Plasma-broadened visible spectra have long been used to infer plasma parameters. In this work we examine the use of high Rydberg states in plasma spectroscopy for low-density plasmas. For low densities the high Rydberg states may be very useful because of their large widths and the fact that they are less susceptible to ion dynamical effects. We have calculated plasma-broadened spectra of the neutral oxygen n=6→n=5 transition in the 7.5-μm region for a temperature around 10 000 K and electron densities 5×${10}^{13}$–${10}^{16}$ e/${\mathrm{cm}}^3$ and found that these spectra can be a useful probe for low-density plasmas. We also describe how selection rules can be used to greatly reduce the computational requirements.

Plasmon scattering by electrons in two laser fields in the additional presence of a strong (quantizing) magnetic field is discussed. A kinetic equation for the plasmon population is derived, from which the damping rate is calculated. We found that plasma waves may be amplified over a relatively narrow range of plasmon wave numbers in the direction perpendicular to the magnetic-field direction. Furthermore, the joint action of the three external fields results in a very large amplification rate, in contrast to the case where no magnetic field is present.

The temporal and spatial evolution of patterns in physical systems due to electrical current flow can be described for a certain class of systems, which includes certain semiconductor and gas discharge systems, by a two-layer model in terms of the electrical current density and the electrical potential. An equation for the nonlinear layer is derived, the characteristic parameters of which can be obtained from experiments at the respective systems without inhomogeneous patterns lateral to the main current direction. The resulting equation takes into account diffusion and drift effects in the nonlinear layer. It turns out that the drift effects occur only if there is a ‘‘net space charge.’’ Two special cases are derived depending on which of the two layers gives the main contribution to the displacement current density, and the typical static and dynamic behavior is studied by numerical calculations. Furthermore, the application of the model to real devices is discussed, and a comparison is made with experimental results obtained with a dc glow-discharge system.

A model for the nucleation of drops in a supersaturated liquid or bubbles in a superheated liquid is proposed. Unlike previous models, this method allows the calculation of a surface energy for an interface where the two phases are not yet in equilibrium with one another. For the example of the nuclear matter equation of state, free-energy barriers for the formations of these small fluctuations are calculated as a function of the density and temperature of the surrounding matter along with a sample computation of nucleation rates.

In this paper, a simple, two-dimensional model of the deoxyribonucleic acid (DNA) is presented. In the model the two polynucleotide strands are linked together through the hydrogen bonds. The phosphodiester bridges in the backbone are described by the anharmonic potential of Toda kind, while the hydrogen bonds are described by the Lennard-Jones potential. Longitudinal wave propagation on ring-shaped DNA molecules is investigated. The model predicts a significant increase in the lifetime of the open states of the hydrogen bonds at physiological temperatures. Thus anharmonicity may play a role in DNA denaturation.

An upper bound for the density of the metastable states of neural networks consisting of analog neurons with graded response is calculated exactly in the limit of infinitely many number of neurons. It is found that the density of the metastable states that are uncorrelated to any memory patterns is remarkably suppressed compared with the case of deterministic neural networks of formal neurons. The result gives a theoretical explanation for the belief that the neural networks of nonlinear analog neurons are very effective in computation. The critical storage capacity is obtained as a function of the analog gain, which should correspond to the ‘‘temperature’’ in stochastic Ising-spin neural networks, exhibiting a small increase compared with the case of the stochastic neural networks.

Recently, attempts have been made to alter the equation of motion of a multiparticle system so that the temperature rather than the energy is constant. The Nosé-Hoover equation of motion is very useful for systems with a large number of particles, but, for a one-dimensional oscillator, the phase-space dynamics is not sufficiently chaotic for a fully statistical description. We propose a modified Nosé-Hoover equation, obtained by enforcing the virial theorem, for which the phase-space dynamics is much more chaotic. This modified Nosé-Hoover equation is easily generalized and may be useful for other systems with a small number of particles.

We report the results of Monte Carlo simulations on a two-dimensional Ising model in a sinusoidally oscillating external magnetic field. We find evidence for a dynamical phase transition, supporting the results of recent mean-field and large-N analyses of this model. We also analyze the hysteresis loops as a function of the amplitude and frequency of the applied field, fitting our data to a proposed areal scaling law.

A recent experiment on the directional solidification of liquid crystals has exhibited traveling waves. In this Brief Report we present numerically obtained solutions for these traveling waves by generalizing the methods previously employed to look for steady-state patterns. The results agree with our earlier predictions based on a stability analysis and complete the bifurcation diagram for the system at hand.

