Using polarization microscopy, we have investigated the director configurations of droplets of a nematic liquid crystal with negative dielectric anisotropy and perpendicular boundary conditions subjected to electric fields. The droplets were suspended in liquid poly(dimethyl siloxane) and electric fields were applied both parallel and perpendicular to the viewing direction. The resulting director pattern is deduced by comparing the experimental transmission patterns with patterns calculated from various director models. For low fields, we observe a director field which is essentially radial, but with some azimuthal twist superimposed and a radial point (hedgehog) defect at the center. At intermediate fields, the hedgehog defect moves away from the center along the electric-field direction, while at the highest fields a line defect appears which lies along the diameter parallel to the field. Comparison of the transmission patterns with model calculations yields good agreement for the low- and intermediate-field cases, and reasonable agreement for the high-field case.

In order to investigate thermodynamic properties and microscopic structure around the crystal-smectic transition, we present constant-pressure molecular-dynamics simulations for soft parallel spherocylinders as a model for liquid crystals. The method of Andersen [J. Chem. Phys. 72, 2384 (1980)] as well as the method of Parrinello and Rahman [Phys. Rev. Lett. 45, 1196 (1980)] are applied to a right parallelepiped simulation box, and the equation of state for this model is evaluated. Thermodynamic properties such as enthalpy and volume as functions of reduced density ${\mathrm{\rho }}^{\mathrm{*}}$ or of temperature show a clear first-order transition. The dependence of ${\mathit{l}}_{\mathrm{\perp }}$ the square root of the specific area of the plane perpendicular to the molecular axis, on ${\mathrm{\rho }}^{\mathrm{*}}$ shows a feature characteristic of two-dimensional melting. We calculate the specific length ${\mathit{l}}_{\mathit{z}}$ in the direction of the molecular axis, which corresponds to the thickness of a smectic layer in the liquid-crystal region. From the ${\mathrm{\rho }}^{\mathrm{*}}$ dependence of ${\mathit{l}}_{\mathit{z}}$ and ${\mathit{l}}_{\mathit{z}}$/${\mathit{l}}_{\mathrm{\perp }}$, we show that the anisotropy of the molecular volume plays an important role in the crystal-smectic transition. We also observe a clear change in both diffusion and structural properties before and after this transition. The mean-square displacements in directions perpendicular to the alignment show that in the smectic phase the moleules diffuse freely within the layers, although the density wave in the direction perpendicular to layers does exist even after the transition.

Dynamic light scattering from polymer gels is complicated by the fact that the scattering intensity and its time correlation function change as different parts of a sample are explored. This results from the nonergodicity of the sample—time averages are not the same as ensemble averages, the result of a finite rigidity that leads to constrained inhomogeneities. We demonstrate a direct technique for ensemble averaging (by moving the sample), present the experimental correlation function containing correlations that do not decay with time, and show that the light scattering results from a superposition of static scattering from immobile inhomogeneities and dynamic density fluctuations from ‘‘gel modes.’’

The longitudinal dielectric susceptibility of a polar (directed) thermotropic main-chain nematic polymer is derived in the mean-field approximation, accounting for long-range interaction forces and the local-field effects in the media. It is shown that this susceptibility exponentially increases for some range of orientational order and then either diverges or saturates at some characteristic degree of order. This is expected in some circumstances to result in a true ferroelectric phase. A simple calculation of this transition is given, assuming that long-range dipolar interactions are the only relevant polar interactions. Other relevant effects and the limitations of our approximation are discussed briefly.

