Recently reported light-scattering studies of ${\mathrm{CaKNO}}_3$ and Salol are reanalyzed, using the extended version of the mode-coupling theory of the liquid-glass transition including activated transport or hopping effects. Problems found in the original fits due to the neglect of hopping terms are largely corrected, and quantitative predictions for the susceptibility minimum below the crossover temperature ${\mathit{T}}_{\mathit{c}}$ are found. The results are also shown to accurately explain the ${\mathrm{CaKNO}}_3$ neutron spin-echo data reported by Mezei [J. Non-Cryst. Solids 131–133, 317 (1991)].

We report results from a Monte Carlo simulation of many polymer chains end-grafted onto the outer surface of a sphere. We find that for small values of the radius of the grafting sphere, the monomer density profiles are quite different from what is obtained in the case of a flat interface. As the radius of the sphere is increased further, we find that the profiles resemble those obtained in the flat case. However, even for a large value of the radius, the density profiles cannot be described by a parabolic form. We have also studied the scaling behavior of the density profile and find that the scaling hypothesis works reasonably well to describe the height of the polymer brush and the density of monomers at the grafting surface. We also investigated the density profile of the free chain ends for different values of the radius of the spherical interface, different chain lengths, and different surface coverages. Self-consistent-field theory suggests the existence of an exclusion zone near the surface from which the chain ends are expelled. We do not observe a definite exclusion zone for most of the values of chain length, radius, and surface coverage studied here. However, some evidence of an exclusion zone is found in one case with high surface coverage.

Lattice Bhatnagar-Gross-Krook models for miscible fluid flow in two (2D) and three (3D) dimensions are introduced. The convection-diffusion (CD) equation and the Navier-Stokes (NS) equation describing the macroscopic behavior of the models are derived using the Chapman-Enskog expansion technique. Corrections to the CD equation of higher order in the flow velocity are obtained, and it is shown how the present models are linked with the existing Boltzmann model. It is also shown how the Navier-Stokes dynamics is explicitly decoupled from the diffusive behavior of the model. The results obtained from both 2D and 3D simulations are observed to be in excellent agrement with the analytic predictions. In particular it is shown that the models are well described by theory for high-Péclet-number flows. We also present simulation results confirming the anomalous (but small) velocity dependence of the CD equation, and we investigate the models’ sensitivity to large gradients in the concentration profile.

An extended phase diagram for an ionic microemulsion system made of water, n-decane, and the ionic surfactant sodium-di-2 ethyl-hexyl sulfosuccinate is deduced from a very extensive set of electrical-conductivity and neutron-scattering measurements. This diagram shows high-temperature phase transitions that explain some original features previously not reported. Furthermore we propose a phenomenological model based on the solution of a Poisson-Boltzmann equation which accounts well for electrical conductivity data we obtain in the lamellar phase.

We continue our studies [J. Stat. Phys. 71, 485 (1993)] of a one-dimensional anisotropic exclusion process with parallel dynamics describing particles moving to the right on a chain of L sites. Instead of considering periodic boundary conditions with a defect as in our studies, we study open boundary conditions with injection of particles with rate α at the origin and absorption of particles with rate β at the boundary. We construct the steady state and compute the density profile as a function of α and β. In the large-L limit we find a high-density phase (α>β) and a low-density phase (α<β). In both phases, the density distribution along the chain approaches its respective constant bulk value exponentially on a length scale ξ. They are separated by a phase-transition line where ξ diverges and where the density increases linearly with the distance from the origin. Furthermore, we present exact expressions for all equal-time n-point density correlation functions and for the time-dependent two-point function in the steady state. We compare our results with predictions from local dynamical scaling and discuss some conjectures for other exclusion models.

Pattern formation is studied by injecting water into a radial Hele-Shaw cell filled with an aqueous solution of hydrophobically terminated polyoxyethylene, which forms a reversible associating network in water. A crossover from fingering pattern to fracturing pattern is demonstrated as the injection rate exceeds a threshold value. The fingering-fracturing transition is sufficiently abrupt that no gradual crossover has been observed within our limits of experimental control, and it is found to be consistent with a Deborah-number scaling, except for homopolymers (where the hydrophobic end caps are replaced by hydroxyl groups) for which the fingering-fracturing transition was never observed.

We present a density-functional approach for the Helmholtz free energy of simple liquids, based on the separation of attractive and repulsive interactions and within the framework of the weighted-density approximations. The approach reduces to the standard perturbation theory of simple fluids for the homogeneous vapor and liquid phases. It gives a good description of the correlation structure in the crystal, based on a local-compressibility equation. The phase diagram of a Lennard-Jones system is obtained and compared with a computer simulation.

Using a Ginzburg-Landau approach, we study the interface fluctuations in ternary mixtures of oil, water, and an amphiphile. The capillary-wave spectra can be understood in terms of interfacial tension and bending rigidity of the amphiphilic monolayers. For large interface widths, the distortion of the interface profile due to curvature lowers the bending rigidity. The interfacial tension is found to depend crucially on the distance to neighboring membranes or walls. In particular, we show exactly that the interfacial tension vanishes in the infinite lamellar phase. The variation of the interfacial tension has observable consequences for a lamellar phase between walls, where we calculate the effect of the wall separation on fluctuation spectra and scattering intensities.

