The nonlinear oscillations of a cylindrical screw-pinch plasma with mass flow aligned parallel to the magnetic field are studied in the special case when the fluid is incompressible, inviscid, and infinitely conducting. The extent to which the solutions of linear stability analysis can be used to construct solutions of the nonlinear-oscillation problem is examined. The disturbance is first taken to be a harmonic wave, with an axial wave number k and a frequency ω, which is a solution to the linear stability equations. Such a disturbance in the linear stability analysis is also found to be a solution to the nonlinear-oscillation equations if it is stable and if the perturbation in fluid pressure is suitably modified. The principle of superposition holds for two or more axisymmetric harmonic-wave solutions in the nonlinear-oscillations problem if each of these solutions has the same phase velocity ω/k. A class of exact solutions for the nonlinear oscillations may be obtained by superposing these axisymmetric harmonic-wave solutions with the same ‘‘phase velocity.’’ The utility and significance of this class of solutions are pointed out.

The thresholds for parametrically excited second-harmonic emissions from laser-produced plasmas from planar, slab targets of carbon, aluminum, and copper have been experimentally measured using a 20-J–5-nsec, Nd:glass laser system at a pump wavelength of 1.0641 μm. Theoretical estimates of these thresholds are obtained, taking into account the homogeneous as well as inhomogeneous and isothermal state of the plasma governed by the electron-ion equilibration time. A critical analysis of the agreement as well as disagreement of the experimental measurements with the existing theories is presented in detail.

One of the most serious obstacles to the attainment of high-gain inertial confinement fusion is the loss of implosion symmetry and mixing of core and shell material, principally as a result of Rayleigh-Taylor instabilities. As a diagnostic of such instabilities, we have investigated the consequences of such mixing on the emergent composite Stark profile of the heliumlike potassium 1${\mathit{s}}^2$–1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ and hydrogenic chlorine 1s-3p lines that are coincident at 3.53 Å (3.51 keV). For the case of a chlorine-filled core compressed by a potassium-bearing shell, detailed radiative transfer calculations with self-consistently calculated Stark profiles reveal changes in the overlapped emission profile of these lines when the potassium is assumed mixed into the core. When the potassium remains localized in a distinct shell, its major effect on the chlorine profile is to produce an absorption feature. When the two elements mix to various degrees, the depth of this feature is reduced. This is explained by pumping of the K xviii 1s2p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ state by the Cl ${\mathrm{L}}_{\mathrm{\beta }}$ line, and obscuration of the potassium emission by the chlorine opacity. Experimental detection of this effect would require spectral resolution of about 2 eV and the ability to discriminate intensity differences of 15% in nearby spectral regions.

Nonlinear dielectrics are investigated by allowing the permittivity to be a function of the modulus of the electric field. Such a function is examined subject to the requirement that the differential permittivity be positive definite. Then the electrostatic approximation is considered. A general relation is derived for the determination of the electric field that contains the space integral of a term involving the electric field and its gradient; the integrand vanishes when the permittivity is constant or the problem is endowed with particular symmetries. Next, a variational formulation is set up for a dielectric surrounding conductors, and the explicit form of the energy is determined. The solution to the electrostatic problem is shown to provide the minimum of a strictly convex functional. Besides being of interest conceptually, both the integral equation and the variational formulation are likely to be the basis for efficient numerical procedures.

The properties connected to the propagation of electromagnetic waves in rectangular waveguides loaded by periodic dielectric gratings have been treated by extending the theory of dynamical scattering by perfect atomic crystals. The theoretical formulation has been developed for the ${\mathrm{TE}}_{10}$ excitation of the periodic load, but it remains valid in the same form when a ${\mathrm{TE}}_{\mathit{n}0}$ (n>1) excitation takes place. The analysis was first developed for two-dimensional periodicities, and later the results were applied to one-dimensional periodicities without modifications to the formalism. The generalization of Bragg’s law to guided propagation has been obtained, and the conditions and limits of applicability of the theory have been discussed. It has been shown that, when a small permittivity contrast between supporting and loaded material is present, the electromagnetic field can be approximated by either one or two waves only. The expressions of the electromagnetic field supported by the periodic medium and the dispersion relation have been obtained. The diffraction pattern, the deviation from the generalized Bragg law, the width of the total reflection range, and the extinction length have been evaluated for a regular array of cylindrical holes on a polyethylene support. We have reported the results of an experiment carried out to verify the accuracy of the theory. The comparison between theoretical and experimental results has shown excellent agreement.