We study the geometric behavior of the neutral modes of the linearized equations from four directional-solidification models in terms of singularity theory. These equations admit well-known diffusive or Mullins-Sekerka instabilities. For a range of solidification velocity ${\mathit{V}}_{\mathit{c}}$<V<${\mathit{V}}_{\mathit{a}}$, a planar solidification front is linearly unstable to a range of disturbances. The standard neutral curve in linear theory exhibits weak wavelength selection for V near ${\mathit{V}}_{\mathit{c}}$. An equivalence transformation of the neutral-stability relation of the nonsymmetric model distinguishes the basic geometric behavior of this system. The neutral-stability relation is an unfolding of a cubic cuspoid normal form. The solution space of this system is a cusp manifold, generated by families of neutral curves each forming a path in the manifold. This manifold connects two unfolding theories, allowing us to show the sense in which ${\mathit{V}}_{\mathit{c}}$ and ${\mathit{V}}_{\mathit{a}}$ parametrize degenerate singular points and to show that these points are structurally unstable as critical points. We show that wavelength selection is enhanced in the neutral curves of the transformed system, and that the singularity set of the manifold demarcates stability regions solely in terms of control variables. A particular neutral curve will be open or closed depending on how its path crosses the singularity set, and the system will not admit hysteresis. The weak wavelength selection is due not only to the thermophysical or control parameters of the material, but to the singular behavior that is intrinsic to the formulation. We show that four solidification models possess cubic normal forms, and that asymptotic limits reveal two different normal forms. The main goal is to point out the geometric structure of a model, and to show how one can distinguish different solidification formulations and asymptotic limits, using simple geometric criteria.

The shape of xenon dendrites has been studied in situ during growth into a three-dimensional ‘‘infinite’’ volume of supercooled melt. The contours of dendrite projections have been extracted from digitized video pictures by an image processing system. In difference to earlier studies of the properties of the dendrite tip, the whole dendrite has been investigated now. Special emphasis was given on the development of sidebranches and the coarsening process in dendrite regions far away from the dendrite tip. No reproducible parameters have been found to characterize individual sidebranches far from the tip. The following geometry parameters of the dendrite have been determined: the radius of curvature R of the dendrite tip, the distance ${\mathit{z}}_{\mathrm{SB}}$ between the tip and the position of the first sidebranch with an amplitude of about 1 R and the amplitude ${\mathit{w}}_{\mathit{p}}$ of the sidebranches as a function of the position ${\mathit{l}}_{\mathit{p}}$ at the fins along the dendrite. These measurements have been performed in the supercooling range 0.025 K≤ΔT≤0.150 K. Parameters which characterize individual sidebranches do not take into account the interaction of the sidebranches through the diffusion field. An alternative set of integral parameters is proposed: the contour length U, the projection area F, and the volume V of a dendrite. These parameters characterize the integral dendrite. They have been measured in the supercooling range 0.025 K≤ΔT≤0.170 K.

The measurements show that parameters characterizing a dendrite are scaled by the tip radius R: (1) The position of the first sidebranch, i.e., the distance ${\mathit{z}}_{\mathrm{SB}}$ from the tip where a sidebranch has the amplitude 1 R is about 18R for any supercooling. (2) The sidebranch spacing S near the tip scales with R, i.e., S/R is independent of supercooling. S/R=3.2±0.4. (3) The amplitude ${\mathit{w}}_{\mathit{p}}$ of the sidebranches which build the envelope increases with ${\mathit{l}}_{\mathit{p}}$ as (${\mathit{w}}_{\mathit{p}}$/R)∝(${\mathit{l}}_{\mathit{p}}$/R${)}^{1.78}$. (4) The projection area F of the dendrite is proportional to the contour length U. The proportionality is 4R. (5) The filling factor V/[(4π/3)${\mathit{L}}^3$] of a sphere with a volume (4π/3)${\mathit{L}}^3$, which contains a dendrite of overall dimension L, is proportional to R.

