The mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction. An N logN algorithm for calculating I is presented. As proposed by Shaw, a minimum in I is found to be a good criterion for the choice of time delay in phase-portrait reconstruction from time-series data. This criterion is shown to be far superior to choosing a zero of the autocorrelation function.

We propose a description of normalized distributions (measures) lying upon possibly fractal sets; for example those arising in dynamical systems theory. We focus upon the scaling properties of such measures, by considering their singularities, which are characterized by two indices: α, which determines the strength of their singularities; and f, which describes how densely they are distributed. The spectrum of singularities is described by giving the possible range of α values and the function f(α). We apply this formalism to the $2^{\infty }$ cycle of period doubling, to the devil’s staircase of mode locking, and to trajectories on 2-tori with golden-mean winding numbers. In all cases the new formalism allows an introduction of smooth functions to characterize the measures. We believe that this formalism is readily applicable to experiments and should result in new tests of global universality.

Three definitions of entropy for a nonequilibrium system of particles, driven homogeneously by external forces and thermostatted homogeneously by a feedback mechanism, are discussed. The first is proposed to be S(t)=-k〈ln$f_{\xi }$〉, i.e., the nonequilibrium ensemble average of the logarithm of the thermostatted equilibrium distribution function $f_{\xi }$. We show here, for a specific example, namely, the Nosé-Hoover thermostat, that the entropy so defined reduces properly to the equilibrium result when the external forces are turned off, that this entropy behaves correctly when the thermostat is turned off, and that the thermostatted steady state is achievable. A reasonable alternative definition from information theory, namely replacing $f_{\xi }$ by the nonequilibrium distribution function f, is shown to give incorrect results. If, however, the distribution function f is coarse grained in time to give f¯, then the resulting coarse-grained information-theory entropy, like the first definition, satisfies the requirements of the nonequilibrium entropy, with the added advantage of being easier to interpret in terms of the number of accessible states. Additional implications are discussed.

The microscopic ‘‘spin-gas’’ model reproduces and physically explains the sequence of liquid-crystal phases, nematic–smectic-$A_d$–nematic–smectic-$A_d$ –nematic–smectic-$A_1$, which was observed with decreasing temperature in recent experiments. The microscopic frustration inherent to smectic structures of dipolar molecules is relieved by permeation fluctuations at the atomic and librational length scales. The molecular tail length theoretically required for this quadruple reentrance agrees with experiment. The calculated ratios of layer thicknesses in the partial bilayer ($A_d$) and monolayer ($A_1$) smectic phases are also in good agreement with experiment.

Numerical studies of integrable (Toda lattice) and nonintegrable (modified Toda lattice and Fermi-Pasta-Ulam model) Hamiltonian systems indicate the possibility of interpreting analogies and differences between the two in terms of dynamical stability properties. At large energy densities, according to Siegel’s theorem, a small perturbation of an integrable system produces chaotic behavior and equipartition of energy. On the other hand, at low energy densities all the models we have considered show a similar ordered behavior and the absence of equipartition. In this region, soliton solutions of the corresponding continuum equations can provide a unified dynamical description of the properties of the discretized systems.

We employ scaling arguments and numerical simulations to investigate the kinetics of general classes of coagulation processes. Within the rate-equation, or mean-field, approximation, a scaling form for the cluster density is used to predict the asymptotic kinetic behavior for the ‘‘product,’’ ‘‘sum,’’ and ‘‘Brownian’’ kernels. These predictions are tested by simulations of the particle coalescence model, a model which corresponds exactly to the rate-equation description of coagulation. Our numerical results indicate the presence of an intermediate-time regime of behavior in coagulation kinetics, which is characterized by effective exponents whose values are consistent with scaling. This new and unexpected regime persists for an extraordinarily long time before a crossover to asymptotic behavior sets in. Furthermore, for the sum kernel, our numerical estimates for the exponents which describe the asymptotic kinetic behavior are in disagreement with current theoretical predictions. Finally, new fluctuation-controlled kinetic behavior below an upper critical dimension equal to 2 is also reported.

