In previous applications of the density-functional theory to plasmas, particle correlation effects were included via the exchange-correlation potential $W_{\mathrm{xc}{}^{e\mathrm{-}e}}$ for the electrons, and the ion-correlation potential $W^{i\mathrm{-}i}$ for the ions, while the electron-ion correlation potentials $W^{e\mathrm{-}i}$ were neglected. These electron-ion correlations appear beyond the random-phase approximation and are expected to be small for liquid metals, but are non-negligible in plasmas of light elements. In this work, we consider an approximation for electron-ion correlations that exploits the properties of the direct correlation function and the local-field correction familiar in the theory of liquids. Calculations that include the effects of temperature on the electron density and on the correlation potentials have been performed for hydrogen (H) and helium (He) plasmas with the plasma-coupling parameter Γ ranging from 0.07 to 5. The effects of electron-ion correlations on the structure factor, ionization, and the interaction energy are discussed.

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first preselected by the initial measurement and the second postselected by the final measurement, describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measurement procedure that fulfills certain requirements of ‘‘weakness.’’ We call it weak measurement. Physical meaning, underlying mathematical structure, and prospects of practical usage of weak measurements are explored.

Analytical fits to the one-component plasma (OCP) equation of state have been derived for internal energies that have reduced all N-dependent effects to within the statistical uncertainties introduced by the Monte Carlo computational process, which themselves are very small. Values of N≳500 adequately represent the thermodynamic limit. Using the fluid internal energies for only N=686, various analytical fits are generated, compared, and discussed. The thermal energy is accurately represented by a simple power-series fit with the leading term given by ${\Gamma }^{1/3}$, but also requires a small correction to the bcc Madelung term that brings that coefficient down to nearly -0.9, the value derived for hypernetted-chain theory. The fluid thermal energy data are reproduced to better than 0.2% over all Γ by our fit(s). The solid phase requires both anharmonic terms to be included in the fit, implying that the previous justification for dropping the first anharmonic correction is unwarranted. The location of the fluid-solid phase transition utilizing these new fits yields ${\Gamma }_{\mathrm{bcc}=178\mathrm{}}$ and ${\Gamma }_{\mathrm{fcc}=192\mathrm{}}$.

Mathematical models of dc glow discharges sustained by electrons emitted by the cathode and accelerated into the cathode fall must take into account the highly nonequilibrium nature of these fast electrons. However, the electric field profile through the discharge is determined mainly by the distribution of ions and slow electrons. In this paper we explore three methods to account for fast, nonequilibrium electrons: the single-beam method, the multibeam method, and particle (Monte Carlo) simulations. Ions and cold electrons are treated using equations of change assuming collisionally dominated motion (i.e., drift and diffusion), and the self-consistent electric field is determined by solving these equations simultaneously with Poisson’s equation. Creation rates for ions and slow electrons are obtained from the fast-electron models. Simulation results indicate that, although the single-beam model is qualitatively correct, it is hampered by its sensitivity to assumptions in the numerical approach, and its tendency to predict negative voltage-current characteristics at low pressures and high voltages, which are not evident in results from the higher-order multibeam model. Although an improvement over the single-beam model, comparison with experimental optical-emission measurements reveals that the multibeam model predicts excitation profiles that extend too far into the discharge. Accurate comparisons are possible with particle simulations, which incorporate angular scattering of fast electrons.

A general framework for introducing noise into binary networks is developed using random iterative maps. The dynamics of these random iterative networks is written in terms of Markov chains and notions of ergodicity discussed. Generic features of the statistical dynamics of such networks are explored and a path-integral formulation of macroscopic dynamics derived. Two examples are used for illustration. First, the Little model is shown to be equivalent to a random iterative network with threshold noise, and this is used to derive the mean-field equations for a network with random dilution. Second, mean-field equations are derived for networks with synaptic noise, whose form depends crucially on how the thermodynamic limit is defined.

We study some statistical properties of a turbulent state described by a generalized Ginzburg-Landau equation and characterized by topological defects.

The dynamic scattering of light by the crystal-melt interface of succinonitrile growing in a three-dimensional Bridgman setup is studied as a function of different control parameters. Strong scattering with an exponentially decaying autocorrelation function is observed during the solidification but not during the remelting. The angular dependence of the signal is characteristic of the diffusion of objects in the liquid. After pumping out gases dissolved in the liquid, we observe a striking decrease of the diffusion coefficient, up to two orders of magnitude. These results can be satisfactorily interpreted in the framework of the microbubble model recently proposed.