The spherical-cell model [F. Perrot, Phys. Rev. A 25, 489 (1982); M. W. C. Dharma-wardana and F. Perrot, ibid. 26, 2096 (1982)] is improved to investigate laser-produced hot, dense plasmas. The free-electron distribution function around a test free electron is calculated by using the Fermi integral in order that the free-electron–free-electron correlation function includes Fermi-degeneracy effects, and also that the calculation includes the discrete-ion effect. The free-electron–free-electron, free-electron–ion, and ion-ion correlation effects are coupled, within the framework of the hypernetted-chain approximation, through the Ornstein-Zernike relation. The effective ion-ion potential includes the effect of a spatial distribution of bound electrons. The interparticle correlation functions and the effective potential acting on either an electron or an ion in hot, dense plasmas are calculated numerically. The Fermi-degeneracy effect on the correlation functions between free electrons becomes clear for the degeneracy parameter θ≲1. The discrete-ion effect in the calculation of the correlation functions between free electrons affects the electron-ion pair distribution functions for ${\mathit{r}}_{\mathit{s}}$≳3. As an application of the proposed model, the strong-coupling effect on the stopping power of charged particles [Xin-Zhong Yan, S. Tanaka, S. Mitake, and S. Ichimaru, Phys. Rev. A 32, 1785 (1985)] is estimated. While the free-electron–ion strong-coupling effect and the Fermi-degeneracy effect incorporated in the calculation of the free-electron distribution function around a test free electron enhance the stopping number, the quantum-diffraction effect incorporated in the quantal hypernetted-chain equations [J. Chihara, Prog. Theor. Phys. 72, 940 (1984); Phys. Rev. A 44, 1247 (1991); J. Phys. Condens. Matter 3, 8715 (1991)] reduces the stopping number substantially.

A preliminary investigation is presented of electron-positron pair production by means of plasma electrons accelerated by relativistic velocities in a strong wake field. The propagation distance of the plasma wake field, which is determined by the depletion of the short laser pulse due to wake-field generation, is much larger than the pulse length. For this case, the total number of electron-positron pairs produced is independent of the plasma concentration. For achievable parameters of the laser pulse, the total number of pairs may be quite significant (∼${10}^6$${\mathit{Z}}^2$, where Z is the nuclear charge of the plasma ion).

A self-consistent multiple-scattering theory of vector electromagnetic waves scattered from a turbulent plasma is presented. This approach provides a general and systematic treatment to all orders in turbulence of the scattering of electromagnetic waves in terms of the properties of the turbulent structure of the scattering system and is applicable in the full regime from underdense to overdense plasmas. To illustrate the theory, a plasma consisting of a finite number density of discrete scatterers with a simple geometry and statistical properties is chosen. In this approach the exact solution for a single scatterer is obtained first. From it the configuration-dependent solution for N scatterers is constructed. Rather than solving explicitly for this solution and then averaging, the averaging operation will be taken first in order to find an approximate equation obeyed by the mean or coherent field. The coherent and incoherent scattering are then determined in terms of the coherent field and the backscatter is evaluated. The coherent and incoherent scattering, our principal results, are expressed in a plane-wave basis in a form suitable for numerical computation. A number of interesting phenomena which may readily be incorporated into the theory are indicated.

We present a simple analytic model for ablative stablization of the Rayleigh-Taylor instability. In this model the effect of ablation is to move the peak of the perturbations to the location of peak pressure. This mechanism enhances the density-gradient stabilization, which is effective at short wavelengths, and it also enhances the stabilization of long-wavelength perturbations due to finite shell thickness. We consider the following density profile: exponential blowoff plasma with a density gradient β, followed by a constant-density shell of thickness δt. For perturbations of arbitrary wave number k, we present an explicit expression for the growth rate γ as a function of k, β, and δt. We find that ‘‘thick’’ shells defined by β δt≥1 have ${\gamma }^2$≥0 for any k, while ‘‘thin’’ shells defined by β δt<1 can have ${\gamma }^2$<0 for small k, reflecting stability by proximity to the back side of the shell. We also present lasnex simulations that are in good agreement with our analytic formulas.

