The structure of the active zone has been explored for several nonequilibrium-growth models (the Witten-Sander model for diffusion-limited aggregation, the screened-growth model, and the cluster-cluster aggregation model). In all of these models the structure of the active zone (spatial distribution of growth probability) can be characterized by fractal dimensionality (or dimensionalities) which is not related in any obvious way to the fractal dimensionality of the nonequilibrium structure itself. In the case of diffusion-limited aggregation the active zone has a fractal dimensionality close to 1.0 in accord with the theoretical results of Grassberger. The distribution of growth probabilities was also investigated for some of these models. Our results indicate that this distribution is a power law with a cutoff at high growth probabilities.

We analytically study the generation of longitudinal plasma waves in an underdense plasma by two electromagnetic waves with frequency difference approximately equal to the plasma frequency, as envisioned in the plasma beat-wave accelerator concept of Tajima and Dawson [Phys. Rev. Lett. 43, 267 (1979)]. The relativistic electron fluid equations describing driven electron oscillations with phase velocities near the speed of light in a cold, collisionless plasma are reduced to a single, approximate ordinary differential equation of a parametrically excited nonlinear oscillator. We give amplitude-phase equations describing the asymptotic solutions to this equation valid for plasma-wave amplitudes below wave breaking. We numerically compare the behavior of the asymptotic equations with that of the original equation and with particle-simulation results.

We investigate the oscillatory supplement to the statistical nonrelativistic binding-energy formula for neutral atoms. The semiclassical approach proves capable of deriving these oscillations. It turns out that their amplitude is proportional to $Z^{4/3}$ (Z is the number of electrons), and that their period is determined by the maximum angular momentum available in Thomas-Fermi atoms, i.e., 0.928$Z^{1/3}$. Our calculation also provides an understanding of the peculiar shape of the oscillations, which show sharp minima and wide, structured maxima.

The effects of pore fluid, effective stress, pore fluid pressure, and temperature on the frequency dependence of elastic wave attenuation in Berea sandstone are interrelated in a series of systematic experiments. The attenuation of both the extensional and torsional modes of cylindrical samples of the sandstone is measured on the frequency range 3–30 kHz. To simulate conditions within the earth, the sandstone is subjected to confining stress to 70.0 MPa and temperature from 24.0 °C to 120.0 °C. Confining pressure and pore fluid pressure are varied independently. Data for two different pore fluids, brine and n-heptane, suggest that a scaling law exists for the pressure and temperature dependence of the attenuation in terms of the pore fluid. The logarithmic decrement of the sandstone is almost frequency independent in a vacuum evacuated sample, but shows a linear frequency dependence, once the sample is saturated. Extrapolation of this linear trend to low frequencies suggests that the decrement in fluid-filled sandstone is effectively frequency independent at seismic frequencies (<100 Hz). The frequency dependence becomes more pronounced as either the effective stress or the temperature is decreased. When the difference between the external stress on the sandstone and the pore fluid pressure is large, the attenuation depends only on the effective stress and is relatively temperature independent. But at low effective stress, the attenuation increases linearly with increasing pore fluid pressure and decreases linearly with increasing temperature. While a specific model is lacking, the attenuation process is apparently influenced most strongly by chemical processes at the pore fluid-matrix interface accompanied by subtle changes in the sandstone matrix dimensions.

We consider the motion of a quantum particle placed in a metastable minima of a potential well and examine the effect of interactions with the thermal reservoir at temperature T. We use the dilute, bounce approximation for the Green’s function. We find a particular value of the dissipative coupling strength for which we can solve the Euler-Lagrange equations exactly, in the range of temperatures between zero and the crossover to the regime where thermal hopping dominates. We obtain analytic expressions for the tunneling rate in this temperature regime.

It is shown that in the absence of a macroscopic external field, the direct correlation function in the planar interface between two fluid phases has a slow decay in the transverse directions. This is in contrast to all earlier assumptions and approximate results. More generally, when several fluid phases meet along a surface of contact, it is found that the direct correlation function decays slowly in the surface of contact. These results hold provided that self-maintained interfaces exist and the intermolecular forces decay rapidly enough at infinity.

