A unitary transformation and a matrix formalism are presented that allow the calculating of the lowest powers of the potential of the Fokker-Planck equation at multicodimensional degenerate Hopf bifurcation points. The potential is given explicitly in terms of the drift. The formalism can be applied to compute the normal form of the corresponding kinetic equations.

We study the effect of an electric field on the rearrangement in a half-filled square lattice gas with repulsive first- and second-neighbor interactions. Below $T_c$ the particles form parallel chains resulting in anisotropic conduction. Monte Carlo simulations show that these chains prefer the orientation parallel to the applied field. The reorientation time strongly depends on the temperature and the magnitude of electric field. A simple mean-field approximation suggests that the steady-state distribution is modified by the field component perpendicular to the chains.

Campa and Cohen [Phys. Rev. A 39, 4909 (1989)] have predicted that dilute, binary mixtures of gases with disparate masses should exhibit a (fast) sound mode whose velocity is considerably greater than expected on the basis of conventional hydrodynamic theory, and which should be observable via light-scattering experiments. Effects that are consistent with this prediction were observed in the Brillouin spectra of the ${\mathrm{H}}_2$+Ar system, but were not detected for the case of ${\mathrm{CH}}_4$+${\mathrm{SF}}_6$. Results for the ${\mathrm{SF}}_6$+${\mathrm{H}}_2$ mixture demonstrate the existence of an analogous slow-mode contribution to the spectrum.

We present a theoretical derivation of the equations governing the motion of liquid soap film taking into account the physical dynamic as well as the chemical one. Generally, the behavior is specific to soap film, but we define some domains of the parameter space where its dynamic corresponds to classical two-dimensional incompressible flows. In this case we give an equation for the thickness of the membrane. We then simulate on a computer various regimes to explain how the thickness is linked to the internal motion.

We elaborate on a result obtained in Sreenivasan, Ramshankar, and Meneveau [Proc. R. Soc. London Ser. A 421, 79 (1989)] which explains the observations of a universal fractal dimension of interfaces close to (7/3. Here we explicitly take into account the influence of local fluctuations in the Kolmogorov scale (due to the multifractal nature of the rate of dissipation) on the surface area. The resulting dimension is shown to be equivalent to the prediction of a simple argument involving coarse graining of the interface.

A Monte Carlo simulation of vortex dynamics is performed on a three-dimensional lattice. There exists a statistically steady state in the infinitesimal viscous case with continuous random injection of vortex rings. In the steady state we observe a Lorentzian distribution of circulation and a scaling relation that is consistent with Kolmogorov’s (5/3 law.

Uniform smectic-A plates, floating freely on top of isotropic droplets, show static instabilities. Above a thickness threshold, the stable state of the smectic plate is an hexagonal network of focal conics. This instability is quantitatively explained by the anisotropy of surfaces tensions, which favors the alignment of smetic layers parallel to the air interface and perpendicular to the isotropic phase. This intrinsic frustration seems general for most smectic-A→isotropic first-order transitions.

Near the liquid-vapor critical point, the diverging thermal-expansion coefficient causes a localized entropy change to produce an immediate temperature change throughout the entire fluid, thereby greatly accelerating the approach to equilibrium.

We show how the extreme compressibility of a pure fluid near its critical point significantly affects its bulk dynamic response to temperature changes through adiabatic processes. We develop equations that describe the dynamics in the absence of gravity, and illustrate the magnitude of the effect with numerical solutions in one dimension. The results are remarkable: 5 mm of critical xenon, quenched from 20 to 10 mK above its critical temperature, cools by over 99% in less than 5 sec. Moreover, adiabatic cooling is faster when the fluid is closer to the critical point.

The response to a boundary heating of a very compressible, low-diffusivity, supercritical fluid (${\mathrm{CO}}_2$) under zero-gravity is studied by solving numerically the full non-linear one-dimensional Navier-Stokes equations. Both short (acoustic) and long (diffusion) time scales are investigated. A new mechanism of heat transport is seen, where the thermal energy is transformed into kinetic energy in a hot expanding boundary layer (the piston), which in turn is transformed in the bulk into internal energy. Steeply profiled waves are observed. In contrast to the ‘‘critical slowing down’’ behavior, the enhancement of heat transport is so important that it is nearly completed after 1% of the diffusion time.

The transfer of negative pions from pionic hydrogen to deuterium has been investigated in gas mixtures of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ as a function of the ${\mathrm{D}}_2$ concentration (C). The concentration dependence of the transfer rate was fitted using a phenomenological model with two parameters. For C→∞ (32±3)% of the pions undergo transfer. The fitted parameters reflect the ratio of pion capture to pion transfer in collisions of pionic hydrogen with protons or deuterons. No pressure dependence for pion transfer was found.

An exact treatment is given of the thermodiffusion model for the growth of a paraboloidal needle crystal from a supercooled melt. By means of successive transformations, the stability analysis of this system is reduced to the solution of a set of eigenvalue equations. This analysis is valid for all values of the supercooling and paves the way for a calculation of the evolution of the dendrite-tip shape with time.

An analytical and numerical study is made of the pattern of growth of a paraboloidal needle crystal from a supercooled melt. The calculations are performed in a fully time-dependent context, which is valid for all values of the supercooling. The principal analytical result is the demonstration that, in a frame co-moving with the dendrite, any perturbation of the tip gives rise to instabilities in the form of traveling waves that are carried away from the axis of the dendrite, and which thus stabilize the tip. These modes are absent in the commonly used quasistationary approximation. This conclusion is confirmed by the numerical results, which show a stable dendrite tip even in the absence of surface-tension anisotropy.

Several loopless percolation models are described, and low-density series are developed for Stephen’s treelike percolation model. Analysis of these indicates that the two-dimensional bond and site models do not have an infinite cluster present at finite dilution.

