We analytically follow the nonlinear evolution of three coupled modes of the two-dimensional Navier-Stokes equation in an externally driven and dissipative case. As the external force amplitude (control parameter) is increased, a node-to-node bifurcation appears, giving rise to new stable equilibria. We find that the most relevant set of three modes contributes to the energy and enstrophy cascades in the same directions as in fully developed turbulence. We model the coupling with the remaining modes as a white-noise contribution, deriving the equilibrium distribution function for the corresponding Fokker-Planck equation.

We report experimental and calculational results of the spatial evolution of the electron-energy distribution function (EEDF) mean electron energy ū, electric field E, and plasma density $N_e$, in the vicinity of a sharp constriction in a low-pressure mercury–rare-gas discharge. We explain many of the features of the EEDF by noting the absence of equilibrium between the electrons and the electric field. Our one-dimensional model of the spatial evolution of the EEDF is in good agreement with experimental results.

The He-like spectrum of 1$s^2$-1snp transitions and satellites in ${\mathrm{Ar}}^{16+}$ have been measured from the plasma of the Alcator-C tokamak. In the wavelength region of λ=3.0–3.4 Å, three groups of satellite lines 1$s^2$2σ-1s2σnl are observed which accompany each of the resonance lines of the orbitals from n=4 to 10. The results of calculations presented were used for identification of the observed spectrum and for discussion of line intensities and wavelengths. Radial-scan measurements were also performed over plasma regions of different electron temperatures. It is shown that such data can be used for estimating the relative importance of dielectronic recombination and inner-shell excitation in the population of satellites.

The average time required for thermally induced escape from a basin of attraction increases exponentially with inverse temperature in proportion to exp($E_A$/kT) in the limit of low temperature. A minimum principle states that the activation energy $E_A$ is the minimum available noise energy required to execute a state-space trajectory which takes the system from the attractor of the noise-free system to the boundary of its basin of attraction and that the minimizing trajectory is the most probable low-temperature escape path. This principle is applied to the problem of thermally induced escape from two attractors of the dc-biased Josephson junction, the zero-voltage state and the voltage state, to determine activation energies and most probable escape paths. These two escape problems exemplify the classical case of escape from a potential well and the more general case of escape from an attractor of a nonequilibrium system. Monte Carlo simulations are used to verify the accuracy of the activation energies and most probable escape paths derived from the minimum principle.

Several static and dynamic properties for ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixtures near the liquid-vapor critical line, measured along their critical isochores, are compared with predictions made via the formalism developed by Onuki. Theory predicts reduced temperatures for the crossover from pure-fluid to mixture behavior and to the asymptotic behavior, as the critical point is approached. For the static properties, the magnitude of the predicted crossover temperatures $t_{S1}$ and $t_{S2}$ is consistent with the experiments. However, for the transport properties, namely, the thermal conductivity and the thermal diffusion ratio, the predicted crossover temperature $t_D$ is much larger than that inferred from experiments. In fact, no qualitative difference in the critical behavior of measured transport properties is found between pure fluids and mixtures, implying $t_D$≲${10}^{\mathrm{-}5}$ for any mixture.

In this paper we present a self-consistent-field calculation for energy levels of He-like ions immersed in dense and hot plasmas. Exchange and correlation energies between bound electrons are shown to be much less perturbed than the single-particle energy. Concurrently, a fully quantum-mechanical impact calculation has been made to obtain the matrix elements of the complex electron line-broadening operator ${\Gamma }_e$. In the special case of the principal series, it is shown that the line shifts given by the two approaches are in good agreement for typical electron temperatures and densities of laser plasmas.

Studies of the growth of aggregates have been limited so far to those cases where the aggregate particles can react with incoming Brownian particles for infinite time. Recently, Miyazima et al. have investigated the effect of a fixed reaction time τ and have found that the long-time aggregates in two dimensions have a fractal dimension $d_f$≃1.04±0.03 for all finite τ values. Here we study square lattices, in which, in the more general case, each aggregate site is randomly assigned an infinite reaction time (with probability q) or a finite reaction time (with probability 1-q). We find a dynamical phase transition at q=$q_c$=0.5 and three different values for ${\mathit{d}}_{\mathit{f}}$: ${\mathit{d}}_{\mathit{f}}$≃1.04(q${<}_{\mathit{c}}$), ${\mathit{d}}_{\mathit{f}}$≃1.5 (q=${\mathit{q}}_{\mathit{c}}$), and ${\mathit{d}}_{\mathit{f}}$≃1.7 (q≳${\mathit{q}}_{\mathit{c}}$), irrespective of the magnitude of τ.

It is shown that the Lyapunov spectra of a class of dissipative dynamical systems with viscous damping are symmetric with respect to a constant determined by the dissipation of the system. A property of the associated linearized flow similar to the symplectic property is established. Furthermore, numerical computations of the characteristic exponents of 15 coupled damped Duffing oscillators driven by a van der Pol oscillator are presented.

