The system-size expansion technique, is used to study the fluctuations both near and far from equilibrium of a charged Brownian particle in a two-component plasma. The method is based on the master equation that governs the conditional probability density function of the velocity. This method yields a macroscopic equation for the slowing down of the heavy charged particle; and in the linear noise approximation, equations for the mean and variance of the fluctuations around the macroscopic behavior are found and a fluctuation-dissipation theorem is demonstrated. The velocity-velocity correlation function and the diffusion coefficient of these particles are also determined in this approximation, both near and far from equilibrium. Numerical examples are used to illustrate the results. The generalization to multispecies plasma is apparent.

An analysis of streamers is presented from the viewpoint of the interplay of the rate processes that contribute to their development. The space-time evolution of a streamer front is described by a sequence of stages that are identified by the dominant rate process determining the local properties of the front and the ‘‘turning point’’ where this process is overcome by others. Numerical and analytical results are used to determine these stages. From this analysis, the properties of positive (cathode-directed) and negative (anode-directed) streamers are elucidated, in particular, the dynamics that lead to the saturation of electron-density and electric-field enhancement. An expression is obtained that relates the dynamics of the positive and negative streamers associated with an initial space-charge distribution.

The stability of a plasma boundary in the presence of a powerful p-polarized electromagnetic wave is studied. It is shown that surface waves that are coupled to plasmons localized in the plasma-vacuum transition layer can be excited. The growth rate that is calculated turns out to be larger than the corresponding value obtained without taking nonlocal effects of the transition layer into account by a factor proportional to the wavelength of the pump wave divided by the width of the boundary region. The threshold is accordingly significantly lower. We believe that the present theory will be useful for the explanation of several nonlocal optical effects arising near the surface of solid-state plasmas.

Stark width and shift measurements of eight S ii and one S iii spectral line (of 4s-4p, 4s’-4p’, and 4p-4d transition arrays) have been performed for the electron density range 6.70×${10}^{22}$–2.08×${10}^{23}$ ${\mathrm{m}}^{\mathrm{-}3}$ and for an electron temperature range 27 000–40 000 K. Stark parameters of all these spectral lines, belonging mostly to higher multiplets, were measured in a linear low-pressure pulsed arc operating in ${\mathrm{SO}}_2$. The obtained Stark width data were compared with the values calculated on the basis of various theoretical approaches and good agreement has been found. The existence of Stark width dependence on the upper-level ionization potential, for S ii spectral lines belonging to the 4p-4d transition array, has also been proved.

We consider the forward and backward scattering of light for large-scale inhomogeneities compared to the wavelength in the dielectric medium. In this paper we discuss a scalar field equation based on the random-phase approximation as a model to represent the scattering intensity from polycrystalline samples. In a discrete and continuous scattering medium, the spatial coherence makes the width of the backscattering intensity very narrow and the phase coherence enhances the small amount of backscattering intensity. The forward- and backward-scattering experiments for the samples are presented, and the optical depths are measured. The observed shapes and widths of the forward scattering are in very good agreement with the theoretical values. We estimate the backscattering intensity from the numerical parameters of the forward-scattering experiments.

We study the nonlinear dynamics of multilayer perceptrons with feedback and propose their application to the analysis of signals with complex time dependence. We show that their dynamics provides a built-in time-warping invariance, as, e.g., required for presentation speed fluctuations in speech recognition. We suggest an appropriate learning rule (open-loop learning), give an analytical stability condition for the resulting multistable states, and determine their basins of attraction. To demonstrate their utility for possible applications, we consider the example of a three-stage feedback multilayer perceptron that is trained to detect words in a sequence of letters and does it with perfect invariance with respect to presentation speed fluctuations.

We study the dynamics of a symmetric analog neural network with a parallel update rule that averages over M previous time steps. We show that convergence to a fixed-point attractor can be guaranteed by a simple criterion that limits the neuron’s gain (maximum slope of the neuron transfer function) to a value proportional to M. A global stability analysis based on a new Liapunov function is presented. The analysis generalizes a previous result for M=1, i.e., standard parallel updating. Multistep updating allows oscillation-free parallel dynamics for networks that have period-2 limit cycles under standard parallel updating. Results are applied to associative memory networks based on the Hebb and pseudoinverse learning rules. In addition, we present a simple analysis of convergence times showing that the number of iterations required for a multistep neural network to converge to a fixed point increases at a rate proportional to M when all other network parameters are held fixed. However, because increasing M allows the gain to be increased without inducing oscillation, in some instances using a larger M can yield a shorter convergence time when the neuron gain is also optimally adjusted.

A general mean-field theory is presented for an attractor neural network in which each elementary unit is described by one input and one output real variable, and whose synaptic strengths are determined by a covariance imprinting rule. In the case of threshold-linear units, a single equation is shown to yield the storage capacity for the retrieval of random activity patterns drawn from any given probability distribution. If this distribution produces binary patterns, the storage capacity is essentially the same as for networks of binary units. To explore the effects of storing more structured patterns, the case of a ternary distribution is studied. It is shown that the number of patterns that can be stored can be much higher than in the binary case, whereas the total amount of retrievable information does not exceed the limit obtained with binary patterns.

