The dynamics of the transition from supercooled liquid to glass is examined in terms of several probes: ergodic measures, self-diffusion coefficients, the Van Hove self-correlation functions, and the shear viscosity. Constant-pressure molecular-dynamics calculations at several temperatures are performed for a Lennard-Jones mixture and binary mixtures of soft spheres. The temperature dependence of the ergodicity diffusion parameters for both systems follow the Vogel-Fulcher law. On the other hand, the self-diffusion coefficients exhibit Arrhenius behavior for the soft-sphere system, but Vogel-Fulcher behavior for the Lennard-Jones system. These observations suggest that loss of effective ergodicity may be the universal feature of glass-forming substances. Various probes of the dynamics of the mixtures studied here suggest that the mechanism for mass transport dramatically changes from a simple diffusive process to one that involves activated transitions. The temperature at which this occurs is higher than the glass transition temperature ${\mathit{T}}_{\mathit{g}}$ and lies in the range 1.1<T/${\mathit{T}}_{\mathit{g}}$<1.3. In this temperature range the effective ergodic times also increase very rapidly and suggest that the relaxation process is dominated by the presence of barriers in configuration space. We also show that the Stokes-Einstein relation between the shear viscosity and the self-diffusion coefficients starts to break down in the temperature range where the ergodic convergence times increase dramatically.

We report numerical simulation of the deposition of spherical particles on a planar surface, by ballistic, straight-line trajectory transport, and assuming irreversible adhesion on contact with the surface or previously deposited particles. Our data indicate that the deposit formed has a loosely layered structure within a few diameters from the surface. This structure can be explained by a model of growth via chain formation. Away from the surface we found evidence of a monotonic, power-law approach to the bulk density. Both density and contact-statistics results suggest that the deposit formed is sparse: the space-filling fraction is about 15%, and the average number of contacts is 2. The morphology of the deposit both near the surface and in the bulk seems to be a result of competition of screening and branching; nearly half of all the spheres are either single-contact dangling ends, or branching nodes with more than two contacts.

We apply the differential formulation of the generalized effective liquid approximation to the study of hard-sphere and hard-disk freezing. We show that the thermodynamic properties of the solid phase are rather insensitive to the compressibility factor of the fluid phase used to map the solid onto the effective liquid. The solid-fluid coexistence data instead are quite dependent on the equation of state describing the fluid phase. Very accurate results, as compared with the simulation data, are obtained for both the freezing of hard spheres and hard disks.

The influence of dipolar forces on the structural and thermodynamic properties of hard spherocylinders is investigated in the isotropic and smectic phases using Monte Carlo simulations. Irrespective of the characteristics of the dipole moment, location (from center to the end of the molecule), strength (${\mathrm{\mu }}^{\mathrm{*}}$ varying from 0 to √6 ), and direction (from parallel to perpendicular to the molecular axis), the stable smectic-A phase is found to have a monolayer structure. In the case of a longitudinal dipole moment the layers are unpolarized; for transverse dipole moments the simulation results give some indication for a net polarization of the system parallel to the smectic planes, although this result should be taken with care because of the slow relaxation of the system towards equilibrium.

The formation of ferroelectric liquid crystals by simple dipolar models is investigated using density-functional theory and absolute-stability analysis. It is emphasized that for such systems well-defined results can only be found by specifying exactly how the long-range dipolar interactions are treated. Explicit formal expressions are derived for mean-reaction-field boundary conditions and these are combined with integral-equation approximations in order to obtain numerical results for fluids of dipolar hard and soft spheres. The calculations predict isotropic-to-ferroelectric nematic transitions in qualitative agreement with computer simulations. The quantitative agreement, however, is rather poor.

Rapid-solidification experiments on metallic alloys in the last decade have provided widespread observations of a novel ‘‘banded structure.’’ We report the results of numerical and analytical studies of the interface dynamics underlying the formation of this structure in a model of directional solidification which includes both solute and heat diffusion and nonequilibrium effects. The thrust of these studies is on the unsteady dynamics of the planar interface and thermal effects. The main conclusion is that the origin of banding can be related to relaxation oscillations of the solidification front, characterized by large variations of the interface velocity, which are dramatically affected by latent-heat diffusion. Without the latter, the oscillations are found to be reasonably well approximated by the phenomenological model of Carrard et al. [Acta Metall. 40, 983 (1992)], and the band spacing is inversely proportional to the temperature gradient. In contrast, with latent-heat diffusion the band spacing is insensitive to the temperature gradient, but is controlled instead by the interplay of solute and heat diffusion. The smallness of the solutal diffusivity to thermal diffusivity ratio is exploited to explain analytically this effect and to derive considerably simpler equations of interface motion that provide an efficient numerical means to study the nonplanar interface dynamics expected to cause dark bands. A reasonable agreement with experiment is found for the spacing of banded structures dominated by light-band microsegregation-free regions in Al-Fe alloys.

