report we are going to show that for a solution of the shape equation of membranes, the spontaneous curvature ${\mathit{c}}_0$ of nonaxisymmetric Dupin cyclide has to be zero, while axisymmetric Clifford solution has no such restriction as shown by Ou-Yang [Phys. Rev. A 41, 4517 (1990)].

The Alfvén waves are shown to be linearly coupled with finite-frequency convective cell modes in a nonuniform cold dusty magnetoplasma. The dynamics of weakly interacting finite-amplitude electromagnetic oscillations is governed by a pair of nonlinear equations. The latter admit dipolar vortices as possible stationary solutions. The present results can have relevance to the nonlinear electromagnetic wave propagation in a space environment such as cometary tails or interstellar clouds.

Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch, and source processes, certain ‘‘bell-shaped’’ distributions may grow explosively in time while preserving the shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or, more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma.

The Stark broadening parameters of several Si ii lines have been measured in a pulsed discharge. Experimental results are compared with theoretical predictions and with other experiments.

We present exact results for the stress distribution for a pyramid-shaped hexagonally packed granular pile in two dimensions. In particular, we show that the load acting on each grain at the bottom layer is identical. The real granular pile, however, has voids inside and thus may show some deviation from the present results.

It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential ̭0). As a numerical apparatus, the theory relates to gauge-dependent errors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced.

We examine the signature of classical chaos on a generic quantum phenomenon, namely, quantum tunneling in a nonintegrable, conservative two-degree-of-freedom Hamiltonian system. We show that, as one passes from the regular to chaotic regime, the quantum tunneling probability versus coupling-constant curve exhibits a significant change of slope in the neighborhood of the critical chaotic threshold (beyond which classical chaos sets in). This shows that the presence of Kolmogorov-Arnold-Moser barriers of classical phase space manifests in quantum phenomena such as quantum tunneling.

The method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by Ott, Grebogi, and Yorke (OGY) is not directly applicable to chaotic Hamiltonian systems. The reason is that an unstable periodic orbit in such systems often exhibits complex-conjugate eigenvalues at one or more of its orbit points. In this paper we extend the OGY stabilization method to control Hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point. We also present an algorithm to calculate the stable and unstable directions. Other issues specific to the control of Hamiltonian chaos are also discussed.

We consider finite driving-rate perturbations of models which were previously seen to exhibit self-organized criticality (SOC). These perturbations lead to more realistic models which we expect will have applications to a broader class of systems. At infinitesimal driving rates the separation of time scales between the driving mechanism (addition of grains) and the relaxation mechanism (avalanches) is infinite, while at finite driving rates what were once individual relaxation events may now overlap. For the unperturbed models, the hydrodynamic limits are singular diffusion equations, through which much of the scaling behavior can be explained. For these perturbations we find that the hydrodynamic limits are nonlinear diffusion equations, with diffusion coefficients which converge to singular diffusion coefficients as the driving rate approaches zero. The separation of time scales determines a range of densities, and, therefore, of system sizes over which scaling reminiscent of SOC is observed. At high densities the nature of the nonlinear diffusion coefficient is sensitive to the form of the perturbation, and in a sandpile model it is seen to have novel structure.

Recently, Takayasu and Tretyakov [Phys. Rev. Lett. 68, 3060 (1992)] studied branching annihilating random walks with n=1-5 offsprings. These models exhibit a continuous phase transition to an absorbing state. Steady-state simulations yielded an estimate for the order parameter critical exponent β different from that of directed percolation. This result is quite surprising, as the universality class of directed percolation is known to be very robust. I have studied the critical behavior of the one-dimensional model with n=1 and 3 using time-dependent Monte Carlo simulations, and determined three critical exponents, all of which are in agreement with directed percolation.

Sharp sufficient criteria for collapse are found for the nonlinear Schrödinger equation in the so-called supercritical case as well as for the Ginzburg-Landau equation in the case of the subcritical bifurcation. It is demonstrated that nonstable solitons in these models, under some additional assumptions, play the role of a ‘‘boundary’’ (saddle points) between collapsing and noncollapsing solutions.

We analyze a deterministic, one-dimensional solid-on-solid model for sputter deposition where the local growth rate is a function V(θ) of the exposure angle θ. For long times an algebraic height distribution N(h)∼${\mathit{h}}^{\mathrm{-}(1+\mathit{p})}$ develops, where the exponent p depends on the behavior of V(θ) close to θ=π and the extremal statistics of the substrate roughness. Analytic predictions for p, based on scaling arguments, are verified by large-scale simulations using a hierarchical algorithm.

It is demonstrated that a recent finite-barrier expansion for jump rates accounts quantitatively for the observed discrepancy between numerically determined exact rates and the Kramers estimates of these rates.

We model a shock wave in an ideal gas by solving a modified version of the compressible Navier-Stokes equations of hydrodynamics, where, following an earlier conjecture by Holian [Phys. Rev. A 37, 2562 (1988)], we use the temperature in the direction of shock propagation ${\mathit{T}}_{\mathit{x}\mathit{x}}$, rather than the average temperature T=(${\mathit{T}}_{\mathit{x}\mathit{x}}$+${\mathit{T}}_{\mathit{y}\mathit{y}}$+${\mathit{T}}_{\mathit{z}\mathit{z}}$)/3, in the evaluation of the linear transport coefficients. The results are found to agree much better with the molecular-dynamics simulations of Salomons and Mareschal [Phys. Rev. Lett. 69, 269 (1992)] than standard Navier-Stokes theory.