An example is given for which spectral fluctuations of a quantum system coincide with those of the Gaussian orthogonal ensemble (GOE), although the system is not chaotic in the classical limit. This shows that GOE-like fluctuations are not an unambiguous fingerprint of ‘‘quantum chaos.’’

A recently derived free-energy model for the inhomogeneous hard-sphere fluid yields analytic, easily calculable expressions for the three-particle direct-correlation functions, in good agreement with extensive Monte Carlo simulations near freezing densities. This enables one to perform a systematic study of the convergence rate of the first terms in the density-functional expansion from a reference uniform fluid state to solidlike density distributions. We find that the convergence is too slow to provide a rationale for a density-functional theory of freezing based on the truncated second-order expansion.

In one-parameter families of Hamiltonians with two degrees of freedom, some periodic orbits may form isolated families, also called ‘‘floating bubbles.’’ In this paper we study, numerically, two examples of floating bubbles and show that the lack of symmetry in a plot of the trace of its monodromy matrix versus the energy implies the connection of these families to other families of periodic orbits through period-n-tupling bifurcations.

Undirected animals with loops are usually associated with a singularity structure described by ${\mathit{A}}_{\mathit{n}}$(c)∝${\lambda }_0^{\mathit{n}}$${\mathit{n}}^{\mathrm{-}\mathrm{\theta }+\mathit{c}}$, where ${\lambda }_0$ is the tree growth constant, c the number of loops, and θ the critical exponent for the total number of animals. It is shown here that for a given class of lattices in all dimensionalities, trees are absent and series-expansion analyses favor a singularity hierarchy described by the self-avoiding walk growth constant with an exponent structure related to the excluded-volume susceptibility.

The piecewise linear relation between the shock-wave velocity ${\mathit{U}}_{\mathit{s}}$ and the particle velocity ${\mathit{U}}_{\mathit{p}}$ is proposed for gases by examining the ${\mathit{U}}_{\mathit{p}}$ dependence of the adiabatic exponent. In each linear segment, ${\mathit{U}}_{\mathit{s}}$ has the asymptotic form ${\mathit{U}}_{\mathit{s}}$=${\mathit{U}}_{\mathit{p}}$, where the ${\mathit{b}}_{\mathit{l}}$’s are the constants determined by the details of the physicochemical process occurring during the shock-wave compression.

The twist viscosity has been measured in a binary liquid-crystal mixture above the nematic–smectic-C transition near the nematic–smectic-A–smectic-C multicritical point using the dynamic Fréedericksz deformation and found to exhibit a monotonic divergence. This study also shows that the splay elastic constant has a relatively mild temperature dependence compared with that of the bend elastic constant.

It is shown that the ratio of the plasmon energy to the binding energy of the last bound S state of the Debye-Hückel potential is approximately independent of density and depends on temperature as ${\mathit{T}}^{1/2}$. A simple analytical condition for plasmon-induced free-bound transitions for the highest excited states of hydrogenic ions was obtained that is met by plasmas of interest.

We present a density-functional calculation of the prewetting line for a solid-fluid interface model that has been studied in the recent Monte Carlo simulation of the problem by Finn and Monson [Phys. Rev. A 39, 6402 (1989)]. We have good agreement for the surface critical point, but not for the wetting temperature, which in our calculation is at the triple-point temperature or below.

Velasco and Tarazona [preceding Comment, Phys. Rev. A 42, 2454 (1990)] have presented density-functional-theory predictions for prewetting at a Lennard-Jones 12-6–9-3 fluid-solid interface and they have compared their results with our recently published Monte Carlo simulation data [J. E. Finn and P. A. Monson, Phys. Rev. A 39, 6402 (1989)]. The agreement is good except for the location of the prewetting line which in the density-functional theory lies at lower values of the pressure relative to saturation than those estimated from the simulations. This leads to prediction of a lower value for the wetting temperature. Velasco and Tarazona suggest that this difference may be due to an underestimation by us of the saturation pressures of the truncated 12-6 fluid. We have performed further Monte Carlo simulations of the coexistence properties of the truncated 12-6 fluid and the results support the accuracy of our method for estimating saturation properties. Thus the difference between simulation and theory cannot be explained in the manner described by Velasco and Tarazona.

A modified form of the Saha equation for a two-temperature plasma is presented, which accounts for the underpopulation of the excited states due to deviation from local thermodynamic equilibrium.

It is recognized that the preceding Comment by Bakshi adds a consistent result to our generalization. However, the usefulness of this result in experimental situations is doubted. A note is added about another point addressed in the Comment [V. Bakshi, Phys. Rev. A 42, 2460 (1990)], i.e., the correct expression for the equilibrium population of an excited state for two-temperature plasmas of which the excitation population distribution is nonlocal thermodynamic equilibrium below a certain level q>1.

We report simulations of a two-dimensional ballistic Lorentz gas on a lattice. A moment-propagation technique allows direct measurements of the velocity correlation function and its moments with low relative errors for all times. We observe the predicted ${\mathit{t}}^{\mathrm{-}2}$ algebraic tails in the velocity correlation function at all studied scatterer densities, unlike what has been reported for continuous systems. In the square lattice a fast [(-1${)}^{\mathit{t}}$] oscillation is observed, consistent with the existence of staggered density modes. For the second-rank tensor correlation function we find an extremely slow approach to the expected ${\mathit{t}}^{\mathrm{-}3}$ tail.