The two-mode dye laser exhibits a quasibistable behavior wherein the lasing switches alternately between the modes at random intervals. This behavior can be described in terms of a first-passage-time (FPT) formalism. A Langevin model of the system has been the basis for most analytical approximations to the problem and here the results of detailed, four-dimensional, Monte Carlo simulations are presented. These results are compared to the various analytical and experimental results available. Attention is paid to the differences in alternative FPT problems and especially to problems involved in comparison with experimental data. One recent major advance in modeling the dye laser has been the introduction of pumping fluctuations into the Langevin equations. Effects of the introduction of pumping fluctuations on the FPT problem are explored and comments are made on previous attempts to account for their presence by the use of averaging techniques.

Experiments on the steady-state, nonlinear behavior of the ${}_{}{}^7{}_{}{}^{}\mathrm{F}_1^{}{}_{}{}^{}$${\mathrm{-}}^7$${\mathrm{F}}_0^{\mathrm{o}}$ 570.68-nm transition of atomic samarium in a laser-driven, near-concentric Fabry-Perot cavity are reported. For zero applied magnetic field, only simple optical bistability, symmetric in both ${\sigma }^{+}$ and ${\sigma }^{\mathrm{-}}$ transmitted polarizations, is observed for a linearly polarized excitation beam. However, for a magnetic field applied parallel to the propagation direction, polarization-sensitive switching appears, with lowest power threshold near the edge of the Doppler-broadened region. Subsidiary measurements of atomic parameters are also given to enable the transition to be experimentally well characterized.

This is a detailed experimental study of the dynamical behavior of a ${\mathrm{CO}}_2$ laser with modulated losses. We describe the observation of period-doubling transitions into chaos that are in good agreement with the predictions of the theory of one-dimensional maps and give examples of temporal evolutions, phase-space portraits, power spectra, and Poincaré sections. With the help of bifurcation diagrams we provide evidence for the appearance of generalized multistability. We also discuss the results of dimensionality tests that we have carried out on both our experimental data and corresponding numerical simulations based on the Maxwell-Bloch equations after the adiabatic elimination of the polarization. We conclude with an evaluation of the Kolmogorov entropy.

We have observed ionization of Mg by both direct and stepwise two-photon excitation of the 3$p^2$ ${\mathrm{}}^1$S state. The line shape of the single-color direct process is strongly modified by the resonance denominator associated with the intermediate virtual state. The measured energy and width of this resonance as determined by the stepwise two-color technique agree well with previous determinations.

Using a Landau potential F=(1/6)${\psi }^6$ +(1/4)g${\psi }^4$+1/2ε${\psi }^2$, where ψ is a suitable order parameter, one can quantitatively explain symmetry-breaking phenomena in Couette-Taylor flow near a tricritical point. Ideas from bifurcation theory have been used to show that ε depends quadratically and g linearly on the aspect ratio and on the angular velocity of the inner cylinder. This agrees well with earlier experimental results in quite a wide area around the tricritical point.

A new method is described for studying shear flow in fluids and crystals using nonequilibrium molecular dynamics (NEMD) based on determining the response of the system to a predetermined homogeneous shear stress. Flow phenomena may be examined which would not be accessible using other techniques. We demonstrate the existence of a yield stress for shear along the (111) plane of an ideal (i.e., defect-free) fcc soft-sphere crystal. The significant differences with previous simulation results using constant strain rate NEMD are discussed in terms of artifacts introduced by sample size effects and crystal geometries in relation to the direction of shear.

The onset of convection in a fluid contained between a hot inner and a cold outer spherical boundary in a radially symmetric gravity field is examined. Due to the spherical symmetry there are usually (2l+1) unstable modes belonging to the lth irreducible representation of the O(3) group. The actual value of l is determined by a properly defined aspect ratio. There are special values of this aspect ratio where two groups of modes simultaneously become unstable. The instability involving the two groups of modes with l=1 and l=2 is considered by investigating the corresponding generalized Ginzburg-Landau equations. By varying the Rayleigh number and the aspect ratio a variety of interesting spatio-temporal behavior is observed. The occurring static, time periodic, and quasiperiodic fluid motions as well as the various types of chaotic fluid flow are examined in detail.