Poloidal rotation velocities in the outer half of ohmically heated Alcator-C plasmas have been determined from the Doppler shift of impurity emission lines. The measurements were made using a high-resolution photon-counting detector, sensitive to wavelengths from ∼1200 to ∼2000 Å, mounted in the exit plane of a 1-m Ebert-Fastie spectrometer. The following transitions were used: 2s2$p^1$P${°}_1$–2$p^2$${}^1$$D_2$ at 1371.292 at 1371.292 Å in O v, 2s${}^2$$S_{1/2}$–2$p^2$P${°}_{1/2}$ at 1242.804 Å in N v (both of which exist near the limiter radius in Alcator-C), and 1s2s ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$–1s2p ${}_{}{}^3{}_{}{}^{}°_2^{}{}_{}{}^{}$ at 1623.63 Å in O vii (which exists at r/a∼0.8). The measured rotation velocities are 4–5×${10}^5$ cm/s in the direction of the electron diamagnetic drift at the radius of the O v emission shell and ∼6×${10}^5$ cm/s at the radius of the O vii emission shell, again in the electron diamagnetic drift direction. Therefore poloidal rotation of the outer half of the Alcator-C plasma with a velocity of several times ${10}^5$ cm/s in the direction of the electron diamagnetic drift is firmly established by these measurements.

We present the results of detailed calculations for the intensity ratios between magnetic-quadrupole and electric dipole radiations that are emitted in the 3$p^5$3d→3$p^6$ transitions from highly ionized argonlike ions with nuclear charges in the range 26≤Z≤70. In arriving at our theoretical predictions, the population densities of the radiating 3$p^5$3d singly excited fine-structure levels were determined by the application of a collisional-radiative equilibrium model, in which we have systematically and self-consistently incorporated the results of fully relativistic multiconfiguration calculations for the atomic energy-level structure and for the elementary atomic collision and radiation rates. In the determination of the population densities of the 3$p^5$3d singly excited fine-structure levels, we have investigated the role of indirect processes involving the 3$p^5$4l4l’ intermediate autoionizing resonances and the 3$p^4$3$d^2$ doubly excited bound states.

The autoionization resonance contributions to the intensities of the magnetic-quadrupole transitions have been found to be more important at high Z than one would predict from simple Z-scaling arguments. We have also studied the modifications of the singly excited level populations which result from the inclusion of both optically allowed and optically forbidden electron collisional transitions among the various low-lying bound levels. By considering transitions along a substantial portion of the argon isoelectronic sequence, it has been possible to identify spectral-line intensity ratios that are sensitive to the electron density over an extensive density range. Particular emphasis has been given to the electron-density region near $N_e$${=10\mathrm{}}^{+13\mathrm{}}$ ${\mathrm{cm}}^{\mathrm{-}3}$, which is characteristic of tokamak and other magnetically confined fusion-research plasmas. The spectroscopic method that we describe for the determination of electron densities is also suitable for application to the analysis of radiative emissions from the argonlike ions of Fe and Ni in solar-flare plasmas, where the electron density is near $N_e$${=10\mathrm{}}^{+10\mathrm{}}$ ${\mathrm{cm}}^{\mathrm{-}3}$. .AE

Spherical implosion experiments have been performed using shaped laser pulses at ${\lambda }_0$=0.53 μm to illuminate deuterium-filled polyvinyl alcohol (PVA) spherical shells. The deuterium fuel was cryogenically cooled to form a uniform frozen fuel layer. Plasma diagnostics included time-resolved x-ray radiography and multiframe holographic interferometry. These and other measurements in conjunction with hydrodynamic simulations establish the importance of shaped laser pulses in achieving high fuel compressions.

Absolute measurements are presented for electron-impact single ionization of ${\mathrm{U}}^{10+}$, ${\mathrm{U}}^{13+}$, and ${\mathrm{U}}^{16+}$, and for double ionization of ${\mathrm{U}}^{10+}$ and ${\mathrm{U}}^{13+}$ from below the thresholds to 1500 eV. Metastable components are observed in all three incident-ion beams. The single-ionization cross sections are enhanced due to indirect ionization processes by factors of 4–20 near their peaks, and the double-ionization cross sections are apparently also dominated by indirect ionization. Good agreement is found with distorted-wave calculations for total ionization of ${\mathrm{U}}^{16+}$, the only case where detailed calculations are available for comparison. Individual or closely spaced resonances are clearly resolved in the single-ionization channels for ${\mathrm{U}}^{13+}$ and ${\mathrm{U}}^{16+}$.

We present results of a Monte Carlo simulation of the recombination of positive methane ions and negative sulfur hexafluoride ions in an electric discharge at atmospheric pressure. The results of the simulation are directly compared with recent experimental measurements of the ion-ion recombination rate in discharges through gas mixtures of methane and sulfur hexafluoride.

We have determined the absolute fluxes of various species injected from a dielectric surface into the surface-flashover-produced anode plasma in a magnetically insulated ion diode by observations of time-dependent line intensities and use of time-dependent collisional radiative calculations. Neutral particles, singly charged ions, and doubly charged ions produced on the dielectric surface were found to be continuously injected during the voltage pulse with the injection of neutral particles and singly charged ions continuing also after the main pulse. The determined fluxes explained the observed rise in the areal density of the plasma electrons. Using observed particle velocity distributions the particle flow in the plasma was calculated. It was found that mainly multiply charged ions and protons reach the plasma ion-emitting region. The flux ratio of doubly charged ions to protons produced by hydrogen ionization in the outer plasma region was found to rise towards the end of the pulse, consistent with the corresponding ratio in the extracted ion beam. The determined plasma composition allowed the electron-cooling processes to be evaluated. Such investigations can be used in plasma source design.