We present calculations of the dc electrical resistivity of a variety of plasmas using rigorous generalizations of the Ziman formula which extend from the usual weak-isolated-scatterer limit to the hitherto inaccessible regime of strong multiple scatterers. All the ingredients necessary for the calculation are computed from first principles in a self-consistent manner, using a density-functional description of the electrons and ions in the plasma. As is usual in density-functional calculations, electron exchange correlation is handled in the local-density approximation. The method uses an average-ion distribution of the plasma environment, together with the assumption of spherical symmetry. The numerical procedures for the regime of strong multiple scatterers turn out to be no more difficult than for the weak-isolated-scatterer limit.

Near-reactor-size, laser-plasma conditions are studied at I${\lambda }^2$ values of ${10}^{14}$ W/${\mathrm{cm}}^2$ μ${\mathrm{m}}^2$ with 1-mm-size plasmas, 3-kJ, 3-ns irradiations on the 1.064-μm Shiva laser. Laser-plasma-coupling issues, such as the competition between stimulated Brillouin scattering and inverse bremsstrahlung absorption and the generation and transport of hot electrons, are addressed. Hydrodynamic phenomena of relevance to direct-drive laser fusion targets are also studied, including the following: the pressures, mass ablation rates, and target velocities achieved; the lateral transport of laser energy away from the initial illumination spot; and the thermal smoothing of laser nonuniformities due to the moderate intensity and the long-pulse-length–induced separation of the critical surface from the ablation surface.

We investigate qualitatively and semiquantitatively the effects on computed dielectronic-recombination rate coefficients of including mixing between basis states of two or more configurations, as opposed to the single-configuration approximation. We have made model-parameter studies for two-electron systems, and have also considered physically realistic three- and four-electron systems. We have attempted to categorize the various circumstances under which configuration-interaction effects are significant, but overall effects appear to be generally small—usually no more than 10–20 %.

The effective diffusivity for a passive impurity in a steady convecting flow is calculated in the experimentally relevant limit of large Péclet number (p=vl/D). The expulsion of the concentration gradients from the region of closed stream lines leads to the enhancement of the diffusivity D by a factor of $p^{1/2}$.

Inductive heating of a stellarator plasma at frequencies higher than the inverse of the resistive diffusion time is studied experimentally. Two magnetic field configurations are investigated: a classical stellerator and a doublestar—a stellarator with two large magnetic islands. Profiles of plasma density, temperature, and induced toroidal current are measured, and it is found that in both configurations the induced current exhibits a substantial (∼180°) phase shift within the plasma. The observed current profiles cannot be described by the classical (rigid-conductor) skin effect and are interpreted in terms of the plasma response to the externally driven modulation of the geometry of the magnetic surfaces.

Equations of motion for nematic liquid crystals under time-dependent shear are derived. Soliton solutions are investigated. When the soliton velocity is large and the shear varies slowly in time, approximate analytic solutions for single solitons of the A and B types are found with use of multiple-scale analysis. These perturbed solitons move with time-dependent velocities but are constant in shape and carry no tails. The velocity is proportional to the shear rate. Numerical calculations of the director equation of motion are performed and are in agreement with the analytic results. A recent experiment in which dark lines (under white light) excited by a periodically moving plate at one end of a nematic cell are observed is analyzed and interpreted according to our theory. Good agreement between theory and experiment is obtained.

The resonant excitation of an electron plasma wave and its effects on the density-profile steepening are theoretically studied by using a modified, warm-capacitor model. Scaling laws characterizing the process are established and the wave structure and density profile are self-consistently determined.

The behavior of a class of dynamical systems is analyzed as a function of time and of Planck’s constant ħ when the latter is small compared with the (classical) action of the system. The case considered is that the classical system (ħ=0) is near a dynamical critical point, and there is a definite scaling of the variables of the classical motion with time. It is shown that the parameter ħ is a relevant variable in the renormalization-group sense, which means that as one scales to longer times, ħ scales to larger values. This is just a way of saying that quantum effects become progressively more important with time, and even if they can initially be ignored, there comes a time $t^{\mathrm{*}}$∝${ħ}^{\mathrm{-}1/\gamma }$ after which the system can no longer be treated classically, i.e., $t^{\mathrm{*}}$ characterizes the crossover away from classical to quantal behavior. This is similar to the effect of noise, which also smears out the deterministic classical phase-space path and destroys the sharp stochastic phase transition; however, unlike noise, the quantum exponent γ is simply related to the classical ones. We present arguments that this is the consequence of a property of the system’s operators in the Heisenberg picture. The cases of a period-doubling cascade to chaos and the disappearance of the last Kol’mogorov-Arnol’d-Moser trajectory in the standard map are specifically discussed. The results are shown to be consistent with numerical calculations.