Current experimental limits on the number of magnetic monopoles bound in matter are based on only a few dozen kilograms of material, and of the former experiments only a handful used superconducting-quantum-interference-device- (SQUID) based detection techniques. Furthermore, all previous searches for trapped monopoles used material formed or gathered from either the surface of the Earth or Moon, where ultramassive grand unified field theory monopoles would not be expected to stop. Using a new type of ultraefficient SQUID magnetometer which allows large volumes of room-temperature matter to pass directly through a superconducting loop, we examined a suite of high-pressure metamorphic rocks which had been buried at depths of up to 25 km and yet remained below the Curie temperature of the ferromagnetic minerals present. In addition, we also examined large volumes of manganese nodules and seawater, for a total mass of 643 kg of rock and 180 kg of seawater. No monopoles were found, suggesting that their cosmic abundance is either extremely low or they are not easily stopped or trapped by passage through a minimum of 25 km of the Earth’s crust. We suggest that the next best place to look for monopoles is in cometary dust.

A model incorporating exciton-phonon interactions has been proposed as a mechanism for localizing and stabilizing energy transport in long-chain proteins. Previous analytical and numerical studies have not adequately addressed the effects of thermal phonons, which may act to disperse exciton energy. We have performed numerical calculations which indicate that excitons are strongly dispersed at biologically relevant temperatures. Furthermore, the propagation of the exciton-phonon system at low temperatures makes a transition from a solitary-wave mode to a stationary, self-trapped mode as the coupling between excitons and phonons is increased. We also report new calculations of exciton–normal-mode coupling in the formamide dimer, which indicate that more sophisticated models are necessary to yield the true coupling constant in proteins.

The observation of spectral lines arising from ${\mathrm{Ne}}^{7+}$ ions in a 0.7-Torr atmosphere surrounding a laser-heated slab target is reported. Such line radiation is mainly emitted from a narrow zone which is located some distance away from the target, depending on the target material used (C, Li, or Al). According to a phenomenological model, the neon gas is initially heated to an electron temperature of $k_B$$T_e$≊200 eV and ionized to the ${\mathrm{Ne}}^{8+}$ (ground-state) species by supersonic radiative and electronic thermal conduction. The ${\mathrm{Ne}}^{7+}$-line radiation results in this model from three-body recombination of the ${\mathrm{Ne}}^{8+}$ plasma as it rapidly cools, following the cessation of the laser pulse and the overtaking by lower-temperature target plasma.

Standard eikonal methods, as asymptotic perturbation expansions in 1/ħ, are incapable of describing fully the dispersive spreading of a wave packet. By simple models, we distinguish the two types of dispersion associated with a packet having initially uniform and nonuniform distributions of wave number. A nonperturbative extension of the eikonal approximation is applied to two initial-value problems for the free-particle Schrödinger equation and compared with exact solutions. The method maintains the ray picture fully. Applications of the method to more general classes of problems are discussed.

We present an approximate method, based on a moment equation, to derive explicit analytic formulas for the growth rate of Rayleigh-Taylor instabilities in fluids with density gradients. We illustrate with several examples and compare the results with our earlier method of treating a continuous density profile as a large number of fluid layers. The emphasis is on obtaining simple analytic formulas for the largest growth rate.

Nonequilibrium phase transitions of kinetic growth percolation, a kinetic growth process which exhibits a percolating-nonpercolating phase transition, are investigated on the basis of a mean-field theory and/or a real-space renormalization-group method. Phase diagrams, critical exponents, and spreading velocities are calculated explicitly for several models describing epidemic processes with immunization or autocatalytic chemical reactions. The existence and the nature of phase transitions and critical behavior are clarified.

Improvements are made in the moment-singularity method for the calculation of densities of state in the vicinity of van Hove singularities using modified moments by simplifying the functional form of the singular behavior that is used to fit the densities. Because the asymptotic behavior of the modified moments determines and is determined by the singular behavior of the density, information about the locations and functional forms of the singularities can be determined directly from the moments themselves and incorporated into the calculation of the density. The use of simplified functional forms to fit the singular behavior facilitates the use of the higher-order (less singular) corrections to the dominant singular behavior. These higher-order corrections to the singular behavior improve the precision to which the locations of the singularities can be determined and the precision to which the exact densities can be fit. The use of simplified functional forms also facilitates the treatment of singularities at the ends of the interval and within band gaps. This is advantageous in the reconstruction of densities whose behavior at the ends of the interval is not fit well by the Chebyshev weight function. The moment-singularity method is illustrated with applications to three different densities of states: (1) the density of a linear diatomic chain with m/M=1/2, (2) the average of the densities of two diatomic chains, one word with m/M=1/2 and the other with m/M=(1/5), and (3) the density of the two-dimensional triangular lattice with nearest-neighbor interactions. The precision of the moment-singularity method is also compared to that of the method of Corcoran and Langhoff for the reconstruction of densities.

