A model equation describing oscillatory convective patterns is derived using the long-scale expansion under conditions of slow exchange at the containing walls. The complex amplitudes of convection waves obey on an intermediate time scale the free Schrödinger equation, and are modulated on a slower time scale, following an evolution equation that is similar to a complexified equation of long-scale stationary convection, but involves nonlinear interactions restricted by resonance conditions. The analysis of pattern selection in the vicinity of the symmetry-breaking bifurcation indicates the prevalence of a square-standing-wave pattern comprising a certain phase-locked (‘‘antiphase’’) combination of perpendicular modes. The stationary antiphase pattern can be destroyed, giving way to a pattern with time-dependent amplitudes, under the influence of weak non-Boussinesq effects.

A systematic study of the zero-surface-tension solutions for a bubble in a Hele-Shaw cell is made. Then the technique used for the Saffman-Taylor finger is applied to find how the actual solution for nonzero surface tension is selected out of this family. We find that only symmetrical bubbles are allowed. In particular, in the limit of zero surface tension we find that the velocity of the bubble is twice the velocity of the fluid at infinity. We also find in the case of Saffman-Taylor fingers that the symmetrical finger is selected against the asymmetrical ones.

A series of entropies, approaching the order-q Renyi’s entropies when the length of orbits tends to infinity, is considered. Their scaling form is determined for chaotic one-dimensional maps. For the characteristic relaxation time a general expression is derived, and it is shown to be closely related to the eigenvalues of a generalized Frobenius-Perron operator. The case of intermittent maps is also considered, and the spectrum of relaxation time is found to reflect the phase transition at q=1. Results of numerical experiments are also presented.

The nonequilibrium driven diffusive lattice gas is studied by dynamic mean-field theory (MFT) at the pair and square levels. In contrast with previous MFT treatments, the present formulation permits study of the original model (isotropic hopping rates) and arbitrary driving field strength. Metropolis and Kawasaki dynamics are considered. As is found in simulations, the critical temperature is elevated in the presence of the driving field. This effect is mediated by anisotropy of correlations. There are several (unphysical) anomalies associated with singularities in the Metropolis rates.

A numerical integration of the equations of motion of a 17-particle chain with nearest-neighbor linear and cubic forces has been carried out in quadruple-precision FORTRAN over a period of 600 model time units. The chain has clamped ends and is excited initially in the 11th mode. The data obtained from the integration constitute a reversible time ensemble. Equilibrium mode energy distributions in this ensemble prove to have a Maxwell-Boltzmann form, and in addition the calculated mode temperatures agree with those obtained from the double-precision statistical ensemble previously reported for the same system and same model parameters [B. I. Henry and J. Grindlay, Physica D 28, 49 (1987)]. It follows that statistical-ensemble averages and time-ensemble averages are equal, and hence the ergodic hypothesis holds for these two data banks.

We construct asymptotic expansions of the (quasi)stationary probability density function and of the mean first-passage time over a potential barrier, for bistable systems driven by weak wideband Gaussian colored noise, when the intensity ε and the correlation time τ of the noise are both small. Previous analyses have led to a variety of often contradictory results and to considerable confusion, which stem from the fact that the problem depends on two small parameters. This results in different expansions, with different ranges of validity, depending on the relative magnitudes of ε and τ. In contrast, we derive expansions that are uniformly valid throughout the entire parameter range of interest. In addition, we identify restrictions on the ranges of validity, in terms of the total power output ε/τ of the noise, of previously derived expansions. We show that only if the power output ε/τ becomes infinite can previously derived expansions be valid. Our results, when specialized to this case, reduce to expansions previously derived. Outside the restricted range, i.e., for finite or vanishingly small power outputs, our expansions contain terms which are new, and which may in fact dominate previously computed terms. In contrast to the use of one-dimensional diffusional approximations previously employed, our approach is based on the exact two-dimensional Fokker-Planck equation. Singular perturbation techniques, previously developed by the authors, are employed to systematically derive the asymptotic expansions.

We examine the contribution of rotational diffusion to quasielastic light scattering (QELS) from fractal colloid aggregates, both theoretically and experimentally. Rotational diffusion makes a substantial contribution to QELS when the size of the clusters is large compared with the inverse of the scattering wave vector, due to the anisotropy of the clusters at all length scales smaller than the cluster size. We evaluate the rotational contributions to QELS by performing a multipole expansion of the light scattered from computer-simulated clusters. Experimentally, rotational contributions are observed through measurement of the wave-vector dependence of the first cumulant. We find excellent agreement between cumulants calculated through our multipole-expansion technique and those obtained in our experimental measurements.

We present a model for a double sine-Gordon (DSG) kink in interaction with an external heat bath which acts on the kink as a systematic dissipative force and a δ-correlated stochastic force. The DSG kink behaves like a ‘‘bound state’’ of two single sine-Gordon kinks which we describe as a center-of-mass variable X(t) and an internal anharmonic oscillator variable R(t) by means of a constrained Hamiltonian formalism using Dirac brackets. We apply our model to DSG kinks which appear in antiferromagnetic chains.