The memory function for the longitudinal current-current correlation function has been measured at low frequencies for fluid krypton, argon, and rubidium with use of the new methods previously described by us [Phys. Rev. A 31, 3802 (1985)]. The memory relaxation time is much shorter than the structural relaxation time for many wave numbers (Q) in the range observed, 0.4–4 A${̊}^{\mathrm{-}1}$. There is a marked variation of the memory function with Q, although its variation with frequency over the range studied, ω<3Q √kT/MS(Q) , is not large. The data for noble gases and an alkali metal are compared and the significance of differences considered. For the discussion of collective modes, the most significant quantity is the ratio of imaginary to real parts of the memory function which we have measured for the first time. Some evidence for propagating modes of high wave numbers is presented and their relationship to peaks in S(Q,ω) and other properties is discussed.

Following some preliminary clarification of microscopic heat current definitions for mixtures, we describe nonequilibrium molecular dynamics algorithms for the evaluation of heat and matter transport coefficients in binary liquid mixtures. Simulations have been carried out for a dense fluid of Lennard-Jones atoms, approximating an equimolar argon-krypton mixture, at a thermodynamic state which has been studied in several previous equilibrium simulations. Our results suggest that the estimates of the mutual diffusion coefficient from these equilibrium simulations are ∼15% too high. Most importantly, we determine the cross-coupling coefficients which characterize the Soret and Dufour effects. These are obtained from two entirely independent sets of simulations and are found to be equal, in accordance with an Onsager reciprocal relation. When we run our algorithms with high external fields, we incidentally find evidence of demixing which is of interest in the general context of nonequilibrium phase transitions.

The Taylor functional method is reexamined for nonuniform classical systems. Some new integral equations relating the average number density with the external field imposed on the system are derived. Instead of truncating the functional expansions after the first term, a simple mathematical scheme is proposed which approximately takes into account all the higher-order terms. Due to their self-consistent nature, the equations obtained are expected to be useful in the phase-transition region.

In this paper, results are presented from a a study on the effect that energy partition between the two electrons emerging from an ionizing collision has on the velocity distribution of an assembly of electrons, in nitrogen, at E/N values of 300 and 1500 Td. The energy at which the secondary electrons enter the distribution ranged from zero to half the available energy. It has been found that as the energy of the secondary decreases, the populations at low energies and in the high-energy tail increase, with a concomitant decrease in the middle of the distribution, and that the distribution becomes highly anisotropic. This is shown to have significant effects on the transport parameters and rate coefficients for electron-molecule reactions.

Five models has been studied to elucidate the role of electron-molecule angular scattering in shaping the velocity distribution for electrons in nitrogen at E/N values of 300 and 1500 Td. The angular dependence of the differential scattering cross sections for elastic and inelastic collisions has been observed to have significant effects on the shape of the velocity distribution, the rate coefficients, and the transport parameters. The velocity distribution is most sensitive to the angular dependence of elastic scattering. Moreover, for a given elastic differential scattering cross section, variations in the angular dependence of inelastic scattering cause significant changes in the distribution. The magnitude of these changes depends on the relative action of the inelastic collisions with respect to the elastic collisions for a given energy interval, i.e., whether the scattering by the inelastic collisions is isotropic, forward, or backward in a given energy interval.

The radial distribution functions between the charged radiator atom and the partially degenerate electrons as well as the ions are calculated on the basis of the hypernetted-chain scheme developed in the earlier papers of this series; strong Coulomb coupling effects of the charged particles and the quantum-diffraction effects of the electrons are appropriately taken into account. The probability densities of the total electric microfields and of the low-frequency component perceived at the radiator are then evaluated for various cases of dense plasma in the potential-of-mean-force approximation, which exactly satisfies the second-moment sum rule without use of adjustable parameters.

