Two-dimensional numerical simulations of self-consistent rf glow discharges in ${\mathrm{N}}_2$ and ${\mathrm{SF}}_6$ gases are presented in this paper. Based on the single-moment fluid model, more accurate flux-corrected transport and reconstructed fast-Fourier-transform techniques are used to solve the continuity and Poisson’s equations, respectively. The evolution of electric fields, ion densities, and electron densities has been displayed by the spatiotemporal contours in a cylindrically symmetric geometry. The influence of gas properties (nonattaching versus strong attaching gas) and background pressures (1 and 2 Torr) are investigated. The sheath near the radial wall of the reactor has been shown its important role in the rf discharges, particularly in the strong attaching gas or at a higher background pressure.

A computer model has been used to investigate frequency doubling of 1-psec duration high-power pulses in potassium dihydrogen phosphate (KDP) for type-II phase matching. It has been found that group-velocity dispersion can be used to advantage by predelaying the ordinary and extraordinary polarizations appropriately in a thin KDP crystal with its axes aligned at 90° to the main conversion crystal. In that situation power conversion >100% from the fundamental to the second harmonic can be obtained with simultaneous ‘‘compression’’ of the output pulse duration by up to a factor of 5.

A classical analog is obtained for Berry’s nonperturbative scheme of adiabatic iteration which computes corrections to Berry’s phase (or Hannay’s angle) for finite values of the adiabatic parameter ε. The iterative method is compared to the Lie version of adiabatic perturbation theory. Both approaches show a divergence of k!${\mathrm{\epsilon }}^{\mathit{k}}$, where k is the order of iteration. It is argued that the divergences are a mathematical artifact of the asymptotic methods used, not related to the physical effect of transitions, nor to the nonconservation of the action variables.

Superintegrable Hamiltonians in three degrees of freedom possess more than three functionally independent globally defined and single-valued integrals of motion. Some familiar examples, such as the Kepler problem and the harmonic oscillator, have been known since the time of Laplace. Here, a classification theorem is given for superintegrable potentials with invariants that are quadratic polynomials in the canonical momenta. Such systems must possess separable solutions to the Hamilton-Jacobi equation in more than one coordinate system. There are 11 coordinate systems for which the Hamilton-Jacobi equation separates in ${\mathit{openR}}^3$. One coordinate system may be arbitrarily rotated or translated with respect to the other, yielding 66 distinct cases. In each case, the differential equations for separability in the two coordinates are integrated to give a complete list of all superintegrable potentials with four or five quadratic integrals. The tables—which may be consulted independently of the main body of the paper—list the distinct superintegrable potentials, the separating coordinates, and the isolating integrals of the motion. If there exist five isolating integrals, then all finite classical trajectories are closed; if only four, then the trajectories are restricted to two-dimensional surface. An extraordinary consequence of the work is the discovery of perturbations to both the Kepler problem and the harmonic oscillator that do not destroy the fragile degeneracy. The perturbed systems still have five isolating integrals of the motion.

This paper studies the defect-mediated melting of a DNA double helix resulting from the occurrence of small melted regions (MR’s) in the helix. We choose MR’s of small and medium sizes and model the DNA replicating fork as an infinite MR. We watch the H bond of these systems stretch as temperature increases until these DNA molecules break down (melt). For all systems we find that the H-bond stretch vibrations near the open region are enhanced not only by proximity to an open section itself but also by the anharmonic properties of the H bonds. In addition, the H-bond stretch amplitudes increase slightly with the size of the finite MR’s and are considerably lower than those of the replicating fork. Finally we find that the melting temperature decreases very slowly with finite MR sizes, especially for small MR defects. This suggests that the calculation on single-base-pair MR’s give the same melting temperature as somewhat larger MR’s. Since small MR’s are more probable one can predict a unique melting temperature.

We apply the difference recursive renormalization-group theory to helical hydrodynamic turbulence with particular attention to the problem of subgrid scale closure. We find that helicity has no effect on the renormalized eddy viscosity and plays no role in the evolution of the resolvable scales.

Agreement between the theoretical and measured resolution dependence of x-ray specular reflection from the ${\mathrm{H}}_2$O-vapor interface shows that the macroscopic capillary model for surface roughness can be extended to length scales as small as 400 Å. Agreement between measured thermal diffuse scattering data and the theoretical form, with no significant adjustable parameters, independently leads to similar conclusions.

Three possible isomers of 13-atom iron clusters are studied using local-density-functional methods that allow the spin of the cluster to be determined self-consistently. The ground state is the icosahedral structure. It has the greatest magnetic moment because of increased symmetry-required orbital degeneracy for electrons of different spins.