Four orthogonal line-focused 351-nm beams have been used to implode 2-mm-long, 100-μm-diam thin Al cylinders. The resulting linear, high-density, high-temperature plasma has characteristics suitable as an x-ray-laser medium.

The diffusion of impurities of low concentration in a surrounding dense medium is studied near the liquid-glass transition point. Within a simplified model we obtain an analytical solution in the long-time or small-frequency regime for a generalized diffusion constant, which is expressed in terms of Bessel functions. At the glass transition of the medium the impurities can either become localized or still be delocalized. In the former case, there exists an Einstein-Stokes relation between the diffusion constant and the viscosity of the medium. In the latter case, the situation is similar to a superionic glass and reduces essentially to the Lorentz model. Explicit results for the generalized diffusion constant in the various regimes are obtained from asymptotic expansions of the Bessel functions.

A self-consistent set of nonlinear and relativistic wave-particle equations are derived for a magnetized beam-plasma system interacting with electromagnetic cyclotron waves. In particular, the high-frequency cyclotron mode interacting with a streaming and gyrating electron beam within a background plasma is considered in some detail. This interaction mode may possibly find application as a high-power source of coherent short-wavelength radiation for laboratory devices. The background plasma, although passive, plays a central role in this mechanism by modifying the dielectric properties in which the magnetized electron beam propagates. For a particular choice of the transverse beam velocity (i.e., the speed of light divided by the relativistic mass factor), the interaction frequency equals the nonrelativistic electron cyclotron frequency times the relativistic mass factor. For this choice of transverse beam velocity the detrimental effects of a longitudinal beam velocity spread is virtually removed. Power conversion efficiencies in excess of 18% are both analytically calculated and obtained through numerical simulations of the wave-particle equations. The quality of the electron beam, degree of energy and pitch angle spread, and its effect on the beam-plasma cyclotron instability is studied.

The origins of liquid-crystal birefringence were investigated. Theory on the quantitative birefringence dispersions of liquid crystals was developed and found to have excellent agreement with experimental results throughout the entire visible and infrared spectral regions. New guidelines for selecting or synthesizing the liquid crystals with the desired birefringence are established. Novel applications of liquid crystals in the infrared region are foreseeable.

The van der Waals theory of surface tension in simple fluids is reformulated in full accord with modern scaling ideas. The resulting theory has the conceptual merit to account consistently for a divergent coefficient of the squared-gradient term. Widom’s exponent relation μ+ν=γ+2β is confirmed, but it is shown to imply a nonclassical exponent for the scaling of the free energy with respect to the density gradient. The amplitude of the critical singularity of the surface tension is predicted to be different from that calculated with the squared-gradient theory as modified by Fisk and Widom, although we cannot make an estimate of the quantitative significance of this result.

A model of a confined atom in a self-consistent field has been developed to describe the high-density effects on atomic bound states in plasmas. Numerical values, asymptotic behaviors, and scaling laws are given for energy levels and spectral line shifts. Concurrently, a suitable quantum-mechanical impact calculation has been performed to obtain linewidths and line shifts. For a typical electron temperature and density of laser plasma, it has been shown that line shifts given by the two approaches are in agreement within 10%.

Shift measurements for the $H_{\alpha }$ (1640 Å) and $P_{\alpha }$ (4686 Å) hydrogenic ion lines of He ii have been done over an electron density range 2×${10}^{22}$ to 2×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$ and for an electron temperature of 4 eV. The plasma was produced in a linear Z discharge. Systematic red shifts linear in density are observed. The experimental data are compared with combined theoretical estimates for electron-impact and ion quadrupole effects. The experimental results are in agreement with our earlier results for $P_{\alpha }$. .AE