The theory of steady-state propagation of a crack in a viscoelastic solid is reexamined in light of recent developments in ostensibly similar free-boundary problems, specifically, dendritic crystal growth and viscous fingering. We find that, at least within the conventional formulation of fracture dynamics, the problem of predicting the growth rate and the shape of a crack does not involve mathematical subtleties analogous to those which have been found in the previously mentioned situations. We derive some general formulas for the variation of the shape of the cohesive zone at the crack tip as a function of driving force, and we compute specific shapes, growth rates, and dissipation patterns for a simple model of the cohesive stresses.

We present detailed results of studies of chaos and chaotic transients involving spin waves in an yttrium iron garnet sphere. We drive the ferromagnetic resonance of this system at the first-order Suhl instability using driving frequencies between 2.0 and 3.4 GHz. In some regions of parameter space we see chaotic transients, while in others we see quasiperiodic oscillations or stable chaos. We characterize these states by various means, such as dimension or amplitude. We also present some results of a three-spin-wave-mode calculation based on the Landau-Lifshitz equation. This calculation produces phenomena similar to some of those seen in the experiment but is not sufficient to reproduce all the behavior that we see. We believe that a calculation involving more spin-wave modes is necessary to reproduce many of our experimental results.

We consider one-dimensional Brownian motion with an accumulating boundary, i.e., an absorbing boundary that grows through the mechanical accumulation of absorbed particles. We show that the diffusion-equation (DE) description of the boundary-growth process is internally inconsistent at short times. Accordingly, we consider this problem in the context of a model that caricatures the Fokker-Planck description in position-velocity space. Asymptotic results for both short and long times are obtained for the model and the former are shown to be internally consistent. The DE predicts that the boundary grows as $t^{1/2}$ for all time, whereas the model reproduces this result only for long times while predicting an initial growth proportional to t. We also obtain a lower bound and an upper bound on the boundary growth predicted by the model description that are valid for all times. An approximation in which the solution for a fixed absorbing boundary is used with the boundary-growth equation is also discussed in Appendixes B and C.

Statistical equilibrium data from a time-ensemble data bank, generated for an anharmonic (15+2)-particle chain [Henry and Grindlay, Phys. Rev. A 38, 2594 (1988)], have been used to calculate coarse-grained distributions for odd-mode velocities, particle velocities, and nearest-neighbor spring extensions. Each distribution proves to be Maxwellian in form. The mode-velocity temperatures agree with the mode-energy temperatures reported previously (Henry and Grindlay, ibid.). The time-ensemble data were also used to calculate averages and correlation functions for odd-mode energies, odd-mode velocities, particle velocities, spring energies, and their products. The dynamical response of the chain in the statistical equilibrium regime is found to be largely described by the behavior of modes 11, 13, and 15. These modes prove to be strongly correlated. The corresponding averages and correlation functions are calculated for a microcanonical ensemble of eight harmonic oscillators and compared with the time-ensemble results for the chain.

Recently, Huberman and Hogg [in The Ecology of Computation, edited by B. A. Huberman (North-Holland, 1988), pp. 77–115] analyzed the dynamics of resource allocation in a model of computational ecosystems which incorporated many of the features endemic to large distributed processing systems, including distributed control, asynchrony, resource contention, and cooperation among agents and the concomitant problems of incomplete knowledge and delayed information. In this paper we supplement an analysis of several simple examples of computational ecosystems with computer simulations to gain insight into the effects of time delays, cooperation, multiple resources, inhomogeneity, etc. The simulations verify Huberman and Hogg’s prediction of persistent oscillations and chaos, and confirm the Ceccatto-Huberman [Proc. Natl. Acad. Sci. U.S.A. 86, 3443 (1989)] prediction of extremely long-lived metastable states in computational ecosystems. Extending the analysis to inhomogeneous systems, we show that they can be more stable than homogeneous systems because agents with different computational needs settle into different strategic niches, and that overly clever local decision-making algorithms can induce chaotic behavior.