A fully three-dimensional (3D) laser-matter interaction code is developed and used to investigate 3D mixing mechanisms in planar targets accelerated by single-sided laser illumination. While linear Rayleigh-Taylor growth rates from 3D perturbed simulations are identical to those obtained from 2D simulations, nonlinear evolution differs significantly. Vortex stretching alters the ablative flow pattern. Subsequently, the 3D Rayleigh-Taylor spikes are larger in cross section than the 2D spikes, indicating a higher rate of mixing.

Davydov’s soliton theory is formulated for finite temperatures by generalizing the simple product trial function. An estimate of soliton temperature stability is presented.

We analyze the long-time behavior of ${\mathit{P}}_0$(t), the probability that a random walker is found at the origin at time t after its start. For continuous-time random walks with algebraic waiting-time distributions ψ(t)∼${\mathit{t}}^{\mathrm{-}1\mathrm{-}\gamma }$ we find in d>2 dimensions a crossover from ${\mathit{P}}_0$(t)∼${\mathit{t}}^{\mathrm{-}\gamma }$ for γ<d/2 to ${\mathit{P}}_0$(t)∼${\mathit{t}}^{\mathrm{-}\mathit{d}/2\mathrm{}}$ for γ≥d/2, which for 1<γ<d/2 is at variance with earlier expectations.

By coupling a kicked quantum system to a bath of harmonic oscillators we derive a logistic map with quantum corrections. We find a period-doubling route to the classical behavior as a dissipation parameter is increased, and other interesting features at intermediate values of this parameter.

A method of solving the sign problem in the Monte Carlo path-integral simulations of quantum dynamics is presented. Our method is based on the distortion of integration contours in conjunction with a stationary-phase-filtering method. Using this importance sampling, correlation functions for the spin-boson model have been computed for real times much longer than βħ.

Competing trends of ordering are shown to allow for a novel low-temperature phase in random-spin systems. In the space of the moments of the distribution of exchange couplings, the renormalization-group flows are characterized by a strange attractor. A random-exchange Potts model on hierarchical lattices is studied to illustrate this phenomenon.

Chaotic dynamics on a strange attractor of low dimensionality can be characterized by a set of recently proposed topological invariants. These are the relative rotation rates of the unstable periodic orbits embedded in the strange attractor. We demonstrate the efficiency of this characterization by extracting the topological invariants from chaotic time-series data for the Duffing oscillator.

The critical scaling of several thermodynamic quantities in circle maps is studied numerically. New scaling relations are found that involve not only Shenker’s ratios α and δ, but also functions of the inverse temperature β. Numerical evidence is presented for the universality of these functions. One of the thermodynamic quantities exhibits a saddle point in the critical region of each Arnol’d tongue. This makes possible a systematic investigation of critical scaling without the necessity of locating a critical line with precision.

The hull (external perimeter) of percolation clusters in two dimensions is a fractal object with fractal dimension DH=74 or DH′=43 depending on how it is constructed. Here it is shown that to each hull construction there corresponds a characteristic length R* such that the fractal dimension of the hull is DH on length scales smaller than R* and DH′ on length scales larger than R*. If r0 is the elementary length used for constructing the percolation cluster and r (>r0) is the elementary length used for constructing the hull, then R* diverges as (r-r0)-a as r→r0, with a≅1.37.

The distribution of mean first-passage times (MFPT’s) in ensembles of disordered lattice segments is characterized for the first time. The median of the distribution corresponds to the predicted typical behavior of the MFPT. The distribution exhibits a power-law decay in its tail with the exponent approaching 1 in the limit of large system size and disorder. Scaling behavior of the distribution was found in the tail region. The tail behavior of the distribution is related to the difference between the typical and the disorder-averaged MFPT.

A class of elementary defects of one-dimensional periodic patterns found far from equilibrium is described. They are ‘‘spatiotemporal grain boundaries’’ between regions in which the parity symmetry of the cellular pattern is broken in the opposite of two senses. The defect cores act as sources or sinks of traveling waves and cellular structures by means of a periodic phase instability closely related to ‘‘phase slips’’ in superconducting wires. An explanation for observations of annihilating collisions between two finite domains of opposite broken parity follows from these results.

Dilute superfluid mixtures bridge the Prandtl number range between liquid metals and water: 0.04<${\mathit{N}}_{\mathrm{Pr}}$<2. The convective equations of motion for superfluid mixtures are the equations for Rayleigh-Bénard convection in a normal single-component fluid plus additional superfluid terms. We have measured the latter through their effect on the critical Rayleigh number ${\mathit{R}}_{\mathit{c}}$. The corrections can be only a few percent for 1.0<T<2.0 K, implying an accessible Prandtl-number range near onset of at least 0.04<${\mathit{N}}_{\mathrm{Pr}}$<1.5.