A detailed study of turbidity, density, and refractive index in the critical region of two samples of a water in an oil ternary microemulsion system, water plus benzene plus benzyl hexadecyl dimethylammonium chloride (BHDC), is presented. Special care is taken to determine the criticality of the samples. The critical point is approached from the homogeneous phase by varying the temperature at fixed concentrations of the components. Along this path Fisher-renormalized Ising exponents are expected. The critical exponents for the correlation length (ν) and osmotic susceptibility (γ) are determined through the turbidity. The critical exponent α can be deduced from the (1-α) behavior of the density and the refractive index. From mere numerical analysis alone turbidity behavior cannot be distinguished between Ising and Fisher-renormalized Ising exponents. However, physical arguments suggest the latter values for the exponents ν and γ. We do not see any anomaly in the density within a resolution of ±3×${10}^{\mathrm{-}6}$. This is consistent with the renormalization of α [${\mathrm{\alpha }}^{\mathrm{*}}$=-α/(1-α)]. A very weak anomaly in the refractive index is detected which is better described by a function of the exponential type, which has been discussed for a quaternary microemulsion near the critical end point, than the (1-α) power behavior.

We describe how spatial variation in the critical pulling speed for directional solidification is induced by breaking the symmetry about the pulling direction. This spatial variation results in localized nucleation of the Mullins-Sekerka instability. After nucleation, the instability spreads via front propagation. The front propagation is studied as a function of pulling speed, leading to a powerful test of the nature of the bifurcation from the planar to the cellular state. Furthermore, growth in the leading edge of the front is studied in detail, as is the resulting cellular array after the front’s passage. We find that front propagation enhances the wavelength selection dramatically compared to the case where the cellular array nucleates everywhere simultaneously.

We develop a theory of polymers in a nematic solvent by exploiting an analogy with two-dimensional quantum bosons at zero temperature. We argue that the theory should also describe nematic polymers in an isotropic solvent. The dense phase is analyzed in a Bogoliubov-like approximation, which assumes a broken symmetry in the phase of the boson order parameter. We find a stiffening of the longitudinal fluctuations of the nematic field, calculate the density-density correlation function, and extend the analysis to the case of ferro- and electrorheological fluids. The boson formalism is used to derive a simple hydrodynamic theory which is indistinguishable from the corresponding theory of nematic polymers in an isotropic solvent at long wavelengths. We also use hydrodynamics to discuss the physical meaning of the boson order parameter. A renormalization-group treatment in the dilute limit shows that logarithmic corrections to polymer wandering, predicted by de Gennes, are unaffected by interpolymer interactions. A continuously variable Flory exponent appears for polymers embedded in a two-dimensional nematic solvent. We include free polymer ends and hairpin configurations in the theory and show that hairpins are described by an Ising-like symmetry-breaking term in the boson field theory.

It has recently been argued [P. Photinos and A. Saupe, Phys. Rev. A 41, 954 (1990)], on the basis of density measurements (as measured by a vibrating densitometer) and the observation of long relaxation times in both these and electrical conductivity measurements, that the nematic-to-lamellar transition in the cesium pentadecafluorooctanoate(CsPFO)–water system involves a significant change in the aggregate structure, probably a transformation from discotic (disk-shaped) micelles to continuous lamellae. With a view to distingushing between these conclusions and previous ones, by the present authors [N. Boden et al., J. Phys. (Paris) 47, 2135 (1986)], which suggested the transition solely involves the onset of translational order without significant changes in micellar structure, we have made a comparison of the densities of a CsPFO${\mathrm{-}}^2$${\mathrm{H}}_2$O (w=0.406) sample as measured by both a vibrating densitometer and a classical dilatometer. The densitometer measurements exhibit discontinuities at both the isotropic-to-nematic and the nematic-to-lamellar transitions: at the isotropic-to-nematic transition, the specific volume increases by 7×${10}^{\mathrm{-}5}$ ${\mathrm{cm}}^3$ ${\mathrm{g}}^{\mathrm{-}1}$ of solution, a result at variance with a predicted decrease of 1×${10}^{\mathrm{-}7}$ ${\mathrm{cm}}^3$ ${\mathrm{g}}^{\mathrm{-}1}$ as calculated from the previously reported pressure dependence of the isotropic-to-nematic transition temperature [M. R. Fisch, S. Kumar, and J. D. Litster, Phys. Rev. Lett. 57, 2830 (1986)]; a large increase in specific volume is also observed at the nematic-to-lamellar transition.