We study interfacial fluctuations in a Ginzburg-Landau model for ternary oil-water-surfactant mixtures by Monte Carlo simulations. Space has to be discretized in order to apply the Monte Carlo method. However, by an appropriate choice of the lattice constant of the background lattice, discretization effects can be largely avoided. Strong fluctuation effects on the phase diagram are observed, which can be explained by a fluctuation-induced lowering of the oil-water interfacial tension. We determine several quantities, which characterize the structure of the microemulsion, such as the internal interfacial area and the Euler characteristic. The microemulsion phase is shown to have a disordered bicontinuous structure. In the lamellar phase, we observe an increase of the interfacial area with increasing separation of the monolayers. A quantitative comparison with the predictions of the effective curvature model of Helfrich [J. Phys. (Paris) 46, 1263 (1985)] yields excellent agreement, when an exponential distance dependence of the interfacial tension is taken into account.

In directional solidification of alloys, the interface pattern assumes a cellular structure, with a periodic array of cells, when the velocity is increased beyond the threshold of planar interface instability. A detailed experimental study in the succinonitrile-acetone system has revealed a branch of cellular structure in which the interface pattern consists of a periodic array of coupled cells or doublets. This doublet interface evolves with two characteristic length scales at the advancing front: a small intraspacing between the cells in a doublet, whose selection is sharp, and a larger interspacing corresponding to the distance between cells in adjoining doublets, whose selection is weak. The dynamics of the time-dependent evolution of a doublet interface is investigated by statistical analysis of tip spacings, by using a Fourier transform of the interface shape and through the study of the variation of shape parameters with time. These dynamical studies have confirmed the selection of doublet interface as a stable solution of the cellular pattern formation. A range of stable regime for an array with doublets is determined and the key factor that controls the formation of regular cells or doublets in an array is discussed. When doublets are unstable, time dependency may follow due to a source mechanism at grain boundaries, which induces strong spatiotemporal chaos.

The effective-temperature concept arising from the two-temperature (2T) kinetic theory for the nonreactive migration of a dilute ion swarm in a neutral gas under the action of a uniform electrostatic field has been tested over a wide temperature range by Monte Carlo simulation (MCS). Such a test over the prescribed temperature span has not been made experimentally because of the inherent difficulty in designing an apparatus which permits the temperature of the ion drift chamber to be varied so widely. The MCS test is here applied to ${\mathrm{Li}}^{+}$ in Xe, which offers the most favorable conditions for the 2T theory to be a valid approximation of the more sophisticated three-temperature theory. Results established that for such cases it is possible to express the mobility ${\mathit{K}}_0$ and transverse diffusion ${\mathit{D}}_{\mathit{T}}$, but not the longitudinal diffusion ${\mathit{D}}_{\mathit{L}}$, in terms of a univariate effective-temperature scale instead of the separate parameters of gas temperature and the ratio of electric field to gas concentration. More remarkably, the ratio ${\mathit{D}}_{\mathit{T}}$/K was found to bear a simple linear relation with ${\mathit{T}}_{\mathit{e}\mathit{f}\mathit{f}}$ over a very wide range.

Molecular-dynamics simulations employing 1024 particles and a high-accuracy spline approximation of the Ewald potential have been used to measure the excess internal energy of the classical one-component plasma in both the fluid and solid (bcc) phases over a wide range (1≤Γ≤2000) of the coupling parameter. The energy data for Γ≤300 are in excellent agreement with previous Monte Carlo calculations for this range, giving an independent corroboration of these calculations. Data in the crystalline regime 170≤Γ≤2000 are used to estimate the coefficients of the anharmonic energy component by least-squares fits. The first coefficient is in reasonable agreement with peturbation-theory predictions, although it is argued that determination of the coefficients in this manner is a rather ill-conditioned problem. The free-energy curves of the fluid and solid phases are found to cross at ${\mathrm{\Gamma }}_{\mathit{m}}$≊173, in agreement with recent estimates.

Nonlinear evolution of the radiative-condensation instability is investigated in the intermediate-wavelength limit, when the growth rate is maximal. The dynamics of a confined plasma is considered. This paper treats the planar geometry. Nonlinear reduced equations are derived for the instability, which account for the nonlocal feedback resulting from mass conservation and the finite size of the system. For a bistable heating-cooling function, it is shown that, in contrast to a number of previous studies where the isobaricity condition was employed, one-dimensional coherent patterns (spatial coexistence of two locally stable thermal equilibria, cool and hot) persist for a very long time.