The scaling structures of the mass and growth probability distributions in the generalized diffusion-limited aggregation (η model) on the hierarchical lattices are derived by making use of the real-space renormalization-group method. In the dielectric breakdown language, the process is formulated as a random multiplicative process of current on the surface of the aggregate. The mass and growth probability distributions are related to the bulk and surface structures of the aggregate. The mass scaling of the clusters generated by the processes is found and compared with the scaling structure of the growth probability distribution. The dependences of the α-f spectra of the mass and growth probability distributions are shown on the parameter η describing the different dielectric breakdown models.

We study the Fréedericksz transition in a twist geometry under the effect of a periodic modulation of the magnitude of the applied magnetic field. We find a shift of the effective instability point and a time-periodic state with anomalously large orientational fluctuations. This time-periodic state occurs below threshold and it is accompanied by a dynamically stabilized spatial pattern. Beyond the instability the emergence of a transient pattern can be significantly delayed by a fast modulation, allowing the observation of pattern selection by slowing down the reorientational dynamics.

We compute the percolation concentration for identical ellipses with aspect ratio b/a in a two-dimensional plane where both the centers and orientations are random. We have obtained a comprehensive set of results ranging from circles to needles which can be well fit by the interpolation formula $p_c$=(1+4y)/(19+4y), where y=b/a+a/b. We also obtain results for random centers and random orientations along the two principal directions which are virtually indistinguishable from the previous case. These results are used to critique the various effective-medium theories that have been developed for the electrical conductance and elastic moduli of sheets containing random elliptical inclusions. An interpolation formula is developed that appears superior to all these effective-medium theories.

An analysis is made of inherent errors in a modified variational method for one-dimensional equations in which it is possible in principle to determine sequentially all excited-state eigenvalues, each by an absolute minimization procedure unconstrained by orthogonalization requirements.

We give a dynamical explanation for the localization of the wave function for the one-dimensional hydrogen atom, with the Coulomb singularity, in a high-frequency electric field, which leads to a necessary condition for classical dynamics to be valid. Numerical tests confirm the accuracy of the condition. Our analysis is relevant to the comparison between the classical and quantal dynamics of the kicked rotor and standard map.

Results of large-scale close-coupling calculations are reported for the ${\mathrm{He}}^{2+}$+H collision system at energies of 1–84 keV/amu. The calculated transfer cross sections are seen to agree very well with most of the available experimental data at lower energies. At higher energies they constitute improved predictions of cross sections, which are needed for plasma diagnostics purposes. A previously proposed model which neglects intershell couplings in the final capture states is assessed with respect to the accuracy of its results for this collision system.

Solutions of reaction-diffusion equations including a creative type of reaction nonlinearity tend to approach dynamically certain explosive localized solutions. The dynamic evolution is described analytically and the time required to reach the final state as well as an intermediate amplitude minimum are determined. The results are obtained to all orders in the nonlinearity and for the cases of one, two, and three dimensions.

A simple theoretical description of nonlinear and nonlocal cooperative phenomena is presented in which the global control mechanism of the whole system is given by the tuned-wave propagation. It provides us with an interesting universal scheme of systematization in physical and biological systems called wave cybernetics, and may be understood as a model realizing Bohm’s idea of implicate order in natural philosophy.

Argon recoil-ion charge-state distributions produced by beams of 0.7-MeV/u ${\mathrm{Cl}}^{5+,8+,10+}$ have been measured by time-of-flight techniques in coincidence with single- and double-charge-changed projectiles. In an essential improvement to the usual multinomial description of ionization in the independent-electron-ejection model, we find the inclusion of one (two) Auger vacancy cascades significantly alters the description of the recoil-ion spectra corresponding to single (double) capture. The single- and double-projectile-electron loss and capture spectra strongly resemble each other, suggesting that loss of one or two projectile electrons is closely associated with loss of one or two target $L$ electrons, respectively. These conclusions are consistent with impact parameters inferred from determinations of mean recoil energy.

Analytical and numerical calculations describe the effects of shaped radiation pulses on two-level systems in terms of quantum-mechanical scattering. Previous results obtained in the reduced case of amplitude modulation are extended to the general case of simultaneous amplitude and phase modulation. We show that an infinite family of phase- and amplitude-modulated pulses all generate rectangular inversion profiles. Experimental measurements also verify the theoretical analysis.

A simple derivation of the Keldysh amplitude for the ionization of an atom by a strong field is presented using a perturbation expansion in the binding potential. It is shown that the "Keldysh approximation" is questionable under conditions of strong ionization, when there is substantial probability of removing the electron from its initial bound state. This is consistent with published numerical studies based on model binding potentials. It is argued that the Keldysh amplitude is not gauge invariant in the usual sense, and that it is effectively canceled in a conventional gauge-invariant formulation of strong-field perturbation theory.

The ${\mathrm{La}}_2$ line of gold has been resolved using a Si (Li) detector combined with a zinc absorber. By analysis of the angular distribution of the 500-keV-proton-induced $\mathrm{Ll}$, ${\mathrm{La}}_2$, and ${\mathrm{La}}_{1,2}$ x-ray lines of gold, the mixing ratio for the magnetic quadrupole and electric dipole radiation has been determined. The mixing has been found to be a factor of 4 larger than previously calculated. The intensity of the $\mathrm{Ls}$ and $Lt$ lines of platinum also has been measured using this absorption technique. The results gave further evidence that the higher-order multipole terms in $L_3$ x-ray transitions of heavy elements were previously underestimated.