Ion-dynamic effects on the spectral line shapes of highly charged hydrogenic emitters in plasmas are reexamined with use of molecular-dynamics simulations. The large effects previously predicted near line center using the independent-ion simulations are confirmed and qualitatively explained. The approach to the impact limit for ion broadening and the coupling between Doppler and Stark broadening have also been investigated.

Hydrogen Lyman-α Stark broadening is calculated for a low-density plasma (N≤${10}^{14}$ ${\mathrm{cm}}^{\mathrm{-}3}$) for detunings smaller than 10 Å in the dipolar and no-quenching approximations. Semiclassical and quantal descriptions are alternatively used to describe the contribution of each collision. The results may be compared with the impact and static approximation limits, thus defining their range of validity and leading to analytical expressions for the relaxation rate in these cases. The effects of the trajectories curvatures and relative velocity variations are analyzed.

We derive a fully convergent collision term of the kinetic equation for charged particles obeying the classical statistics, within the static approximation to the local-field correction. The coefficient of the ionic shear viscosity is then calculated through a solution to the kinetic equation for dense, high-temperature plasmas appropriate to the inertial-confinement-fusion experiments and to the interior of the main-sequence stars. An analytic expression for the generalized Coulomb logarithm of the shear viscosity is obtained through parametrization of those numerical results.

The phase diagram of an externally modulated Rayleigh-Bénard system of binary mixtures near the codimension-two (CT) point is analyzed. The amplitude equation associated with this system is considered and the dynamical behavior is obtained by numerical integration of the equations of motion. We find that close to the CT point the system exhibits chaotic behavior, which in some region of the phase diagram coexists with the conductive state. It is suggested that these features may be observed experimentally even for small amplitude of the modulation as compared with the critical temperature difference Δ$T_c$ of the unmodulated system.

The field structures in the overdense region of an inhomogeneous magnetized plasma are studied. It is indicated that owing to the mutual conversions between the extraordinary electromagnetic wave and the electron plasma wave, the electromagnetic wave will regenerate in the overdense plasma.

Soft-x-ray low-resolution experimental spectra are obtained for a large set of targets irradiated at 2×${10}^{14}$ W${\mathrm{?}}^{\mathrm{-}2}$ by 0.26-μm radiation. X-ray conversion efficiencies in various spectral ranges are studied as a function of atomic number. To calculate the emissivity, we develop a simple, multiple-Z atomic-physics model based on a screened-hydrogenic description for the atomic structure and on a non-local-thermodynamic-equilibrium modified Saha approach to plasma-ionization properties. We are able to replicate experimental soft-x-ray spectra by using a discrete summation of emissivities over a few temperatures with appropriate weighting factors determined from the experiment or through a separate hydrodynamic-code simulation. The modulations in the Z dependence of the x-ray conversion efficiency in various spectral ranges are well described and interpreted. The comparison of theory and experiment enables us to identify a few ‘‘universal’’ parameters independent of the atomic number for given irradiation conditions.

A new method is presented to calculate vectorial correlation functions for a system of free asymmetric-top molecules. The analytical expression of the rotation matrix of an asymmetric top is determined first by using a special set of functions. Next, this matrix is developed into a Fourier series. Final results, obtained after averaging over a canonical ensemble, appear in the form of rapidly converging series of integrals of free spherical-rotor correlation functions. This development contains no approximation and is well adapted to numerical treatment. It also represents a convenient starting point to develop rotational models for extended diffusion.

The theory of infrared and anisotropic Raman spectra of pure van der Waals liquids is developed without introducing any a priori factorization of the rotational-vibrational correlation functions. Extensive use is made of the fact that the Hamiltonian of a pure liquid sample is invariant, both under permutations of the molecules and under rotations of the liquid sample as a whole. The total and self-correlation functions are expanded into series. Their leading term corresponds to the product approximation and higher-order terms provide successive corrections. These corrections are shown to be small. Moreover, in spite of the presence of molecular interactions, infrared absorption and anisotropic Raman scattering in pure liquids exhibit mainly monomolecular characteristics of vibrational and rotational motions.

We investigate the response of a layer of a fluid heated from below (the Rayleigh-Bénard problem) subject to a systematic rotation and a small random angular velocity about the same axis, simulating approximately the effect of a weak random stirring. We find that to the lowest three orders of perturbation this preserves the bifurcation of spatial patterns, shifting merely the Rayleigh number at which the most probable amplitude becomes finite, to higher values.