The usual theories of selection in dendritic growth involve an analytical extension in the complex plane and a search of singularities for the profile function. We show here that the complex plane is in fact the liquid phase and that the zone of singularity lies on the growth axis. We find a selection mechanism, by using localized perturbations, for the dendritic growth even when the surface tension is isotropic. We show that it is possible to act on the complex plane and to modify at distances the growth rate and the shape of the solidification front. Moreover, we stress here the influence of localized perturbations on the measurement of the constant of stability ${\mathrm{\sigma }}^{\mathrm{*}}$ of the needle crystal.

An extensive numerical study of level-spacing properties of rational and irrational polygonal billiard systems is carried out. It is found that level statistics of both rational and irrational polygonal billiards deviate from a Gaussian-orthogonal-ensemble-type fluctuation. It is also explored in detail whether the polygonal billiards with the infinite genus number provide different level-spacing characteristics from those with the finite genus number. Some delicate problems in dealing with several types of pseudointegrable systems are also discussed.

The conditions for the existence of negative-energy electrostatic waves (which could be nonlinearly unstable and cause anomalous transport) are investigated for the case of an inhomogeneous force-free Vlasov-Maxwell equilibrium with sheared magnetic field. The method of investigation consists in evaluating the general expression for the second-order wave energy derived by Morrison and Pfirsch [Phys. Rev. A 40, 3898 (1989); Phys. Fluids B 2, 1105 (1990)] in the form given by Correa-Restrepo and Pfirsch [Phys. Rev. A 45, 2512 (1992)]. In Cartesian coordinates, the equilibrium magnetic field is given by ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$=${\mathit{B}}^{\mathrm{}\left(0\right)\mathrm{}}$(sinay${\mathbf{e}}_{\mathit{x}}$+cosay${\mathbf{e}}_{\mathit{z}}$). In this case, there is an electric current parallel to the magnetic field, and the charged particles of any species belong (according to the values of their constants of the motion) to either one of two essentially different groups, either to the group of gyrating particles (the overwhelming majority in all cases of interest), which move around the field lines, their motion being confined to a certain y region around y=${\mathit{scrY}}_{\nu }$, or to the group of swinging particles, which move freely in the y direction. The two groups of particles must be investigated separately.

Owing to the presence of the electric current associated with nonvanishing a, the equilibrium distribution function ${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$=${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$(scrH,scrU) [with scrH(v) the energy and scrU(v,y) a certain velocity variable] of at least one particle species ν must be anisotropic, unlike in the homogeneous case. If any ${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$ has the property ${\mathit{v}}_{\mathit{y}}$∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$>0 for some scrH and scrU, negative-energy waves exist for any wave number k, irrespective of its magnitude and orientation. If ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0 holds, only the waves with a component ${\mathbf{k}}_{\mathrm{\parallel }0}$ of k in the direction of ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$(${\mathit{y}}_0$) can possess negative energy. If ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0, but A≡${\mathit{k}}_{\mathrm{\parallel }0}^2$〈${\mathit{w}}_{\mathrm{\parallel }0}$〉 〈${\mathbf{e}}_{\mathit{B}}$(${\mathit{y}}_0$)⋅(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂v)〉≳0(${\mathit{w}}_{\mathrm{\parallel }}$0 is a parallel velocity, the 〈 〉 represent a certain averaging process), there are negative-energy waves with no restriction imposed on either ${\mathit{k}}_{\mathrm{\parallel }0}$ (other than ${\mathit{k}}_{\mathrm{\parallel }0}$≠0) or the spatial variation of the perturbation perpendicular to ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$.