In order to produce electron beams with the minimum possible energy spread we have investigated the possibility of replacing the usual thermocathodes with a photoemissive source such as GaAs. A comparison carried out between these two sources indicated the latter as the best device to obtain a very-low-energy spread. Beam relaxation after emission also leads to an increase in the energy spread. Therefore an experimental study on the nature of relaxations occurring in electron beams, yielded both by a thermocathode and by a photocathode, has been performed. More specifically, we investigated the possibility of reducing the transverse-longitudinal and the longitudinal-longitudinal relaxations. With this aim, the features of adiabatic acceleration, which damp the pure longitudinal relaxation, have been examined. The experience gained during the measurement cycle demonstrated that an adiabatic structure, accelerating electrons emitted by a GaAs photocathode, leads to the best performances.

An approach for estimating the luminosity in linear colliders in the presence of spherical aberrations is developed within the framework of the recently proposed thermal-wave model for relativistic-charged-particle-beam propagation. By taking into account a quadrupolelike lens with octupole deviations, the transverse beam motion is governed by a two-dimensional Schrödinger-like equation, with an anharmonic potential. To first order in perturbation theory and in the thin-lens approximation, we analytically find the transverse beam density, the spot size, and the luminosity reduction factor at the interaction point in terms of the initial conditions. Some numerical estimates are also given.

The application of a focused laser beam to accelerate particles using the longitudinal electric-field component is investigated one step beyond the paraxial-ray approximation. Vacuum acceleration to high energies along the axis of an asymmetric Hermite-Gaussian beam is in principle possible, but the interaction distance is short (one Rayleigh length on each side of focus). The use of a gas can increase the energy gain per focal passage by a factor of 2.4, while permitting arbitrary spacing of drift tubes and lenses of a lens waveguide. Drift tubes are therefore not needed. A beam loaded with a graded-index gas, in which phase and particle velocities are equal over the interaction trajectory, permits three-dimensionally stable particle trajectories. This property is explained by the anisotropy of the medium in a comoving reference frame. The functions of acceleration, focusing, and bunching of particles can thus be performed simultaneously by a single optical beam that is guided in a lens waveguide.

The cyclotron-resonance laser (CRL) accelerator is a novel concept of accelerating continuous charged-particle beams to moderately or highly relativistic energies. This paper discusses prospects and limitations of this concept. In particular, the nonlinear coupling of an intense traveling electromagnetic wave with an electron beam in a guide magnetic field is studied, and the effects of wave dispersion on particle acceleration are analyzed. For a tenuous beam, it is shown in a single-particle theory that the maximum energy gain and the maximum acceleration distance for the beam electrons in CRL accelerators with optimal magnetic taper exhibit power-law scaling on the degree of wave dispersion (measured by the parameter ω/${\mathit{ck}}_{\mathrm{\parallel }}$-1). The maximum energy gain is found to be independent of the wave amplitude, and the accelerating gradient is proportional to the wave amplitude. A self-consistent multiparticle model, which confirms the validity of the scaling laws, is used to study the characteristics of CRL accelerators in moderately high-current, microwave regimes. The parameter regimes of experimental interest are identified. The possibility of building continuous-wave CRL accelerators is discussed. Finally, the results of simulation modeling of a multimegavolt, X-band, electron CRL accelerator are presented.

We have developed a three-dimensional free-electron laser (FEL) theory in the small-signal high-gain regime based upon the Maxwell-Vlasov equations including the effects of the energy spread, the emittance, and the betatron oscillations of the electron beam. The radiation field is expressed in terms of the Green’s function of the inhomogeneous wave equation and the distribution function of the electron beam. The distribution function is expanded in terms of a set of orthogonal functions determined by the unperturbed electron distributions. The coupled Maxwell-Vlasov equations are then reduced to a matrix equation, from which a dispersion relation for the eigenvalues is derived. The growth rate for the fundamental mode can be obtained for any initial beam distribution including the hollow-beam, the water-bag, and the Gaussian distribution. Comparisons of our numerical solutions with simulation results and with other analytical approaches show good agreements except for the one-dimensional limit. We present a handy interpolating formula for the FEL gain of a Gaussian beam, as a function of the scaled parameters, that can be used for a quick estimate of the gain. The present theory can be applied to the beam-conditioning case by a few modifications.