We present two learning mechanisms for networks of formal neurons analogous to Ising spin systems. The ‘‘projection rule’’ guarantees the errorless storage and retrieval of a set of information patterns: In other words, it allows us to compute the magnetic interactions so as to make a given set of states the ground states of the spin system (in zero external field). Several analytical results are derived for this rule; computer simulations and examples of applications to error correction are presented. Another learning mechanism, termed the ‘‘associating rule,’’ is also described; going beyond the memorization process, it allows us to design networks satisfying a set of dynamical constraints such as a given set of stable states and/or transitions and/or cycles. It provides a new tool to perform such functions as associations between information and concepts.

Dynamic ensemble theory is tested numerically for an ensemble of 1000 classical one-dimensional oscillators obeying canonical ‘‘Nosé-Hoover’’ dynamics. This dynamics couples each oscillator to a canonical heat bath characterized by a temperature and a relaxation time. Some initial oscillator conditions correspond to regular phase-space orbits of the Kolmogorov-Arnol’d-Moser torus type while others generate wider-ranging chaotic trajectories. Among the regular oscillator orbits is a set of trajectories resembling ‘‘double bedsprings,’’ with ‘‘quantized’’ values of the oscillator energy and mean-square displacement. The number which indexes these orbits corresponds to the number of coils between turning points. Despite the existence of this relatively complex mixture of regular and chaotic trajectories, the Liouville equation correctly describes phase-space flows, in both the steady equilibrium canonical-ensemble case as well as in the nonsteady cases which evolve from strongly nonequilibrium initial conditions. The source of apparent irreversibility seen in the nonsteady evolution of the oscillator ensemble is identified as a ‘‘second-law’’ attractor, usually characteristic of large thermodynamic systems. The attractor is that relatively small but highly probable portion of phase space for which observation times exceed recurrence times.

A replacement is proposed for the usual Liouville equation for the evolution of the distribution function of a statistical ensemble of classical, homogeneously thermostatted systems. The correct description of the entropy evolution is an essential criterian for such a replacement to satisfy, since we show from numerical realizations of a physically realistic model system that the Liouville equation is not satisfactory in general. On the other hand, both the Liouville equation and the proposed replacement correctly describe the evolution of ordinary mechanical observables, such as the energy. The particular form of the proposed replacement is shown to describe correctly a variety of experimental conditions.

A kinetic model for irreversible surface reactions, recently proposed by Ziff, Gulari, and Barshad, is studied in the site and pair approximations. The latter approach predicts the phase diagram correctly, and yields quantitative predictions which are in very close agreement with simulation, in the vicinity of the first-order kinetic transition.

We propose two classes of models for hopping-controlled reactions in which one of the reactants forms a random distribution of static traps and the hopping distances of the other reactants (random walkers) are independent random variables with a preassigned distribution. Specifically, in the discrete model, at each step the random walkers are allowed to make hops of all possible lengths of integer units up to a preassigned maximum value L, all with equal probability. In one of the continuous models, the hopping distances are Gaussian-distributed independent random variables with a mean L. In the other continuous model, the distribution of the hopping distances r follow an exponential distribution, namely, exp(-‖r‖/L). We predict the L dependence as well as the time dependence of the reaction rates (the decay of the particle density as a function of time) for these models analytically. We also verify some of these predictions by Monte Carlo computer simulations.

A slowly varying Hamiltonian with one degree of freedom and nearly closed orbits has an adiabatic invariant. This adiabatic invariant is conserved to all orders in ε, the slowness parameter, except for orbits that cross a separatrix. The present work discusses the change of the adiabatic invariant during this crossing process through order ε. First, a calculation of the change of the adiabatic invariant is presented. This calculation is general and, hence, encompasses previous results for specific cases. The change in the adiabatic invariant is shown to depend on a maximum of five parameters, which are functions of the Hamiltonian of interest. Second, the statistics of this process are derived. Finally, these results are applied to the motion of a particle in a wave with changing amplitude and phase velocity.

We have investigated the route to chaos for a nondissipative Hamiltonian system governed by a model equation which describes the motion of a particle in a two-wave system. Using a generalization of the Krilov-Bogoliubov-Mitropolskii perturbation scheme, we analyzed the equation of motion to uncover the basic structure of the solutions which was revealed by a Fourier power-spectrum analysis. From such an analysis of a few representative examples, we deduced that chaotic motion sets in when the associated power spectrum acquires a raised level noiselike structure. The mechanism for arriving at such a structure was found to be the indefinite cascading nonlinear coupling between the different oscillations present in the system. The details of the operation of this mechanism are described, and a discussion of these results is included.