We discuss the Schrödinger equation with a time-dependent Hamiltonian that can be written as a linear combination of operators which span a finite-dimensional Lie algebra. The equations of motion for the operators in the Heisenberg representation are shown to be useful in calculating matrix elements and transition probabilities, as well as in obtaining the time-evolution operator. A general time-dependent one-dimensional bilinear Hamiltonian is considered as an illustrative example, and the product form for the time-evolution operator is shown to be global.

We present a theory that describes the random sequential adsorption of a two-component mixture of hard disks of greatly differing diameters on a flat surface. The jamming limit of the large disks can be obtained from a numerical solution of two coupled first-order differential equations. In the special case of a mixture of disks and point particles the equations take on a simple form, and the kinetics and jamming limit can be determined essentially exactly for certain ranges of the adsorption rate constants.

Improved algorithms have been developed to simulate both off-lattice and hypercubic-lattice diffusion-limited aggregation (DLA) in dimensionalities d in the range 2≤d≤8. For the two-dimensional cases using off-lattice clusters containing up to ${10}^6$ particles, we find that the effective fractal dimensionality is essentially independent of cluster size s for clusters containing more than a few thousand particles and has a value of 1.715±0.004 (significantly higher than the mean-field value of (5/3). For d=3, 4, and 5, it appears to be possible to approach quite close to the asymptotic (s→∞) regime and the effective fractal dimensionality for off-lattice clusters is equal to the mean-field value given by D=($d^2$+1)/(d+1) (within a few tenths of 1%). For d≥5 we were not able to approach near enough to the asymptotic limit to make an accurate estimate of the limiting fractal dimensionality. However, the simulation results are consistent with the mean-field theory predictions. For d≤4 the effects of lattice anisotropy can be seen in the overall shapes of the clusters and the dependence of the cluster radius of gyration on s. For d≥5 clusters containing ${10}^5$ sites are still in the fluctuation-dominated regime and the dependence of $R_g$ on s is essentially the same for both off-lattice and hypercubic-lattice models. For d=2 the effective value of ν¯, which describes how the width of the active zone grows, increases with increasing cluster size and approaches a value of 1/1.715.

In this paper we discuss the concepts of quantum integrability and nonintegrability. Based on the concept of a complete set of commuting observables and the Hilbert-space structure of a quantum system, the definitions are given for the quantum-dynamical degrees of freedom and quantum phase space from which the quantum integrability is defined. A criterion for quantum integrability then emerges; the system is integrable if it possesses dynamical symmetry. Breaking of dynamical symmetry is connected with the nonintegrability of systems and thus is the inherent mechanism of chaotic motion. A number of examples are discussed.

Results are presented of measurements of Δɛ/$E^2$ versus temperature for the isotropic–smectic-A transition in p-decyloxy-benzylidene-p-amino-2-methyl-butyl-cinnamate (DOBAMBC). For the first time a negative value of the pretransitional effect was observed. In all previous research on the nonlinear dielectric effect in liquids, critical fluctuations gave a large, positive increment. Experimental data satisfy the power relation Δɛ/$E^2$≃-19.3/(T-$T^{\mathrm{*}}$) (${10}^{\mathrm{-}18}$ ${\mathrm{m}}^2$ ${\mathrm{V}}^{\mathrm{-}2}$) for T>$T_c$ and ΔT=$T_c$-$T^{\mathrm{*}}$≃3.4 °C.

A molecular system adsorbed on a dielectric surface is modeled as a damped harmonic oscillator driven by a sinusoidal external force. The exact propagator and wave function through the Feynman path-integral method are obtained. The second quantization of this system is carried out. Expectation values of several physical quantities are evaluated. The amplitude for transitions between harmonic-oscillator states and damped driven oscillator states are obtained explicitly, and the result is applied to a two-level system.