The radial distribution functions between a charged radiator atom and plasma particles, investigated in the preceding paper, are applied to the calculation of shift of the spectral lines arising from average polarization of dense hydrogenic plasmas due to the Coulomb field of the radiator. Dependence of the line shift on the radiator charge, the plasma density, and temperature is numerically investigated and is compared with other theoretical predictions.

Radiation hydrodynamics of laser-irradiated plane foils is studied numerically in the frequency-averaged diffusion approximation. Open and closed geometries are considered. It is shown that radiatively driven ablative heat waves play an important role for materials with medium atomic number Z and become dominant for high-Z matter. Scaling relations are given and the role of the opacity is pointed out.

A representation of the hierarchy of kinetic equations formulated earlier [Phys. Rev. A 33, 2068 (1986)] for reacting charged-particle swarms in gases is obtained in the Sonine polynomial basis. We specialize to electron swarms and compute transport and rate coefficients, distribution functions, and other quantities of physical interest for both model and realistic electron-molecule scattering cross sections, in a wide variety of cases.

An electrostatic electron plasma wave excited at the beat frequency of two incident laser beams is seen to decay efficiently into an ion acoustic wave and a scattered electron plasma wave in a hot collisionless plasma in the presence of a transverse static magnetic field. The Vlasov equation in terms of guiding center coordinates has been solved to find the nonlinear response of electrons in the plasma. It is observed that a strong external magnetic field may reduce the growth rate of the decay instability appreciably and the growth rate is independent of the density of the plasma.

Intermicellar structure factors extracted from small-angle neutron scattering are analyzed in terms of the primitive model of ionic solutions. A well-defined closure to the Ornstein-Zernike equation is shown to be capable of handling colloidal solutions with high charge and size asymmetry. The micelle-micelle structure factor predicted by a combined hypernetted-chain Percus-Yevick approximation compares favorably with the experimental results for lithium and sodium dodecyl sulfate (LiDS and NaDS) solutions with or without added electrolytes. Compared to the mean spherical approximation the hypernetted-chain Percus-Yevick approximation treats the correlations among ions more accurately and, therefore, the full micellar charge and actual size is used in the analyses even at low volume fraction (concentration) of micelles.

With basis in number theory, scaling relations for the sine map have been investigated, generalizing the work of Shenker which concentrated on ‘‘golden’’ rotation numbers (equivalents of the golden mean). Scaling functions are found, and exponents associated with the convergence rate, defined for periodic irrationals. In the light of the fact that the step structure obtained by iterations of the sine map exhibits a kind of self-similarity, correspondences to scaling laws for Cantor’s discontinuum have been studied. We define a ‘‘similarity dimension’’ which is found to scale with Shenker’s exponents, as the sine map attains a zero-slope third-order inflection point. Moreover, we examine the subset of steps having associated a denominator, which is a power of 2, and find a correlated fractal dimension which is half the fractal dimension of the original Cantor set. Inspired by these results, we have considered the driven damped pendulum equation and tried to recover corresponding scaling laws. Surprisingly, another scaling exponent z̃apeq21.5 is found where Shenker’s exponent zapeq21.05 was to be expected. Finally, the period-doubling route to chaos inside the hysteretic region for the pendulum equation is discussed, and qualitative agreement with the behavior of the one-dimensional sine map obtained.

The initial decay rate of the dynamical scattering function for semidilute polymer solutions is calculated as a function of solvent quality with the aid of the ε-expansion method, which has been semiquantitatively reliable for various properties of polymer systems. In the present calculation, the hydrodynamic screening effect, which presumably is relevant for larger wave numbers, is not taken into account. Comparison of the results given here and experimental results should reveal the significance of the screening effect. Calculational tools for semidilute solutions are streamlined and systematized in the appendixes, and the static scattering function is also given as a function of the solvent quality.