This paper is a generalization of Kubo’s stochastic theory of spectroscopic line shapes which appeared in 1962 under the same title. Using a stochastic, Hermitian Hamiltonian to phenomenologically incorporate absorber-perturber interactions resulting from molecular collisions, we are able to reproduce Kubo’s derivation of the simple Lorentzian line shape: I(ω)=${\pi }^{\mathrm{-}1}$Γ[(ω-${\omega }_0$${)}^2$+Γ ${}_{}{}^2{}_{}{}^{}$${]}^{\mathrm{-}1}$ in which the width Γ is related to the mean-square strength, $Q_3$, of a diagonal stochastic Hamiltonian by Γ=2$Q_3$. Our generalization of this line shape is I(ω)=(1/π){1+(1-ω/Ω)[(${\mathrm{\Gamma }}_2$ ${\mathrm{-}\mathit{\Gamma }}_1$)/2Γ]}Γ/[(ω-Ω${)}^2$+Γ ${}_{}{}^2{}_{}{}^{}$${]}^{\mathrm{-}1}$, where ${\Gamma }_1$ and ${\Gamma }_2$ measure the degree of anisotropy in the off-diagonal part of the stochastic Hamiltonian. With perfect isotropy their contribution vanishes, but we are still left with additional corrections to the simple Lorentzian: Γ=2Q(1+${\mathrm{\omega }}_0^2$/${\mathrm{\epsilon }}^2$${)}^{\mathrm{-}1}$+ 2${\mathrm{Q}}_3$ and Ω=${\omega }_0$+Δ, where Δ=2Q(${\mathrm{\omega }}_0$/ε)(1+${\mathrm{\omega }}_0^2$/ε ${}_{}{}^2{}_{}{}^{}$${)}^{\mathrm{-}1}$. Our result does reduce to Kubo’s in the absence of off-diagonal stochastic terms. The parameter ε measures the non-Markovianness of the stochastic Hamiltonian and yields white noise in the limit ε→∞. Our results are valid for this limit regime. The frequency shift Δ is a measure of the non-Markovianness.

Optical second-harmonic generation (SHG) was used to probe the structure of freely suspended films of 4’-n-octyl-4-cyanobiphenyl (8CB) in the smectic-A phase. The intensity of the SHG from ultrathin films with thickness varying from 2 to 10 molecular layers appeared quantized, but its behavior suggested no modifications of molecular arrangement in the layers in the presence of the two ‘‘free’’ surfaces. A macroscopic theory for the SHG from a film with stratified nonlinear susceptibility is presented and compared with the experimental observation.

We study the chaotic motion of a particle in an asymmetric potential well, for which the equation of motion is x¨+0.4ẋ+x-β$x^2$-4$x^3$=0.115 cos(ωt). For 0≤β≲0.008, a splitting into the right and left attractors occurs due to the symmetry rule. (This rule is fully generalized.) The left attractor does not appear for β>0.008. The ω regions of the periods of the dominating right attractor increase when β increases from 0 to 0.006,...,0.008 the increase of the ω region of period 3 (→6→12→...) being anomalously strong. The behavior for 0≤β≲0.006 can be described with a cubic map. For 0.008<β≤0.1, a steepening parabola-type return map can be found for the right attractor consistently with the fact that the calculated motion is similar to the behavior of the one-dimensional unimodal z=2 maps. The absence of period 3 (→6→12→...) appears as an abrupt steepening of the return map.

Consider an infinite thermodynamic system A, an open subsystem $A_V$, with fixed volume V, of A, and an open subsystem $A_{V\mathcal{’}}$, with fixed volume V’, of $A_V$. Evidence is presented to support the following thermodynamic fluctuation rule: At any time, the probability of finding the thermodynamic state of $A_{V\mathcal{’}}$ in some range, given the thermodynamic state of $A_V$, is independent of the thermodynamic state of A, even if the volume $V— is less than the correlation volume of $A—. This rule was confirmed by Monte Carlo simulation of the two-dimensional ferromagnetic Ising model. Both thermodynamic properties and the local correlation function were examined. Another rule, which states that, for a given state of $A_V$, the fluctuation probability distribution for the thermodynamic state of $A_{V\mathcal{’}}$ depends on the volumes only as Δt=(V’${)}^{\mathrm{-}1}$-$V^{\mathrm{-}1}$ was also tested. It works well at volumes larger than the correlation volume, but was shown to break down at volumes less than the correlation volume. In addition, an easily justified rule stating that the average value of a density of a globally conserved additive quantity of a subsystem equals that of the infinite system was tested and found to work well. These rules are part of an effort to extend thermodynamic fluctuation theory to volumes less than the correlation volume.