Several different models are used to investigate reaction-limited cluster-cluster aggregation and the crossover from diffusion-limited to reaction-limited aggregation. The results obtained from these models are consistent with each other, if finite-size and finite-concentration effects are taken into account. For reaction-limited aggregation in three dimensions we find, in the case where the probability that two clusters will combine depends only on the time that they spend in contact with each other, that the mean cluster size S(t) increases exponentially with time t and that the cluster-size distribution $N_s$(t) (of clusters of size s at time t) decays as $N_s$(t)∼$s^{\mathrm{-}\tau }$ with τ having a value larger than 1.5. For the case where the probability that two clusters will combine depends only on the number of times they collide with each other, we find a power-law growth in the mean cluster size, S(t)∼$t^z$ with z∼2.0–2.5, and a cluster-size-distribution exponent τ close to 1.0. Our results indicate that the approach to asymptotic behavior may be quite slow and that the effective fractal dimensionality of the clusters depends both on the aggregation kinetics and on the extent of aggregation. We find that if the rate of bonding between two clusters depends on their collision frequency, then the exponent τ has a value close to 1 for the aggregation of small rigid clusters and close to 2 for the aggregation of large floppy clusters.

The assumptions underlying the revised Enskog kinetic theory are used to determine the dynamics of correlations between time-displaced many-particle density fluctuations in an equilibrium hard-sphere fluid. The resulting formula for the two-particle density autocorrelation function leads to a new expression for the spectrum observed in the depolarized interaction-induced light scattering.

The nematic–to–smectic-A transition in liquid crystals is analogous to the normal to superconducting transition in metals with the Frank director n in liquid crystals playing the role of the vector potential A in metals. The liquid-crystal analog of an external magnetic field is a field, arising, for example, from molecular chirality, leading to a nonzero ∇×n in the equilibrium nematic phase. The cholesteric (twisted nematic) phase is the analog of a normal metal in an external magnetic field. In type-II superconductors in an external magnetic field, the Abrikosov flux lattice phase with partial flux penetration intervenes between the low-temperature Meissner phase and the high-temperature normal-metal phase. In this paper we study the analog in liquid crystals containing chiral molecules of the Abrikosov phase in superconductors. Using a covariant form of the de Gennes free energy, we find that in mean-field theory a state, which we call the twist-grain-boundary (TGB) state, with regularly spaced grain boundaries consisting of parallel screw dislocations, intervenes between the smectic and cholesteric phases. We calculate the liquid-crystal analogs of the upper and lower critical fields $H_{c2}$ and $H_{c1}$. The properties of the TGB phase depend on the angle 2πα between axes of dislocations in adjacent grain boundaries. α can be rational or irrational. When α=p/q for mutually prime integers p and q, the TGB state has a q-fold screw axis and quasicrystalline symmetry for crystallographically forbidden q. Our calculations ignore exponentially small terms favoring lock in at rational α. We calculate the x-ray scattering intensities in the cholesteric phase near the TGB phase boundary and in the TGB phase for rational and irrational α. We also discuss experimental difficulties in observing the TGB state and the possible effects fluctuations not included in mean-field theory might have on its existence.

A one-sided diffusion-limited model for dendritic growth in two dimensions is simulated numerically by means of a Green’s function in quasistationary approximation. Anisotropy in the surface tension is found necessary for dendritic growth. Scaling behavior of the growth rate and tip radius is found as function of the undercooling and anisotropy, in agreement with recent results for needle crystals. The sidebranches scale with the stability length. The numerical procedure is described in some detail.

General implicit formulas for the quick computation of the energy levels of spherically symmetric Schrödinger Hamiltonians have been written down to second 1/N order. This time the shifting parameter has been chosen, order by order, so that the sum of corrections to the zeroth-order energy evaluation vanishes, as proposed previously. Explicit second-order formulas for the energy levels of power potentials have also been given.

Measurements of the doubly differential cross sections with respect to the ejected energy W and the solid angle of detection for electron-impact ionization of carbon monoxide are reported at an incident energy of 800 eV. The ejected angle was varied from 30° to 150° in steps of 15°. The cross sections were obtained by use of a crossed-beam time-of-flight apparatus with an effusive gas source and pulsed electron beam. The relative measurements were placed on an absolute scale by matching the experimental elastic differential cross sections to absolute measurement. Singly differential and total ionization cross sections are presented along with an analysis of the near-threshold autoionization spectrum.

We formulate a numerical method for treating the time-dependent scattering of an electron from a potential in the presence of a classical oscillating radiation field. The Schrödinger equation is solved in momentum space, which obviates the need to impose artificial boundaries and facilitates the extraction of the rapidly varying part of the wave function. We present results of a test application to a one-dimensional system with atomic potential β exp(-‖x‖/R) exposed to a short pulse.

This paper shows how the photoionization rate for sodiumlike selenium is greatly enhanced by including the two-step process of resonant photoexcitation of an L-shell electron followed by autoionization to the neonlike ground state. The photoionization rates for pumping with various line sources and continuum sources are presented and the direct photoionization rate is shown to be smaller than the resonant photoexcitation-autoionization rate for many different photon sources.

Systematic measurements on I(K${\alpha }_4$)/I(K${\alpha }_3$) x-ray satellite intensity ratios by photon excitation in Mg and several of its compounds are reported and discussed in the light of the available data.

A kinetic approach is derived to take into account nonideality effects in the rate coefficients of plasmas. First results are given for a reacting hydrogen plasma.

A method for investigations of the ground and excited states and the dynamical evolution of coupled quantum-classical systems is presented. A time-dependent self-consistent-field procedure is used where the time evolution of the wave function is evaluated with use of fast Fourier transforms and the coupled classical motion is treated via classical molecular dynamics. Different modes of simulations are demonstrated for electron attachment to NaCl and water clusters.

Tunneling of initially squeezed wave packets in asymmetrical double-well potentials is studied; the fractal nature of the trajectory, previously found in the case of symmetric potentials, is re- obtained.