No such changes are, however, detectable in the dilatometer experiments. This has led us to conclude that the excess specific volumes characterizing the nematic and lamellar phases in the densitometer experiments must be associated with some nonequilibrium state of the sample, induced by the vibration of the sample container. These effects are specific to the liquid-crystal phases, not to the isotropic solution phase, and must therefore arise because of the long-range structural organization of the former. It appears that the vibrating densitometer cannot be used to measure densities of amphiphilic liquid-crystal phases. Hysteresis and long relaxation times observed in electrical conductivity measurements in the lamellar phase are associated with partial focal conic textures; they do not arise from changes in aggregate structure.

We consider a simple model to study the competition and screening between branches of anisotropic structures growing in a Laplacian field. Growth conditions are found where the symmetry between the different growing branches is spontaneously broken. In the case of two branches, we obtain an analytic expression for the ratio of the lengths in the stationary regime as a function of the angle between the two needles. We also find that a symmetric pattern with n branches is unstable for n>6 in the simplest diffusion-limited-aggregation-like case. These results are generalized to the more general problem of dielectric breakdown.

In a dc gas-discharge system we observe experimentally periodic and turbulent behavior of solitary structures, the latter having the form of filaments. It can be shown that turbulence develops due to four kinds of fundamental interactions between the solitary structures: creation, annihilation, elastic reflection, and clustering. It is believed that the experimental results are of general importance for pattern formation in distributive active media.

We have extended the previous analysis of the quantum inverse problem for the Alfvén wave propogation by incorporating boundary conditions other than the periodic ones. Our approach is that of Sklyanin [Func. Ana. Appl. 21, 164 (1986)], which allows one to introduce different boundary conditions at the two ends. A generalized Bethe ansatz is used to deduce the eigenvalues of the Hamiltonian. An immediate outcome of our analysis is the effect of finite-size corrections, which is essential to study scale invariance and conformal properties of the model.

Electron-cyclotron-current-drive (ECCD) experiments performed in the DIII-D tokamak have produced rf-driven currents of up to 100 kA. The experimental results, which exceed predictions using linear theory, are enhanced by the presence of a residual, toroidal dc electric field. These ECCD experiments are performed with plasma conditions sufficient to result in strong localized deposition of the rf power and good confinement of the rf-generated current carriers. These improved conditions permit a test of theory under reactor relevant conditions. Theoretical predictions obtained using a Fokker-Planck code are in good agreement with the experimental results when effects due to electron trapping and the residual dc electric field are included.

The heating of matter driven by thermal radiation is studied by means of a simple model, under conditions where the material cannot freely expand. Supersonic and ablative regimes are identified when the radiation field is not in local thermodynamic equilibrium with the matter and, in a later phase, when equilibrium is reached. The scaling laws characterizing the magnitudes of the heated material are found for the different regimes. Application to an ion-beam-fusion target is examined and the effect of an active tamper that pushes the ablated material is analyzed.

Experimental Stark widths of the 3s ${}_{}{}^2{}_{}{}^{}3\mathrm{p}$ ${}_{}{}^2{}_{}{}^{}\mathrm{°}$ transitions in the Li-like ions C iv, N v, O vi, and Ne viii are reported. The measurements were performed for a set of plasma parameters so that the density and temperature behavior of the Stark widths could be observed and compared with calculations. The experimental results did not show a scaling with ${\mathit{Z}}^{\mathrm{-}2}$, where Z is the spectroscopic charge number, which is expected from theoretical calculations in the electron-impact approximation. Furthermore, deviations from linear scaling appear for Z=8.

The Eggarter-Cohen theory for the mobility edge of electrons in a distorted system has been used, with some modifications, to carry out calculations about the recently found localization-delocalization transition of excess electrons in dense neon gas at temperatures close to the critical point. It is shown that the original choice of the de Broglie wavelength as the sampling length for the intrinsic fluctuations does not reproduce the experimental mobility data. On the contrary, the use of the classical mean free path as the sampling length allows us to reproduce the experimental mobility data over their six-order-of-magnitude decrease as a function of the gas density.

A special superposition of oppositely propagating circularly polarized monochromatic plane waves defines a stationary electromagnetic oscillation in a cavity, with E parallel to B. Inside a plasma, this type of oscillation induces an ac current J that is parallel to the magnetic field B, and is hence force free. In the low-frequency limit, a transient dc plasma current is driven by the special oscillation field. It is shown that these oscillations cannot interact with an externally imposed field ${\mathbf{B}}_0$, so that they exist only if J∥B∥${\mathbf{B}}_0$.

A complete construction of cables with vanishing Lorentz self-force is given (solution of the cylindrically symmetric force-free problem for nonconstant α). A key component of the result is that boundary conditions are intrinsic and cannot be imposed, which implies that many previous solutions of the problem are in fact spurious. Two force-free current ropes are constructed as an illustration. These results have applications in magnetic fusion; space physics, solar physics, and astrophysics; force-reduced superconducting magnet windings; and superconducting cables for power transmission.