An oscillator neural network model that is capable of processing local and global attributes of sensory input is proposed and analyzed. Local features in the input are encoded in the average firing rate of the neurons while the relationships between these features can modulate the temporal structure of the neuronal output. Neurons that share the same receptive field interact via relatively strong feedback connections, while neurons with different fields interact via specific, relatively weak connections. The model is studied in the context of processing visual stimuli that are coded for orientation. The effect of axonal propagation delays on synchronization of oscillatory activity is analyzed. We compare our theoretical results with recent experimental evidence on coherent oscillatory activity in the cat visual cortex. The computational capabilities of the model for performing discrimination and segmentation tasks are demonstrated. Coding and linking of visual features other than orientation are discussed.

The Willshaw model is a neural network with binary synaptic strengths. In the Willshaw model with local inhibition, only one neuron in each block of q neurons is active. We formulate the model using the Potts spin variables and extend the dynamics to a stochastic one. The equilibrium states of the system are characterized by a set of variables representing the overlap between a group of patterns and the network state. Stable Mattis-like solutions exist at zero temperature, and the phase transition is found to be of the first order. A related model whose Hamiltonian is linear in interaction is also studied. The linear model does not function as an associative memory, suggesting that functioning of the Willshaw net stems from the binary truncation of the synaptic strength.

The reversible association of globular protein molecules in concentrated solution leads to highly polydisperse fibers, e.g., actin filaments, microtubules, and sickle-cell hemoglobin fibers. At high concentrations, excluded-volume interactions between the fibers lead to spontaneous alignment analogous to that in simple lyotropic liquid crystals. However, the phase behavior of reversibly associating proteins is complicated by the threefold coupling between the growth, alignment, and hydration of the fibers. In protein systems aggregates contain substantial solvent, which may cause them to swell or shrink, depending on osmotic stress. Extending previous work, we present a model for the equilibrium phase behavior of the above-noted protein systems in terms of simple intra- and interaggregate interactions, combined with equilibration of fiber-incorporated solvent with the bulk solvent. Specifically, we compare our model results to recent osmotic pressure data for sickle-cell hemoglobin and find excellent agreement. This comparison shows that particle interactions sufficient to cause alignment are also sufficient to squeeze significant amounts of solvent out of protein fibers. In addition, the model is in accord with findings from independent sedimentation and birefringence studies on sickle-cell hemoglobin.

We perform a singular-perturbation analysis of the Fisher equation in arbitrary dimensions. This analysis gives us an approximate, asymptotic solution of the Fisher equation for a broad class of initial conditions. Specifically, we find that a domain growing from a seed initial condition has an asymptotic velocity of 2 in all dimensions. However, the interface of the analytic solution is excessively sharp, suggesting that the singular-perturbation approach has intrinsic limitations.

We have shown that the mobility tensor for a particle moving through an arbitrary homogeneous stationary flow satisfies generalized Onsager symmetry relations in which the time-reversal transformation should also be applied to the external forces that keep the system in the stationary state. It is then found that the lift forces, responsible for the motion of the particle in a direction perpendicular to its velocity, have different parity than the drag forces.

An apparent connection between integrability and the existence of a periodic solution of the variational equations around the straight-line solutions of planar Hamiltonian systems has been suggested [F. T. Hioe, Phys. Rev. A 39, 2628 (1989)]. Such solutions always exist if the gradient of the second integral and the Hamiltonian are independent on the straight lines. In any other case, the existence of such periodic solutions can be shown only if the second integral satisfies certain conditions.