We report a measurement of the change in the total volume of a biological lipid-water system when water molecules are removed from the fully hydrated lyotropic liquid-crystal phase, where the water molecules are near a polar interface, to the surrounding bulk water. The commonly used assumption of linear additions of constituent volumes predicts that the water mole fractions of these lipid-water phases should be independent of hydrostatic pressure. The discrepancy between this prediction and our high-pressure x-ray-diffraction measurements is due to a decrease of 0.1 A${\mathrm{̊}}^3$ in the total volume of the system per molecule of water incorporated into the fully hydrated lipid-water aggregate from the bulk water.

Using random walkers on a square lattice we have simulated a diffusion-reaction process A+B→C; initially, the reactants are segregated on either side of a straight boundary. Quantities studied include the position and width of the reaction front and the position-dependent reaction rates and densities of the reactants. Our results agree with the scaling theory of Gálfi and Rácz for the long-time behavior of the system indicating that the scaling assumption is valid and that the neglect in the scaling theory of concentration fluctuations and of the discrete (particle) nature of the reactants is not important. Furthermore, although the scaling theory is not explicitly constructed for the case of unequal diffusion coefficients of the two initial species, our results indicate that it is correct in this regime as well.

An upper bound is determined for the turbulently generated axial electromotive force in reversed-field pinches, constrained solely by energy conservation in the approximation of incompressible magnetohydrodynamics. The field reversal is predicted and comparisons are made with the minimum-energy state with the invariant magnetic helicity.

A methodology for generating sample functions for colored noise which has some relative advantages over existing ones is outlined. This involves simulating a stochastic process in terms of harmonic functions, the amplitude of which is related to the power spectral density of the noise. The computational advantages of the fast Fourier transform are utilized and the numerical integration of the noise equation is avoided. In light of this methodology, existing algorithms for colored-noise simulation are critiqued and compared with the present one. Numerical results for a particular case study, namely that of an overdamped particle in a bistable potential, are presented and the results are compared with existing theories.

We apply the fixed-scale transformation method, developed for Laplacian fractal growth, to compute the fractal dimension of standard percolating clusters and of clusters generated by invasion percolation with and without trapping. In all cases we obtain values within 1% from the exact or numerical results. This provides an important test for this theoretical framework, fundamentally different from the renormalization group, as an alternative tool to study fractal structures generated by both equilibrium and irreversible growth processes.

We derive an exact solution for the mean first-passage time for an arbitrary one-dimensional system driven by the colored Ornstein-Uhlenbeck noise. We show that this exact solution can be systematically interpreted in terms of random telegraph signals. Using random telegraph signals as a tool we fully solve the difficult problem of non-Markovian boundary conditions associated with such a problem. The analytic solution with these boundary conditions give a complete solution of the escape time in the presence of colored noise.

We study the stability of the stationary, spatially localized states of traveling-wave convection recently described by Niemela, Ahlers, and Cannell [Phys. Rev. Lett. 64, 1365 (1990)] and by Anderson and Behringer [Phys. Lett. A 145, 323 (1990)] by bombarding them with propagating wave packets. At sufficiently large incident amplitude, this can lead to the destruction of the localized state and to a transition to a new state. Sufficiently far above the onset of convection, this process is triggered by spontaneously arising propagating fluctuations, causing convection to fill the experimental cell.

The effect of nearest-neighbor bond-orientational ordering on the magnetically induced Fréedericksz transition in tilted hexatic liquid crystals is examined. It is shown that the coupling between the molecular tilt and the bond-orientational field can drastically modify the behavior of the Fréedericksz transition in tilted hexatic materials. In particular, it is found that upon an increase of the applied external field, the system can exhibit either an ordinary second-order Fréedericksz transition, a first-order one, or a second-order Fréedericksz transition followed by a first-order tilt-bond reorientation transition.

The theory of x-ray diffraction for smectic-A films is presented. The effect of the smectic layer fluctuations and correlations and the molecular form factor on the interlayer structure and the x-ray diffraction pattern is discussed. The application of the presented theory to smectic-C, smectic-I, smectic-${\mathit{A}}_{\mathit{d}}$, and smectic-${\mathit{A}}_2$ films is suggested.

Considering two-dimensional evolution of an interface, we identify qualitatively different regimes dependent on the initial smoothenss of the front characterized by the parameter γ that describes how fast an initial Fourier coefficient ${\mathit{A}}_{\mathit{k}}^0$ decreases with k, when k→∞, where ${\mathit{A}}_{\mathit{k}}^0$=${\mathit{e}}^{\mathrm{-}\mathrm{\alpha }\mathrm{-}\mathrm{\beta }\mathit{k}\gamma }$. It is shown that for γ>2, after some time, the front’s shape has a starlike well-defined needle structure. The number of needles increases with time, and the needles develop into cusps in finite time. For γ≤2, the starlike symmetry is broken and we have a less regular form. The conclusion is that for an almost flat initial front (α≫1, β≪1) the critical smoothness is γ=2.