In an idealized model of a traveling-wave amplifier operating in the linear regime it is assumed that all the transients have decayed. This implies that the electromagnetic wave has an amplitude which is constant in time but may vary in space according to the interaction process. In an idealized model of an oscillator, the situation is reversed. The amplitude of the electromagnetic wave is constant in space and it may vary in time. We present a generalized formulation of the interaction in a traveling-wave tube which includes reflections and spatial and temporal transients. Within this framework it is shown that, in an amplifier, the reflections cause time variations of the amplitude that are ultimately revealed as a broadening of the spectrum. The ‘‘transition’’ to an oscillator is also investigated. In the case of an oscillator, it is shown that in addition to the well-known temporal transient (lethargy) there is a spatial transient. This is due to the fact that it takes part of the system length for the ‘‘fresh’’ electrons entering the oscillator to get bunched. Beyond this transient the amplitude is constant in space, as anticipated by the idealized theory.

Particle-in-cell simulations of a dielectric Cherenkov maser experiment are used to analyze the emissive characteristics of an annular relativistic beam in a dielectric-lined waveguide. Good agreement with recent experimental results is obtained. The large gain in the device follows linear theory until saturation, when particle bunching and trapping is observed. The beam density becomes highly modulated with pulse length ∼λ/2, where λ is the guide wavelength. The performance of the device in the high-current regime is highly nonlinear. A simple nonlinear theory, confirmed by numerical results, shows that the field saturates at a value corresponding to ${\mathrm{\omega }}_{\mathit{b}}$=Δω/2, where ${\mathrm{\omega }}_{\mathit{b}}$ is the electron bounce frequency in the wave and Δω is the detuning parameter.

We propose a model of gain saturation in free-electron lasers operating with a bunched electron beam. A simple method to evaluate the steady-state intensity as a function of the optical cavity length is given and the result is in close agreement with the intensity measured in the Los Alamos free-electron-laser experiment [B. E. Newnam et al., Nucl. Instrum. Methods A 237, 187 (1985)].

A two-dimensional nonlinear model of a grating free-electron laser is formulated that includes the effects of self-field forces, finite beam emittance, energy spread, and gyromotion of electrons in a guide magnetic field. The start-oscillation current and energy spread requirement for operation at either 100 or 10 μm are determined. The designs call for an electron beam of moderate energy (<1 MV). The extraction efficiency is determined by numerical simulation. Three different examples are studied in order to elucidate the nonlinear stage of the interaction. We analyze the examples of an infinitely thin beam, a finite-thickness beam with laminar flow, and a finite-thickness beam with full transverse motion. For a thick beam we find the interesting result that the effect of electron gyration about the beam axis is to enhance the extraction efficiency as compared to that for a beam with laminar flow. The numerical results for the extraction efficiency are found to be in close agreement with analytical estimates based on a model in which the electrons are trapped in the slow wave associated with the grating structure.

Boundary conditions for the photon-diffusion equation with internal surface reflections are obtained for one, two, and three dimensions, both from transport theory and from approximate solutions of the corresponding Milne equations.

We investigate an alternative model for the propagation of directed waves in strongly disordered media. The basic ansatz of our approach is that impurity scattering events can be described by the action of random S matrices. This approach has two important advantages over those considered in previous works. First, it yields a numerical discretization in which unitarity is manifestly preserved. Second, the model enables one to compute certain averages over disorder exactly. The beam positions [〈${\mathit{x}}^2$〉] and [〈x${\mathrm{〉}}^2$] characterize the transverse fluctuations of a directed wave front, where 〈...〉 indicates an average over the wave profile for a given realization of randomness, and [...] indicates quenched averaging over all realizations. We confirm the well-known result that the beam width [〈${\mathbf{x}}^2$〉] grows linearly with the propagation distance, t. We also obtain numerically in two and three dimensions (2D and 3D) the behavior of the beam center [〈x${\mathrm{〉}}^2$] as a function of t. The results suggest that [〈x${\mathrm{〉}}^2$] scales as ${\mathit{t}}^{1/2}$ in 2D and as lnt in 3D. We show how these scaling laws emerge in a natural way from the problem of two interacting random walkers. Connections to the problem of directed polymers in random media are also explored.

Using a collective-coordinate approach, we study kink propagation along nonlinear systems with local, randomly distributed inhomogeneities. We develop a general method to compute dynamical variable statistics which can be generalized to a number of soliton-bearing systems, and we apply it to the sine-Gordon equation as an example.