The percolation behavior of spherical particles with attractive interactions is studied with use of Monte Carlo simulations. These systems differ from lattice Ising systems, which have been previously analyzed, in the necessity to define a shell parameter δ to specify a connected cluster. For small values of δ, correlations due to the attractive interactions drastically lower the percolation threshold in the vicinity of the gas-liquid critical point. For larger values of δ, these shifts are smaller, but the effects of long-range correlations show up as enhanced finite-size effects. The simulation results are discussed in the light of recent experiments which measure the temperature and concentration dependence of the conductivity in interacting microemulsions.

Existing theories for acoustic anomaly of critical binary mixtures, including both the specific-heat and dynamic-viscosity approach and both mode-coupling and renormalization-group theory, are found to give the same expressions for critical amplitudes of reduced dispersion and absorption after appropriate modifications of the theories from two standpoints: (1) Concentration fluctuations experience the temperature difference from the critical temperature $T_c$ and the sound wave modulates both the temperatures T and $T_c$ and (2) thermodynamic quantities with critical anomaly should be correctly generalized to dynamic ones. The unified expressions of critical amplitudes have not only a temperature dependence but also a frequency dependence, indicating that the dynamic scaling does not hold in an exact sense for the acoustic anomaly. The modified Kroll-Ruhland theory gives new reduced expressions for dispersion and absorption. The difference in scaling functions among various theories is discussed.

Free-ion yields were measured in isobutane and in solutions containing sulfur hexafluoride, at densities from the liquid at 295 K to the supercritical fluid. A modified Onsager model was used to estimate the most probable thermalization distances $b_{\mathrm{GP}}$ (GP denotes a Gaussian power-law distribution). The density-normalized distance $b_{\mathrm{GP}\mathrm{d}}$ in isobutane increased from 6.3×${10}^{\mathrm{-}6}$ kg/${\mathrm{m}}^2$ at 295 K to a maximum of 10.5×${10}^{\mathrm{-}6}$ kg/${\mathrm{m}}^2$ at 395 K, and then decreased to 5.6×${10}^{\mathrm{-}6}$ kg/${\mathrm{m}}^2$ at 408 K ($T_c$). The maximum, which is evidence of conduction-band enhancement of $b_{\mathrm{GP}}$, was suppressed in solutions containing small amounts of ${\mathrm{SF}}_6$. The ${\mathrm{SF}}_6$ captured the electrons while they were still at epithermal energies, and terminated their flight away from their sibling ions. The values of $b_{\mathrm{GP}}$ and the free-ion yields were thereby decreased.

The line ratio of a dielectronic satellite to the main optically allowed line in Fe xxv has been measured in plasma discharges with a non-Maxwellian electron distribution such as those produced in tokamaks at low electron density or during heating experiments by means of Landau damping of electromagnetic waves launched into the plasma. The effect of nonthermal electrons has been clearly established in a series of experiments performed in the Frascati tokamak FT and the expressions for line intensities in these plasma conditions have been worked out. A data-analysis procedure is also presented which can give quantitative information about the nonthermal-electron content in the plasma.

A quantification of the degree of classical chaos manifested in the quantized energy spectra of two–degree-of-freedom coupled Morse-oscillator systems with sufficiently dense energy levels is attempted by use of Brody’s repulsion parameter which characterizes his nearest-neighbor level-spacing distribution function. A close relationship is established numerically between the mass-ratio dependence of the Brody parameter and that of the relative area of the chaotic regions on the Poincaré surfaces of section in the corresponding classical system. It is shown that in the strong-coupling limit the distribution appears to tend to the Mehta-Gaudin distribution from the random matrix theory, suggesting that in this limit it is almost impossible to distinguish between the quantized version of the classical K system and those of other systems with a fairly small number of regular trajectories. The present analysis also demonstrates that the Brody parameter serves as a useful indicator for measuring the degree of mode coupling and for detecting an isolated local mode in the system.

A theory is developed for the interaction of coherent electromagnetic (EM) radiation with a free electron gas and for the influence of the plasma on the photon statistics of the radiation field. Two important possibilities for generating squeezed states are shown: Squeezed states can be generated by the interaction of a one-mode laser with a plasma in a cavity; squeezed states can be generated by transmitting coherent radiation through the plasma. The maximal squeezing of the radiation obtained in the latter case is equal to the reciprocal of the dielectric constant of the plasma. Inside the plasma the EM field is represented by quasiphotons. Their dispersion relations are derived by using Bogoliubov transformations together with a self-consistency requirement for the motion of the electrons interacting with these quasiphotons. The squeezing processes are found to be strong when the frequency of the radiation is a little above the plasma frequency. By adding a constant magnetic field in the direction of propagation of the EM wave different amounts of squeezing are obtained for right- and left-circularly polarized EM waves.

