A convenient method for measuring the dc Kerr effect on the stage of a polarizing microscope is described. Two novel illustrations of this technique are presented: a low-field determination of the pretransitional Kerr effect in the isotropic phase of a nematic having a negative dielectric anisotropy and measurements of the birefringence on both sides of the nematic-isotropic ($N-I$) phase boundary as the $N-I$ critical point is approached by applying very high electric fields to a nematic with positive dielectric anisotropy.

We continue our study of local interface models for dendritic growth by presenting detailed numerical simulations of the evolution of snowflake patterns. The local model we employ is quantitatively valid for early stages of the dendritic growth process and is qualitatively similar to the true diffusion-controlled dynamics as far as single-tip behavior is concerned. We show that a critical value of the crystal anisotropy must be exceeded before the system settles into stable tip and repeated side-branching behavior. Varying the anisotropy and measuring the dendrite velocity enables us to get a quantitative picture of the tip dynamics. In addition, we study global features of the evolving patterns, and find exponential growth for the curve complexity, $\xi \equiv \left[\frac{\left(\mathrm{arclength}\right)}{{\left(\mathrm{area}\right)}^{\frac{1}{2}}}\right]$. Our results are not consistent with a simple version of the marginal stability hypothesis of Langer and Müller-Krumbhaar.

Thermodynamic properties of strongly coupled classical ions in the polarizing background of degenerate electrons are analyzed by numerical experiments. The effect of finite electron temperature is taken into account. The internal energy, the pressure, the pair-correlation function, and the structure factor of ions are obtained, and the effects of electronic screening on these quantities are clarified.

A new approach is developed to solve the integral Boltzmann equation for the evolving velocity distribution of a source of ions, undergoing electrostatic acceleration through a neutral gas target. The theory is applicable to arbitrarily strong electric fields, any ion- to neutral-mass ratio greater than unity, and is not limited to spatially isotropic gas targets. A hard-sphere collision model is used, with a provision for inelasticity. Both axial and radial velocity distributions are calculated for applications where precollision radial velocities are negligible, as is the case for ion-beam extraction from high-pressure sources and drift tubes operated with strong electric fields.

We have performed a nonequilibrium molecular-dynamics (NEMD) computation of thermal conductivity for a simple dense fluid near the triple point using the differential NEMD method and a translationally invariant algorithm recently proposed by Evans. We have simulated a set of thermal gradients in the range 75.8 K/cm to 2.54 × ${10}^8$ K/cm. Our main conclusion concerns the response of the energy current at $\overrightarrow{\mathrm{K}}=\overrightarrow{0}$, which is linear in the range indicated. To check the efficiency of the present NEMD technique we have compared the nonequilibrium results with our own and Levesque's equilibrium Green-Kubo results. The agreement found is remarkable.

An asymptotic evaluation of the specific heat of an ideal relativistic Bose gas confined to a cuboidal enclosure ($L_1\times L_2\times L_3$) is carried out, under periodic boundary conditions, taking into account the possibility of particle-antiparticle pair production in the system. Finite-size corrections to the standard bulk behavior are calculated explicitly in the regions $t>\mathrm{}0\mathrm{}$ and $t<\mathrm{}0\mathrm{}$, where $t=\frac{(T-T_c)}{T_c}$, such that $\left|t\right|\ll 1$ and $\left|L_{i}t\right|\gg 1$. While for $t>\mathrm{}0\mathrm{}$ finite-size corrections turn out to be exponential for all geometries, for $t<\mathrm{}0\mathrm{}$ this is true only in the case of a film; for other geometries, such as a cuboid or a rectangular channel, these corrections conform to a power law instead. Finally, we consider the situation in the core region, where $\left|L_{i}t\mathrm{}\right|=O\left(1\mathrm{}\right)\mathrm{}$, and examine the location $t^{*}$ and the height $c_{\rho }^{*}$ of the specific-heat maximum; finite-size corrections in this region turn out to be $O\left(L_{<}^{-1\mathrm{}}\right)$, where $L_{<}$ denotes the shortest side of the enclosure.

We define a family of models to describe cluster growth in random media. These models depend on a temperaturelike parameter and interpolate continuously between the Eden model and the invasion model recently introduced in the study of flow in porous media. Numerical results are presented in two dimensions for a version of these models where growth is biased in a given direction. Directed-invasion clusters are fractal with the same exponents as directed-percolation clusters, but for the other cases studied the clusters are compact. They remain compact even when a "trapping" rule prevents internal holes from being filled.

A mode-coupling formalism is developed for nonequilibrium stationary systems which are close to thermodynamic criticality. Formulas for the calculation of dressed transport coefficients in such systems are found. Applications of the formalism are presented in the following paper.