Periodically varying roll patterns have been produced in molecular-dynamics simulation of two-dimensional Rayleigh-Bénard convection using a hard-disk fluid in a square container with nonslip walls. In order to achieve the sufficiently high Rayleigh numbers required for clearly resolved time-dependent behavior the calculations involved systems containing almost 6×${10}^4$ particles, an order of magnitude greater than the number needed to observe stationary convection patterns.

This Brief Report demonstrates the relationship of eddy-viscosity models to subgrid stresses. A formula that determines the relative importance of the cross stress and the Reynolds stress for the net eddy-damping and backscatter contributions is derived. The cross-stress term with sharp-cut filtering is identified as an important quantity to model. These concepts could prove useful as a basis for constructing specific models for the Reynolds and cross stresses.

We present a lattice-gas model for two-dimensional immiscible fluid flows with surface tension that uses strictly local collision rules. Instead of using a local total color flux as Somers and Rem [Physica D 47, 39 (1991)], we use local colored holes to be the memory of particles of the same color. Interactions between walls and fluids are included that produce arbitrary contact angles.

Experiments are reported on fractal copper electrodeposits. An electrochemical cell was designed in order to obtain a potentiostatic control on the quasi-two-dimensional electrodeposition process. The aim was focused on the analysis of the growth rate of the electrodeposited phase, in particular its dependence on the electrode potential and electrolyte concentration.

The conduction-band energy ${\mathit{V}}_0$ (relative to vacuum) and the effective mass ${\mathit{m}}^{\mathrm{*}}$ of quasifree excess electrons in fluid neon and helium are calculated as a function of number density n. The calculations are carried out within the framework of the Wigner-Seitz model for nonpolar fluids, using highly accurate pseudopotentials to represent the electron–rare-gas-atom interactions. The calculated values of ${\mathit{V}}_0$(n) and ${\mathit{m}}^{\mathrm{*}}$(n) are found to be in good agreement with the available experimental data.

The discrepancy between recent experimental results [S.U. Vallerien et al., Phys. Rev. A 42, 2482 (1990)] and previous theories [R. Blinc and B. Zeks, Phys. Rev. A 18, 740 (1978)] concerning the dielectric spectrum of smectic-${\mathit{C}}^{\mathrm{*}}$ liquid crystals is resolved by further theoretical considerations. In addition, two modes are predicted above 1 GHz.

In their numerical investigation of the two-dimensional growth of a pair of needlelike viscous fingers, Peterson and Ferry [Phys. Rev. A 39, 2740 (1989)] discovered that when the angle between the two needles is less than 0.920 154 rad, then a ‘‘shadowing’’ transition occurs, with one needle growing longer than the other. I show that this is a standard pitchfork bifurcation, with the critical angle being exactly (1- √2 /2)π.

In this Brief Report we present simulation-calculation results of the transient diffusion-limited reaction A+B→0 on Sierpinski gaskets embedded in Euclidean spaces of dimensions d between 2 and 13. We find that the asymptotic temporal behavior of the density decay follows the power-law relation ρ(t)∼${\mathit{t}}^{\mathrm{-}\mathrm{\alpha }}$, with α=d̃/4, d̃ being the spectral dimension. This result for Sierpinski gaskets contrasts with a recent general finding by Sheu, Lindenberg, and Kopelman [Phys. Rev. A 42, 2279 (1990)].

We have generalized our previous scaling arguments [Sheu, Lindenberg, and Kopelman, Phys. Rev. A 42, 2279 (1990)] for diffusion-limited A+B→0 reactions to encompass various possible connectivity properties and reaction conditions on fractal structures. The theory now allows for a more complete range of possible reaction surface configurations. While our original result (which is a special case) places a bound that is consistent with very recent simulations on critical percolation clusters, the generalization is needed to account for the behavior on finitely ramified structures such as Sierpinski gaskets and Peano curve fractal constructions. Our results yield upper and lower bounds for the oscillations of the reactant decay exponent which are typical for hierarchical structures. Our approach unites under a single framework situations such as the A+B→0 reaction and the A+A→0 reaction that were previously treated separately.