Some properties of a two-dimensional charged Bose gas interacting with a ln(r) potential are investigated on the basis of a self-consistent-field formalism which includes the short-range correlations between bosons through a local-field correction depending on the pair correlation function. Numerical results for the static structure factor, pair correlation function, spectrum of elementary excitations, and the response of the system to a static impurity charge are presented. Our results show the same qualitative behavior as those of the three-dimensional analog but the correlation effects are somewhat more pronounced in two dimensions.

It has been shown that either periodic or random density perturbations, when present in an underdense region of a laser-produced plasma, can cause resonance absorption to occur even for nominally normally incident radiation upon a smooth (planar) critical surface.

The Kramers equation is solved numerically for circular diffusion in an arbitrary periodic potential V(θ), where θ is the angular coordinate. In the limit β→0, where β becomes proportional to the rate of escape from the potential wells, the far-infrared power absorption coefficient shows many different peaks due to resonance in highly nonlinear systems as described by Bogoliubov and Mitropolsky for ordinary, nonlinear, differential equations. The far-infrared resonance spectrum (FIRRS) is sensitive to the details of V. In structured (associated or hydrogen-bonded) molecular liquids such as water or acetonitrile, or in liquid crystals, the FIRRS peaks can be resolved experimentally. These peaks provide, in principle, detailed information on the effective intermolecular potential in systems of interest such as nematogens. The FIRRS spectrum is sensitive to an applied, uniaxial, external, static, electric or magnetic field.

Homogeneous plasmas are generated by irradiation of thin plastic foils with two laser beams delayed in time and focused on each side of the foil. We have studied the interaction of the second beam with the quasihomogeneous underdense plasma generated by the first beam. The intensity and the time-resolved spectra of the backscattered light are analyzed. We have measured the contribution of the stimulated Brillouin instability in the backreflected light. Its level is very low: (5–10)% at 0.53 μm and less than 0.1% at 0.26 μm at ${10}^{15}$ W/${\mathrm{cm}}^2$ for plasmas of L/λ∼100–200, where L is the density-gradient scale length.

The temporal behavior of the excess entropy production $P_{\mathrm{ex}}$ is investigated in linear electrical networks and in systems which can be described either by the linearized equations of viscous hydrodynamics or of resistive magnetohydrodynamics. As a result of inertial effects $P_{\mathrm{ex}}$ is an oscillatory quantity. A kinetic potential is constructed which contains $P_{\mathrm{ex}}$ additively. It is an upper bound of $P_{\mathrm{ex}}$ and decreases monotonically in time, enforcing $P_{\mathrm{ex}\to 0}$ as t→∞.

Using large two-dimensional diffusion-limited aggregates, we obtain very accurate estimates for the fractal and chemical dimensions of these aggregates, the spectral and random-walk dimensions, the resistivity exponent, and investigate the trapping phenomenon on these fractals both at short and long times. Our results indicate that neither the Alexander-Orbach conjecture nor that of Aharony and Stauffer for the random-walk dimension holds for these aggregates, although the latter one appears to be a very accurate approximation. We propose that the chemical and fractal dimensions of these aggregates are equal at all dimensions. Our results also indicate that the theoretically predicted asymptotic (long-time) behavior of trapping on these aggregates may be well outside of the experimental range.

Conditions are derived under which the steady-state probability density of a multivariate stochastic process, driven by exponentially correlated broadband noise, can be obtained in an analytical form, provided the steady-state density of the corresponding white-noise process is known explicitly. The general results are illustrated by three examples: optical bistability, a laser model with detuning, and a model of Brownian motion.

A theory has been developed for thermal fluctuations of electromagnetic surface waves propa-gating normal to a dc magnetic field along a plasma-plasma boundary. It is shown that for relatively weak magnetic fields the energy of these fluctuations can be emitted from the plasma. This emission is investigated in conditions which are typical for laser-produced plasmas when a spontaneously generated magnetic field exists. The spectral distribution obtained reveals both an amplitude and angular asymmetry which can be used for diagnostic purposes.