This result agrees with that obtained for a homogeneous plasma by Morrison and Pfirsch [Phys. Fluids B 3 (2), 271 (1991)] in the context of drift-kinetic theory. If both ${\mathit{v}}_{\mathit{y}}$(∂${\mathit{f}}_{\nu }^{\mathrm{}\left(0\right)\mathrm{}}$/∂${\mathit{v}}_{\mathit{y}}$)<0 and A<0, negative-energy modes also exist. In this case, the characteristic length for the variation of the perturbation perpendicular to ${\mathbf{B}}^{\mathrm{}\left(0\right)\mathrm{}}$ is ≲${\mathit{a}}^{\mathrm{-}1}$, which, since ${\mathit{a}}^{\mathrm{-}1}$ is the shear length and is usually very large, is not an important restriction, and the possible parallel wave numbers are generally limited to a certain interval related to the magnitude of the gyroradius of the gyrating particles, this also being so in the homogeneous case. The results of that case are of course regained by taking the limit of vanishing shear, a→0. The present results show that large perpendicular wave numbers ${\mathit{k}}_{\mathrm{\perp }}$ are not necessary for the existence of negative-energy waves in the system under consideration, a feature that enhances the relevance of these modes.

Experiments on the grid excitation and subsequent propagation of solitons in a positive-ion–negative-ion–electron plasma are described. In the experiments, the ratio of the negative-ion density to the positive-ion density in a quasineutral plasma is a parameter that can be varied. Hence solitons that are described by either the Korteweg–de Vries or the modified Korteweg–de Vries equations can be experimentally investigated.

A recent model treating the structure of ‘‘simple plasmas’’ as that of high-temperature liquid metals is used here to calculate the equation of state of dense beryllium plasmas, for values of compression between 0.2 and 6, and temperatures up to 100 eV. This model gets rid of the standard simplified descriptions of ionic distributions (isolated ion sphere, uniform positive background, etc.); it applies when the electronic structure justifies the use of a binary pair interaction. This interaction is calculated, for every density and temperature, using the self-consistent electronic charge density obtained in a density-functional-theory calculation. The statistical mechanics of the ion fluid is treated via a modified hypernetted-chain integral equation. The various contributions to the equation of state are presented and discussed, and comparisons with other theories are made.

The uniformity of electron temperature (${\mathit{T}}_{\mathit{e}}$) along an x-ray laser plasma produced by a line-focused laser was investigated with precise space- and time-resolved measurements. Thomson scattering of a uv probe by the plasma was used to measure the spatial variation of ${\mathit{T}}_{\mathit{e}}$ along the line focus. This characterization was complemented by spatially resolved L-shell x-ray spectroscopy. Electron temperatures obtained from the n=4→2 F-like to Ne-like line ratios agree well with the results from Thomson scattering. Interferometry and x-ray imaging were also used to aid in the diagnosis of the plasma. The inhomogeneities observed are typical of those to be expected in x-ray laser experiments and can lead to significant reduction of the inferred gain on the Ne-like transitions.

A resistive model including additional dc currents and electrodes enables understanding and analysis of rf discharges in the low-frequency range (ω≪${\mathrm{\omega }}_{\mathit{p}\mathit{i}}$). A general and exact analysis based on asymptotic solutions results in analytic representations of relations between sheath voltages, bias, and rf voltage. For sinusoidal rf voltage an expansion of sheath voltages and discharge current into Fourier series, e.g., important for probe measurements, and a general relation between these series is presented. From the power balance a lower bound of a sinusoidal rf voltage is derived. The model is extended for different densities and electron temperatures along the sheath edges. Correction and error estimation show the asymptotic solution to be well suited.

The longitudinal and transverse collective modes in a nonrelativistic electron-positron plasma are studied in two cases: a static uniform magnetic field is present or absent. The dispersion relations for the longitudinal and transverse collective modes in the absence of a magnetic field and those for the longitudinal mode in the presence of a magnetic field (Bernstein mode) are found to be similar to those for the one-component electron plasma. The transverse modes in the presence of a magnetic field, on the other hand, are found to be quite different from the electron-ion plasma: The dispersion relations for the left- and right-circularly polarized waves propagating parallel to the magnetic field are found to be identical. In addition to the transverse plasma oscillations, the low-frequency Alfvén mode exists, while the whistler mode does not exist. For waves propagating perpendicular to the magnetic field, the extraordinary wave becomes a pure transverse mode. In the cold-plasma limit, there is only one resonance at the cyclotron frequency and one cutoff frequency for the extraordinary mode, in contrast to the electron-ion plasma, where there are two hybrid resonances and two cutoff frequencies.