We have used x rays in the 9–15-Å band emitted from a solid target of ${\mathrm{BaF}}_2$ irradiated by ∼120 mJ of 248-nm radiation in a 650-fs full width at half maximum Gaussian laser pulse to characterize spectroscopically the resulting ultrashort-pulse laser-produced plasma. The emission was spectrally resolved but space and time integrated. By comparing the spectrum with unresolved-transition-array calculations and measurements of plasma emission from longer-pulse experiments, it is clear that ions as highly stripped as titaniumlike barium are present. We have successfully modeled the observed spectrum by assuming an optically thin source in local thermodynamic equilibrium (LTE) and using the super-transition-array theory [A. Bar-Shalom et al., Phys. Rev. A 40, 3183 (1989)] for emission from a hot, dense plasma. The model indicates that the emitting region is at comparatively low temperature (200–300 eV) and high electron density (${10}^{23–}$${10}^{24}$ ${\mathrm{cm}}^{\mathrm{-}3}$). The degree of agreement between the model and the measured spectrum also suggests that the emitting plasma is near LTE. We conclude that the emission in this band arises from a solid-density plasma formed early in time, and is thus localized in both space and time. This interpretation is reinforced by lasnex [G. B. Zimmerman and W. L. Kruer, Comments Plasma Phys. Controlled Fusion 11, 51 (1975)] simulations that indicate that emission in this band closely tracks the laser pulse.

Linear waves are investigated in the framework of the relativistic anisotropic magnetohydrodynamics in a fully invariant formulation. Dispersion relations are derived for the relativistic analog of slow, intermediate, and fast waves in a plasma with an anisotropic stress tensor. Relativistic Chew-Goldberger-Low dispersion relations are obtained also.

In this paper we present a concise expression of the classical electromagnetic radiation spectrum of a moving charge. It is shown to be equivalent to the often used and much more complicated form derived from the Lienard-Wiechert potentials when the observation distance R satisfies the condition R≫γλ. The expression reveals a relationship between the radiation spectrum and the motion of the radiation source. It also forms the basis of an efficient computing approach, which is of practical value in numerical calculations of the spectral output of accelerated charges. The advantages of this approach for analytical and numerical applications are discussed and the bending-magnet synchrotron radiation spectrum is calculated according to the approach.

Linear and nonlinear theory is presented for the generation of gyroharmonic radiation from spatio-temporally modulated electron beams in cylindrical waveguides. Selection rules for axisymmetric beams are derived that show coupling at the mth temporal harmonic to be absent for all TM modes, and for TE modes other than those with an azimuthal mode index of m. Estimates from linear theory are given for the effects of spreads in axial momentum and guiding-center radius. A nonlinear multimode theory is developed in order to treat mode saturation and mode competition for TE modes in a down-tapered guide magnetic field. Numerical simulations of the multimode nonlinear generation of fifth-harmonic radiation at 94 GHz from a 150-kV, 6.667-A, α=2 beam show that nearly 90% of the initial transverse energy of the beam can be converted to fifth-harmonic radiation in the ${\mathrm{TE}}_{51}$ mode, and that less than 2.5% of the beam energy is converted to other harmonics. Use of a linearly tapered guide magnetic field gives lower saturated fifth-harmonic conversion efficiency than does use of a nonlinear taper. But the linear-taper case shows greater resilience to axial momentum spread than does the nonlinear taper case. The spent beam is nearly monoenergetic and phase coherent at saturation, suggesting that overall harmonic-conversion efficiencies can approach 100% if a single-stage depressed collector is used to recover the spent beam energy.

Issues related to the transition to stochastic relativistic and nonrelativistic motion of electrons in an electromagnetic wave propagating obliquely to a uniform magnetic field, such as stability, structure of the diagrams of characteristics, and the morphology of the bifurcation sequence in the latter, are thoroughly investigated. The spatiotemporal distributions of the electron energies, relativistically and nonrelativistically, are also examined. Major, qualitative, as well as quantitative differences in all aspects related to the transition to stochasticity and energy distribution are found. These dramatic differences lead to the conclusion that, at least as far as stochasticity is concerned, the nonrelativistic approximation is invalid even in the weakest possible relativistic case. However, from the theoretical point of view, the nonrelativistic model investigated here is in itself a very rich dynamical system with unusual behavior.

In this paper, various characteristics, such as the small-signal gain, oscillation threshold, and self-mode-locked oscillation behavior, of a waveguide-mode free-electron laser using a long-pulse relativistic electron beam are described. Analysis of the wave forms of the output radiation and the modulation of the electron beams was carried out in order to demonstrate the existence of coupling between different oscillation branches through the electron beams.

Based on the perturbation theory with multiple scales, we have developed a technique to study the evolution of particle distribution as a function of oscillation amplitudes in a hadron storage ring. With a renormalization scheme for the zeroth-order term, a uniformly valid perturbation expansion for the distribution function is obtained. For localized nonlinear perturbations such as the beam-beam interaction at colliding points, this renormalization scheme results in a functional mapping for the particle distribution and the diffusion processes of particles in the beam can be studied numerically without resorting to the tracking of individual particles. A case involving a single nonlinear kick in the ring is presented to illustrate the method in detail.