We have studied experimentally the dynamics of soap froths in two dimensions. We observe two temporal regimes: a transient in which the average bubble area increases in time faster than a power law, and long-term behavior in which the average bubble area increases (over the decade observed) as a power law with exponent α${=0.59\mathrm{}}_{\mathrm{-}0.09}^{+0.11\mathrm{}}$. The crossover between these two regimes depends on the initial preparation. In initially disordered systems the rate of area growth increases smoothly and monotonically, whereas in initially ordered systems the rate first overshoots its long-term value and then decreases. The system does not, however, equilibrate during the lifetime of the bubble lattice. We have also verified that Von Neumann’s law for the growth rates of bubbles holds statistically. Lewis’s hypothesis of a linear relation between a bubble’s number of sides and its area fails for few-sided bubbles. Finally we present a simple phenomenological model for the growth of the average area. This model allows us to define a parameter ?(t) quantifying the disorder as a function of time.

The analytic forms of the mean-spherical-model solutions for potentials with spherical-harmonics expansions can be used to model the generalized bridge functions in the reference hypernetted-chain integral equation to much greater effect than the original solutions. The method is applied to the calculation of the electric microfield distribution in a plasma, shown by Iglesias [Phys. Rev. A 27, 2705 (1983)] to be equivalent to finding the structure of a ‘‘fluid’’ whose angle-dependent potential has both real and imaginary parts. The results are in excellent agreement with simulation data.

A gas displacing a high-viscosity liquid in a porous medium generates a fractal finger structure similar to that obtained in diffusion-limited aggregation (DLA). This structure is controlled by the surface dynamics of the growing active zone. The dynamics of viscous fingering in a two-dimensional porous model has been investigated. We have studied the radius of the active zone and the screening length of the active zone as a function of time in the DLA regime. In this regime the fingering structure grows mainly at the tips, and the inner region is screened by the outer fingers. The length of the longest finger as a function of time is accurately described by the results of a new form of DLA simulation which in addition to DLA structures gives the time dependence in a form suitable for comparison with experiments.

The stress distribution on the surface of a fractal embedded in an elastic medium has been explored with use of diffusion-limited-aggregation (DLA) clusters fixed in a network of bonds and nodes which form a triangular lattice. The distribution of forces on the bonds in the network which are connected to the fixed nodes in the cluster has been obtained for clusters containing 100–3200 sites. Our results indicate that in the asymptotic limit of large cluster sizes the distribution of forces on the surface of the fractal can be described by using the scaling form N(ln(F))=ln(S)h(ln(F)/ln(S)), where S is the size (number of nodes or number of surface bonds) of the DLA cluster and N(ln(F))δ ln(F) is the number of surface bonds for which the natural log of the normalized forces lies in the range ln(F) to ln(F)+δ ln(F). These results indicate that the stress distribution in the surface of a fractal can be described in terms of a fractal measure with an associated infinite hierarchy of scaling exponents and a continuous spectrum of singularities given by f(α)=Dh(-$D^{\mathrm{-}1}$α). .AE

The first measurements of dielectronic recombination rate coefficients associated with the 2s→2p excitation in the Be-like ions ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, ${\mathrm{O}}^{4+}$, and ${\mathrm{F}}^{5+}$ are reported. We observed the amount of electron capture attending the passage of MeV/nucleon ion beams through a collinear, magnetically confined, space-charged-limited electron beam as a function of relative energy. The initial beams contained large numbers of ions for which the metastable states of the term 2s2p ${\mathrm{}}^3$P were populated, and the fraction of ions in the metastable states to those in the ground-state configuration 2$s^2$ were measured. The experimental rate coefficients are consistent in magnitude and shape with rates determined from distorted-wave calculations of the dielectronic recombination cross sections. The large fraction of metastable states in the initial ion beams had a pronounced effect on the shape and magnitude of the rate coefficients.