We present a theoretical study and a numerical simulation of the formation and development of the cathode region (cathode-fall and negative-glow ones) in ${\mathrm{CO}}_2$ and ${\mathrm{N}}_2$ discharges from the inception of the discharge to its stationary state. The model is a self-consistent one: the distribution of the electric field is found from the charge carriers and the hydrodynamic moment equations (density, velocity, energy) are solved by a sophisticated flux-corrected transport method. The ionization and excitation source terms are calculated using an electron-energy distribution function which takes into account the electron-density gradient and the local electric field. The results show that this choice is more realistic in representing the spatiotemporal evolution of the cathode region. Our theoretical results are compared with the experimental ones obtained by other authors and a good agreement is observed concerning the current intensity and the spatial distribution of light in the cathode region in ${\mathrm{N}}_2$.

The state-specific drift velocity of ${\mathrm{Ca}}^{+}$ ions in the 3 ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{3/2}^{}{}_{}{}^{}$ metastable state and of ${\mathrm{Cd}}^{+}$ in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ highly excited state in a helium glow-discharge plasma have been precisely measured by using a tunable single-mode diode laser and the state-specific mobility of excited ions has been discussed. The results show that the mobility of ${\mathrm{Ca}}^{+}$ ions in the metastable state is determined by momentum-loss collisions and is almost identical with the value for ${\mathrm{Ca}}^{+}$ in the ground state. In the experiment with a thin cylindrical tube, the apparent value of the mobility is dependent on the diffusion in the radial direction. On the other hand, the apparent mobility of ${\mathrm{Cd}}^{+}$ ions in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ state is much smaller than the calculated result for ${\mathrm{Cd}}^{+}$ in the ground state, but the value increases significantly with Cd vapor density. This is explained by the fact that ${\mathrm{Cd}}^{+}$ ions in the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ highly excited state decay quickly by the radiative process and the apparent mobility of the ${\mathrm{Cd}}^{+}$ ions in this state in the plasma is dependent not only on the radiative lifetime but also on the excitation mechanisms for the state.

The multifractal structure of flow distribution is investigated in the river-network model of Scheidegger [Bull. IASH 12, 15 (1967)]. It is shown that the partition function Z(q)==${\mathit{tsum}}_{\mathit{i}}$${\mathit{I}}_{\mathit{i}}^{\mathit{q}}$ scales as Z(q)≊${\mathit{L}}^{\mathrm{\zeta }\left(\mathit{q}\right)}$ where ${\mathit{I}}_{\mathit{i}}$ is the flow of water passing over the bond i within the river network, the summation ranges over all bonds, and L is the size of the river network. In the limit of a sufficiently large q, ζ(q)/q gives the exponent of the drainage basin of a river. The exponent also equals to the fractal dimension ${\mathit{d}}_{\mathit{f}}$ of a single river. The f-α spectrum of the normalized flow distribution is calculated. It is found that the fractal dimension ${\mathit{d}}_{\mathit{f}}$ of a river is exactly given by ${\mathit{d}}_{\mathit{f}}$=2-α(∞). The flow distribution shows a characteristic multifractal structure for the river network. The river-width distribution also shows the multifractality if the width w of a river scales as w≊${\mathit{I}}^{\mathrm{\beta }}$.

The influence of an applied electric field on the impact ionization and on the mass-action law of a nonideal hydrogen plasma is discussed. The coupling of field and many-body effects leads to a minimum behavior of the impact-ionization coefficient as a function of the plasma density.

A diagrammatic technique has been worked out in the framework of nonequilibrium statistical mechanics as developed by Prigogine and co-workers to tackle the problem of radiation emission from a relativistic electron in an ambient plasma embedding an axial-wiggler magnetic field. The theory is exact in that the diagrams contributing towards the self-consistent-field approximation have been summed up exactly and one obtains a time-dependent response function. The kinetic regime has been obtained by eliminating the memory by taking an asymptotic limit in time. Explicit calculations have been affected to obtain functions like the Čerenkov angle and the refractive index as well as the power emitted by the system. It has been shown that the radiation emitted has very peculiar polarization features.

We have derived expressions for the longitudinal and transverse resistive wall coupling impedances for a beam pipe of arbitrary cross section in the ultrarelativistic limit. These expressions involve the integral of the square of the tangential magnetic fields along the wall, which can be obtained from the solution of the two-dimensional Poisson equations with a monopole and dipole singularity, respectively. Explicit results are given for beam pipes of elliptical and rectangular cross sections, including the limiting cases of a circle and a pair of parallel plates.