For realistic boundary conditions we have calculated the linear solutions and the bifurcation structure of standing waves, which can occur for a negative separation ratio Ψ in binary fluid convection. In contrast to the case of unrealistic—free and permeable—boundaries, the linear solutions for standing waves (and also for traveling waves) have a phase which depends on the vertical coordinate (z). One consequence of this fact, a surprising temporal behavior of the stream lines of the fluid motion, is shown in detail. Furthermore, depending on the Lewis and Prandtl numbers, the standing waves have one or three tricritical points. Together with the amplitude equation for traveling waves the coefficients for the coupled amplitude equations are determined. These equations have to be used describing the post-threshold behavior of a Hopf bifurcation in the case of small amplitudes.

We propose a mechanism for the crossover between first-order and continuous transitions in confined liquid crystals that is based on a dimensional crossover of both the space and the order-parameter variables. We estimate the relevant parameters by carrying out explicit mean-field calculations of the global phase diagram of an appropriate lattice model. We discuss in some detail the effects on the phase diagram of the fluctuations neglected by the mean-field approximation.

Thermal conductivity, diffusivity, and specific-heat studies were carried out simultaneously over the smectic-A–nematic transition in alkylcyanobiphenyl liquid crystals with different nematic ranges. The critical exponents of all the thermal parameters have been calculated and discussed in terms of the dynamic scaling law of the asymmetric planar magnet model, which applies to three-dimensional XY-like transitions.

A continuous-time random walk with a coupled space and time dependence of the waiting-time distribution recently introduced by Klafter, Blumen, and Shlesinger [Phys. Rev. A 35, 3081 (1987)] is reconsidered. A simple probabilistic analysis of the problem is presented, and the diffusion behavior in one of the four possible regimes is found to differ from the prediction of Klafter, Blumen, and Shlesinger.

The preceding Comment of Bouchaud and Georges [Phys. Rev. A 41, 1156 (1990)] while introducing an interesting method to treat Lévy walks, makes implicit use of a decoupled continuous-time random-walk scheme. We discuss this quite subtle point and show that the coupled approach leads to the results previously derived by us.

The charge distributions and production cross sections of recoil ions accompanied by projectile electron loss and capture have been compared in 1.05-MeV/amu ${\mathrm{Ne}}^{\mathrm{q}+}$ (q=2, 4, 6, 8, and 10) +Ne collisions. While singly charged recoil ions are dominant in pure ionization processes, the production of highly charged recoil ions is strongly enhanced in collisions involving simultaneous charge change (by both electron loss and capture) of projectiles, and the charge distributions of recoil ions are found to be similar for both projectile loss and capture processes. These results have been analyzed with an independent-electron model and indicate that the dominant contribution to the production of higher-charge recoil ions comes from L-shell ionization, with some contribution from K-shell ionization of targets, accompanied by violent multiple ionization of projectiles.

We apply the dynamical group of the hydrogen atom to level statistics of hydrogen in strong magnetic fields and study the transition region between regularity and chaos in detail. We find a resonancelike anomaly in the Brody parameter which coincides to an amazing accuracy with the appearance of a low rational winding number.

The rules governing the evolution of nonlinear dynamical systems are systematically detected by constructing a hierarchical tree of symbol sequences. Relations between local partial dimensions and Lyapunov exponents are obtained from equations for the probabilities of symbol sequences on the logic tree. These relations are nonlinear and involve an open hierarchy of equations, which shows that the dimension spectrum f(α) cannot be obtained in closed form from the sole knowledge of the local Lyapunov exponents.

It is known that attempts to improve the signal-to-noise ratio of measured chaotic signals through low-pass filtering lead to wrong results from subsequent calculations of the attractor dimension. We show that the use of acausal filters avoids this problem. The benefit in recovering the chaotic signal from noise is demonstrated to be considerable.

We consider here the effect of noise on homoclinic crossing. It is shown, by means of a stochastic Melnikov function, that the noise may, on the average, suppress and, in the case considered here, induce homoclinic crossing.

We present and demonstrate an accurate, reliable, and computationally cheap method for the calculation of free energies in Monte Carlo simulations of lattice models. Even in the critical region it yields good results with comparatively short simulation runs. The method combines upper and lower bounds on the thermodynamic limit entropy density to yield not only an accurate estimate of the free energy but a bound on the possible error as well. The method is demonstrated on the two- and three-dimensional Ising models and the three-dimensional, three-states Potts model.

We interpret experimental pressure-drop measurements from a complex gas-solids flow system in terms of recently developed methods for chaotic time-series analysis. The results strongly support the conjecture that the flow can be described by a low-dimensional strange attractor that changes as a key turbulence parameter is varied. The analysis methods also appear to permit clear separation of the chaotic and noise components in the signal.