An intense relativistic electron beam with an elongated cross section, propagating in the ion-focused regime through a broad, uniform, unmagnetized plasma, is shown to suffer a transverse flute instability. This instability arises from the electrostatic coupling between the beam and the plasma electrons at the ion-channel edge. The instability is found to be absolute and the asymptotic growth of the flute amplitude is computed in the ‘‘frozen-field’’ approximation and the large skin-depth limit. The minimum growth length is shown to be much less than the betatron period, with the consequence that focusing is rendered ineffective. It is further shown that growth is much reduced when the beam propagates through a narrow channel where the ion density greatly exceeds that of the surrounding plasma. In this limit, a modest spread in betatron frequency produces rapid saturation. The effect of plasma electron collisions is also considered. Results of beam breakup simulations are noted.

A momentum-dependent generalization of the simple pendulum is introduced, which will be called the asymmetric pendulum. A general study of the topology of the system is made. Analytic results concerning the frequency of the periodic motion and the separatrix equation are derived. The interaction between this pendulum and an external time-dependent perturbation, leading to a two-resonance system, is studied in detail. The width of the stochastic layer around the separatrix is estimated both numerically and analytically. The observed separatrix asymmetry is discussed.

A statistical-mechanical lattice model is proposed to describe the acyl-chain main phase transition in a hydrated lipid bilayer. The model is built on a two-dimensional multistate lattice model to describe the intramonolayer interactions within the two separate lipid monolayers of the bilayer. The coupling between the two monolayers is modeled both indirectly by hydrophobic acyl-chain mismatch interactions that ensure compatibility between the two monolayers, and by a direct intermonolayer attractive dispersion force. The nature of the phase transition is studied by computer-simulation methods involving standard Monte Carlo simulation, as well as the extrapolation method of Ferrenberg and Swendsen [Phys. Rev. Lett. 61, 2635 (1988)] and the Lee-Kosterlitz technique [Phys. Rev. Lett. 65, 137 (1990); Phys. Rev. B 43, 3265 (1991)]. It is found that the absence of a phase transition in a set of uncoupled monolayers is restored by a weak intermonolayer interaction. The bilayer properties in the transition region are described with particular emphasis on the lateral density fluctuations and the resulting dynamic bilayer heterogeneity. The theoretical results are discussed in relation to experimental data.

Kaufman’s NK model for genetic evolution and adaption is analyzed for for K=N-1. In this case it describes adaptive walks on random fitness landscapes, and its dynamics is equivalent to the Metropolis algorithm for Derrida’s random-energy model at zero temperature. We derive analytical expressions for the average length and duration of adaptive walks, and for the variance about these averages. The results are exact to leading order in N, the number of genes. We also find that the lengths of walks are Poisson distributed to leading order in 1/lnN, and that the duration of walks essentially is exponentially distributed to leading order in 1/N.

A variant of Kauffman’s NKC-model for the coevolution of haploid organisms is shown to have two phases: a frozen phase in which all species eventually reach local fitness maxima and stop evolving, and a chaotic phase in which a fraction of all species is at local maxima, while another fraction evolves towards maxima. In doing so, they set other species back in evolution, thereby maintaining a steady fraction of evolving species. The evolutionary activity of the steady state is a natural order parameter for the ecosystem. Closed expressions are given for this order parameter and for the system’s relaxation time. The latter quantity diverges at the phase boundary, showing the system is critical there. All results were obtained analytically for the maximally rugged case of K+1=N, and to leading order in N, the number of genes in a species.