The mode-coupling formalism, developed in the preceding paper, is applied to heat-conducting fluid systems near the gas-liquid critical point. Expressions for the nonequilibrium dressed thermal diffusitivity and kinematic viscosity are presented. The main findings are as follows: The dressed transport coefficients become anisotropic. For a wave vector parallel to the temperature gradient, the transport coefficients gain a new divergent contribution. For a wave vector perpendicular to the temperature gradient, the equilibrium form is retained.

In this paper we have made a theoretical investigation of the stimulated Brillouin and Raman backscattering of laser radiation at the upper hybrid frequency in a laser-produced plasma, taking into account the effects of a spatially uniform self-generated magnetic field of the order of a few megagauss. The Vlasov equation has been employed to obtain the nonlinear electron density perturbation due to the low-frequency short-wavelength electrostatic mode and the current density due to the high-frequency, unmagnetized, scattered laser radiation in the plasma. This kinetic treatment is valid for plasmas produced by both ${\mathrm{CO}}_2$ and Nd-glass lasers and short-wavelength perturbations. It is noticed that the growth rates for both Brillouin and Raman backscattering increase with the self-generated magnetic field.

The properties of the nematic-isotropic interface of some members of the homologous series of 4-cyano-4′-($n$-alkyl)biphenyl liquid crystals [$n$-pentyl (5CB), $n$-hexyl (6CB), $n$-heptyl (7CB), and $n$-octyl (8CB)] are studied by optical reflectometry. The thickness of the interface is obtained by measuring the ratio of the actual reflected intensity to the value expected for a sharp interface. We find an effective thickness of order 400 Å in 5CB, 7CB, and 8CB, and of order 750 Å in 6CB. As shown by some authors, the effective thickness $L$ is related to the superposition of two different contributions: an intrinsic diffuse profile due to density and order-parameter variations across the interface and an apparent diffuse profile of the interface due to surface capillary waves. Both of these contributions are accounted by us in our theoretical analysis. The intrinsic thickness is obtained in a satisfactory agreement with the predictions of the Landau—de Gennes theory. The easy polar angle is obtained by measuring the intensity anisotropy for the reflected extraordinary and ordinary waves. In all these samples the director is found to be tilted with respect to the vertical axis with a tilt angle which ranges from 48.5° in 8CB to 64.5° in 6CB. The anchoring energy coefficient $W$ at the interface is obtained by applying an orienting torque by means of a horizontal magnetic field and by measuring the corresponding variation of the surface polar angle. We find $W$ ranges from 0.84 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$ ${\mathrm{rad}}^2$ in 6CB to 8.5 × ${10}^{-4\mathrm{}}$ erg/${\mathrm{cm}}^2$ ${\mathrm{rad}}^2$ in 8CB. The experimental results are discussed in terms of the Landau—de Gennes expansion of the free energy and of the Parsons theory of the surface tension. All the phenomenological coefficients of this latter theory are obtained for the first time.

An experimental apparatus is set up to check, via analog circuits, the recent theoretical predictions of Graham and Schenzle [Phys. Rev. A 26, 1676 (1982)] on a Brownian particle with damping $\gamma$ in the presence of a fluctuating double-well potential, the fluctuations of which are characterized by the correlation time $\frac{1}{\lambda }$. They pointed out the basic role played in the overdamped regime by the parameter $r\equiv \frac{\gamma }{\lambda }$, which leads the system either to the Itô regime ($r\to 0$) or the Stratonovich one ($r\to \infty$). In the weak-noise region, these predictions are found to be correct. It is shown furthermore that with increasing intensity of the multiplicative noise the system exhibits a gradual transition from this to an inertial regime which can be accounted for by using the approach recently followed by Seshadri, West, and Lindenberg [Physica (Utrecht) A 107, 219 (1981)]. It is also shown that this transition is a synergic effect based on the cooperation of nonlinearity, inertia, and energy pumping.

The Landau theory of blue phases (BP) in cholesteric liquid systems is further developed by systematically including the effect of higher harmonics in the structure factor on the free energy. The inclusion of a third harmonic results in two new body-centered-cubic (bcc) structures, $O_b^8$ and $O_c^8$, in addition to the bcc $O^5 \left(I432\right)$ and $O_a^8 \left(I{4}_{1}32\right)$ and simple-cubic $O^2 \left(P{4}_{2}32\right)$ structures previously obtained [Phys. Rev. A 28 1114 (1983)] in the two-harmonic framework. Introducing a fourth harmonic does not lead to any further structures or significant changes in the free energies. Detailed results of the Landau-theory calculations are compared with experimental data and those obtained with other models. It is shown that, in general, the observed properties of BP I and BP II are consistent with the structure assignment BP $\mathrm{I}\leftrightarrow O_c^8$ and BP $\mathrm{II}\leftrightarrow O^2$. Some points requiring further investigation and clarification are indicated.