A noise-reduced diffusion-limited-aggregation (DLA) model is explored on lattices with threefold, fourfold, and sixfold symmetry. In this model noise reduction on lattices with n-fold symmetry (n≤6) leads to clusters with n distinct arms whose structure is similar to very much larger DLA clusters grown without noise reduction. The structure of these clusters can be described in terms of the exponents ${\nu }_{?}$ and ${\nu }_{\perp }$ which describe how the length and width of the cluster arms grow with increasing cluster mass (M). Oscillation in the effective values of these exponents for large noise reduction factors makes it difficult to obtain the asymptotic (M→∞) value of ${\nu }_{?}$ and ${\nu }_{\perp }$. However, our results indicate that ${\nu }_{?}$ is close to (2/3 for n=3 but distinctly smaller than (2/3 for n=6. The results also indicate that ${\nu }_{?}$>${\nu }_{\perp }$ for n=3 but that ${\nu }_{?}$-${\nu }_{\perp }$≃0 for n=4 and 6. The simulation results are consistent with the idea that DLA clusters are fractals and for n≳4 they may be self-similar.

Data from dynamical experiments are often studied with use of results due to Shaw et al. and to Takens, which generate points in a space of relatively high dimension by embedding measurements which are typically one dimensional. A number of questions arise from this, the most obvious being how should one choose the dimension of the embedding space. In this paper we show that a method which seems promising at first sight, estimating the rank of the matrix of embedded data, is unfortunately not useful in general. Previous encouraging results have almost certainly been due to numerical problems which can, in part, be avoided by a careful application of singular-value decomposition. We show that this process does not give useful dynamical information, though it is often useful in noise control.

The overdamped Langevin dynamics of the elastic dumbbell is analyzed introducing moment expansions and deriving exact results for multiple time correlations. In the case of penetrable nonadsorbing surface, the probability of having the oscillator on the same side at a sequence of equally spaced instants of time belonging to a finite interval is expressed as a ratio of multiple integrals. In the limit of very densely distributed observation times, we obtain the analytical expression of this probability related to the unreacted fraction with adsorbing surface. We also give the first correction for small discrete intervals. The calculated unreacted fraction coincides with the diffusion equation result obtained using the Smoluchowski boundary condition. The method, not the result, is potentially extensible to oscillators with inertia.

In this paper we analyze a model containing the unfolded normal form of the imperfect pitchfork bifurcation with additional terms representing additive white noise and a linear Ornstein-Uhlenbeck noise. After linearizing the model about a branch of stable steady states, we investigate the variance of fluctuations about these steady states as a function of a control parameter. We apply our model to experimental data obtained by Griswold, Lorensen, and Tough [Phys. Rev. B 35, 3149 (1987)] on the transition between superfluid turbulent states T-I and T-II in liquid-helium counterflow experiments. Our model accounts qualitatively for the steady states, relaxation times, and the variance of fluctuations which were measured in this system. Furthermore, our model predicts the existence of a curve of unstable steady states which have not yet been observed. Perturbations from the known steady state in the direction of these new unstable steady states are expected to lead to qualitatively new dynamics.

A discrete-time approximation of the Feynman path integral is derived, for which the potential is approximated at each step by a quadratic polynomial; this is more accurate than the usual approximation for which the potential is approximated by a constant. This approximation is studied for several simple examples, by Monte Carlo calculations of the path integral.

Optical activity measurements in the isotropic phase just above the liquid-crystal transition temperature were performed for various concentrations of the chiral liquid crystal 4’’-(2-methylbutylphenyl)-4’-(2-methylbutyl)-4-biphenylcarboxylate (CE2) in the nonchiral liquid crystal 4-n-pentylbenzenethio-4’-n-heptyloxybenzoate (7¯S5). The mixtures investigated possessed extremely high chirality, with pitches varying from about 250 nm in the 40-wt. %-CE2 sample to approximately 100 nm in pure CE2. The pretransitional optical activity results clearly show that coupling between the structural modes of the ordered phase grow more and more important as the chirality increases. The agreement between these data and theory is quite good, thus permitting an estimation of the critical temperature for two of the structural modes.

An extension of the connected moments expansion to nonlinear Hamiltonians is presented. The new method enables construction of rapidly convergent series for the ground-state energy which requires a relatively small amount of numerical effort.