We use the Gauss-Laguerre method to perform Maxwell averaging of distorted-wave collision strengths for transitions among the lowest three terms of singly ionized strontium. Rate coefficients are readily derived from the thermally averaged collision strengths Υ. By suitably scaling Υ, we form reduced collision strengths ${{\rm Y}}_{\mathrm{red}}$ that are finite at all temperatures. Each ${{\rm Y}}_{\mathrm{red}}$ is plotted as a function of reduced temperature $T_{\mathrm{red}}$, which maps the entire range of T onto the interval [0,1]. We use the least-squares method to fit ${{\rm Y}}_{\mathrm{red}}$ by a five-point cubic spline. This fitting procedure has an rms error of less than 1% and is performed on a microcomputer by an interactive program with graphic display.

We discuss the enhancement of the absolute sulfur K x-ray intensity observed in the electron bombardment of ${\mathrm{SF}}_6$ over that from ${\mathrm{H}}_2$S or ${\mathrm{SO}}_2$ in terms of the contribution to the total K-shell vacancy production cross section from the excitation of the well-known molecular-state resonance in ${\mathrm{SF}}_6$ below the ionization threshold. The equality of the K x-ray intensity observed from the photoionization of the sulfur gases by an ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ radioactive source is also understood since the resonance is not excited in this case.

We report results of the numerical solution of the time-dependent Schrödinger equation for the photodetachment of a one-dimensional model ion by a weak ultraviolet laser in the presence of a strong ‘‘infrared’’ laser. If there are no shape resonances near threshold, we find that the shift in the photodetachment threshold as the intensity of the infrared laser varies is equal to the ponderomotive energy of the infrared field. This contrasts with a recent experimental study of two-color photodetachment of ${\mathrm{Cl}}^{\mathrm{-}}$.

The Keldysh-Faisal-Reiss theory of nonresonant multiphoton ionization seems to give reasonably good agreement with experiments for production rates in the above-threshold-ionization peaks. The theory has some conceptual difficulties, since physically equivalent Hamiltonians give radically different results when treated by this method. An alternate form of the S matrix is used here in which approximation must be made upon the exact wave function evolving from the initial state rather than the time-reversed form used in the Keldysh-Reiss treatment. The exact initial state is approximated by an adiabatic form which results in an S matrix that eliminates the conceptual difficulties described above.

Alternative x-ray line-ratio techniques, using heliumlike and lithiumlike dielectronic satellite lines, are proposed for the measurement of electron temperature and state of ionization in dense plasmas, such as laser-produced and Z-pinch plasmas. These techniques are illustrated by application to the emission spectrum of the implosion core of a laser-imploded microballoon.

In this Brief Report, we investigate the modulational instability of electrostatic drift waves in an inhomogeneous plasma with respect to quasi-one-dimensional modulations that primarily propagate along the drift direction (like the drift solitons given by Lakhin, Mikhailovskii, and Onishchenko [Phys. Lett. A 119, 348 (1987); Plasma Phys. Contr. Fusion 30, 457 (1988)]).

We consider the truncation of exact equations of motion in a finite fermion system. The truncated von Neumann hierarchy for the densities and correlations violates the probabilistic interpretation if one neglects three-particle and higher correlations. Even for a two-body system, truncation may induce a chaotic behavior on the Hartree-Fock level.

Truncated Taylor-series representations of $r_{12}^{\mathrm{-}1}$ yield a variety of resummation alternatives to the corresponding Legendre expansion defining a basis-set–dependent Hamiltonian which allows a faster harmonic convergence of orbital methods. In this way, configuration interaction calculations of He, Li, and Ne ground-state energies converge to within a major fraction of the correlation energy with considerably less effort.

The difference in the range of protons and antiprotons in matter, an example of the Barkas effect, is observed in a simple time-of-flight apparatus. The ranges of 5.9-MeV antiprotons and protons differ by about 6% in a degrader made predominantly of aluminum.