The existence and stability of three-dimensional envelope solitons in nonlinear media are investigated. In the first part, the scalar exponential nonlinear schrödinger equation is considered to demonstrate the main method for a simple example. In the second part, the investigation is based on the vectorial exponential nonlinear Schrödinger equation, describing envelope solitons in plasma physics and nonlinear optics. When considering the stability of the stationary spherically symmetric solutions, one finds that (i) for large ${\eta }^2$ (nonlinear frequency shift) three-dimensional solitons are completely stable; (ii) a stability threshold in ${\eta }^2$ exists; and (iii) below this threshold, instability occurs. Physically, these results mean that the amplitudes for stable solitons are bounded from below by ${\eta }^2=0.101\mathrm{}25$. The proof is based on a Liapunov functional for stability. The exponential nonlinear Schrödinger equation is a quite simple model for plasma cavitons. Therefore in the third part of the paper, the investigation is generalized to the vectorial nonlinear Schrödinger equation for the high-frequency electric field and the hydrodynamic equations for the ions. The low-frequency part of the electron density is calculated by a Boltzmann distribution including the ponderomotive and ambipolar potential. Again, this model can be handled analytically. It is physically reasonable and covers the main processes apart from kinetic effects. A Liapunov functional is constructed from the constants of motion; it shows the same definiteness properties as in the previous more simple case. Thus the existence of stable spherically symmetric envelope solitons is proved. In the final part of the paper the existence of stable nonenvelope solitons, described by Korteweg—deVries—type equations, is briefly reviewed.

The dielectric functions of electron liquids which take into account short-range electron-electron correlations via the static local-field corrections are examined in the light of the frequency-moment sum rules. The formulation is given for degenerate as well as classical electron liquids in arbitrary ($d$) spatial dimensions, which is suitable for comparison between the two- and three-dimensional cases. By using the virial equations of state it is shown that such dielectric functions cannot satisfy the compressibility sum rule and the third-frequency-moment sum rule simultaneously. In the degenerate case, the plasmon, single-pair, and multipair contributions to the sum rules are analyzed, and the reason for this incompatibility is discussed.

We calculate, including many-body effects, that the three lowest bound states of ${\mathrm{Mg}}^{-}$, $2p^{6}3s3p^2{}_{}{}^4{}_{}{}^{}P$, $2p^{6}3p^3{}_{}{}^4{}_{}{}^{}S_{}^0{}_{}{}^{}$ and $2p^{5}3s3p^3{}_{}{}^6{}_{}{}^{}P$, have electron affinities 0.360, 0.514, and 1.321 eV, respectively. The transition $3s3p^2{}_{}{}^4{}_{}{}^{}P\to 3p^3{}_{}{}^4{}_{}{}^{}S_{}^0{}_{}{}^{}$ is found to have an electric dipole oscillator strength of 0.295. The lifetimes of the $J=\frac{1}{2}, \frac{3}{2}, \mathrm{and} \frac{5}{2}$, ${}_{}{}^4{}_{}{}^{}P$ levels are estimated to be 7.8, 9.8, and 1.6 ns, respectively.

To demonstrate its attractiveness, the distribution function for the atomic coherent states called the $Q$ representation is used to describe the evolution of superfluorescence. An exact Fokker-Planck equation in the phase space is obtained. It indicates that the dynamics is almost completely classical, even in the very beginning. This implies that all the fluctuations in superfluorescence must originate from the initial distribution corresponding to a complete inversion. Therefore, in a sense, the initial tipping angle possesses physical reality and is not fictitious.

The Laplace-transformed Heisenberg equations of motion are resummed in such a way that the resulting iterative series expansion of any operator is given in terms of exact perturbed operator self-energies. We show how to incorporate this result into a recently introduced Liouvillian Green's-function and self-energy approach to nonequilibrium statistical mechanics. The spontaneous emission of a two-level atom is discussed as a simple example of this new resummation technique.

In a recent paper a mathematical identity was obtained which generalizes Onsager's reciprocity theorem to situations far more general than the ordinary linear case. However, the relationship of an important matrix that appears in the analysis to the dynamics of the system was not given. In this paper we show how this can be done for two particular cases, and, furthermore, we derive a differential equation that must be satisfied by the microcanonical average of that matrix in the general case.

We comment on some experimental and theoretical results of a recent paper by Hemmati, Fairbank, Jr., Boyer, and Collins [Phys. Rev. A 28, 567 (1983)].