Applicability of the mean spherical approximation (MSA) and hypernetted-chain approximation (HNCA) to the analysis of intermicellar structure factors was examined. For a strongly coupled micelle-counterion system at high volume fraction the MSA partial structure factors are close to the corresponding HNCA solutions provided the micellar charge is appropriately reduced in the case of MSA. The same agreement for the micelle-micelle structure factor can still be maintained at low volume fraction by using the previously proposed rescaled MSA. In certain cases, the experimental intermicellar structure factor can be satisfactorily reproduced within the HNCA by assuming the micellar charge to be substantially lower than the mean aggregation number of the micelle.

The spontaneous formation and evolution of stationary cellular interfaces arising in directional solidification of a binary alloy are discussed in terms of bifurcation theory. Algebraic bifurcation equations for the amplitudes of the cells are derived from the nonlinear equations of motion with the interface velocity as a control parameter. It is shown that the form of these bifurcation equations is determined by the system’s symmetry and by nonflux boundary conditions imposed at the sidewalls. The generic transitions from planar to cellular interfaces and between cellular interfaces of different wavelengths are determined and the effects of variations of system parameters on the bifurcation diagrams are analyzed. A variety of new phenomena, such as various types of hysteresis and cellular island formation, secondary bifurcations describing beats and mode jumping among interfacial cells, and tertiary Hopf bifurcations to standing waves, is discovered, which one can expect to find in solidification experiments on purely topological grounds.

The results of a study of the dielectric response of the liquid crystal BOH8-MPOOBC in the frequency range 5 Hz to 13 MHz, in the vicinity of the phase transition to the ferroelectric phase, in an aligned cell of 2.7 μm thickness, are presented. At small ac probe fields, critical-like behavior is observed in the dielectric permittivity and the characteristic relaxation time of molecules in the bulk of the sample. At high ac probe fields, a second relaxation appears due to the reorientation of molecules at the cell surfaces. The dielectric strength of the bulk relaxation grows linearly with the spontaneous polarization. The viscosities of the surface and bulk processes, as determined from measured characteristic times and spontaneous polarization, increase in a thermally activated manner for temperatures within the ferroelectric phase. Comparison of frequency-dependent optical response and dielectric response measurements at small applied fields shows that both are due to the same bulk molecular reorientation process.

Monodomain samples of the $S_F$ and $S_G$ liquid crystalline phases were studied to determine the orientation of the principal-axes system of the time-averaged field gradient tensors for various deuterated sites in the compound 4-n-nonoxybenzylidene-4’-butylaniline(9O.4). The monodomain samples were prepared by cooling an aligned $S_A$ sample, suitably oriented in a 4.7 T magnetic field, into the $S_F$ and $S_G$ phases. Studies of the angular dependence of the deuterium spectra show a different orientation for the principal axes of the averaged field gradient tensor from deuterated sites on the molecular core and the chain. In the $S_F$ phase it was discovered that while the direction of tilt could switch its orientation in the presence of a field, so could the principal axes associated with deuterated sites on the molecular core and chain but each under different field orientation. Orientational flow imposed by the magnetic field is clearly different for the core and chain sublattices. Magnitudes of tilt angles, the averaged quadrupole coupling constant ν${¯}_Q$, and asymmetry parameter η¯ are measured. Based on these values a molecular model for the $S_F$ phase composed of two distinct sublattices, one formed by the aliphatic chains showing no in-plane orientational order and the other formed by the aromatic cores showing local herringbone order, are proposed.

The relation between thermodynamics and inequalities between means, studied earlier, is extended. If heat capacities $C_i$ are allowed to be negative, as they are in the case of a black hole, it is shown that the weighted arithmetic and geometric means have the following relationships: ${\mathrm{pT}}_1$+${\mathrm{qT}}_2$≥$T_1^p$$T_2^q$ if p and q have like signs; ${\mathrm{pT}}_1$+${\mathrm{qT}}_2$≤$T_1^p$$T_2^q$ if p and q have unlike signs. Here p≡$C_1$/($C_1$+$C_2$) and q≡$C_2$/($C_1$+$C_2$) so that the weights still add up to unity. This result is shown to be readily accessible from thermodynamics. Similarly, if constant-energy and constant-entropy equilibrations of two bodies lead to final temperatures $T_E$ and $T_S$, respectively, then it is shown that $T_S$<$T_E$ if $C_1$ and $C_2$ have like signs and that $T_E$<$T_S$ if $C_1$ and $C_2$ have unlike signs. Extensions of an inequality are also given which apply to a mean defined as the upper limit of an integral. This theorem covers the inequalities between the main weighted means as special cases.

We discuss the existence and properties of strange nonchaotic attractors for the damped pendulum equation with two-frequency quasiperiodic forcing. In particular we present evidence that the equation does indeed exhibit strange nonchaotic attractors and that these attractors are typical [in the sense that they exist on a (Cantor) set of positive Lebesgue measure in parameter space]. We also show that the strange nonchaotic attractors have distinctive frequency power spectral characteristics which may make them observable in experiments involving physical nonlinear phenomena which can be modeled by the damped-forced-pendulum equation (e.g., Josephson junctions and sliding charge-density waves). Finally the transition to chaotic behavior is illustrated.

We present a soluble model of an atomic system driven by a train of δ-function impulses. The atomic Hamiltonian describes an atom with one bound state and one continuum representing an autoionizing resonance. The model is soluble or requires very simple numerics. The results depend strongly on the shape of the resonance. Population trapping is discovered for a Gaussian-shaped continuum. Corrections coming from the counterrotating terms are discussed.

We have measured the phase diagrams of mixtures of chiral and racemic CE4, CE5, and CE2 in order to study the effect of varying chirality on the existence of blue phases in chiral liquid crystals. We observe three blue phases—BPI, BPII, and BPIII—which progressively appear at the isotropic phase boundary as the chirality is increased. The temperature widths of both BPI and BPIII become wider with increasing chirality, while BPII becomes narrower and vanishes at high chirality. We argue that this may be a universal feature of blue-phase temperature-chirality phase diagrams and discuss our results in light of previous theory and experiment.

We present an analysis of the recently measured velocity-dependent linear polarization effect in associative ionization (AI) collisions between Na(3p) atoms which, for the first time, permits a ranking ordering of all the molecular states contributing to the total cross section as a function of collision velocity. We find that ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$(σσ) and ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$(σσ) are the dominant states contributing to AI at velocities greater than 1000 m/s, and that contributions to AI decrease in the order: ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$(σσ),${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}+}$(σσ),>${\mathrm{}}^3$${\mathrm{\Pi }}_{\mathrm{g}}$${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathrm{g}}$,${\mathrm{}}^1$${\mathrm{\Pi }}_{\mathrm{u}}$, ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$,>${\mathrm{}}^3$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$(ππ),${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$(ππ),${\mathrm{}}^3$${\mathrm{\Delta }}_{\mathrm{u}}$,${\mathrm{}}^1$${\mathrm{\Delta }}_{\mathrm{g}}$, ${\mathrm{}}^3$${\mathrm{\Sigma }}_{\mathrm{g}}$${\mathrm{d}}^{\mathrm{-}}$,${\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{u}}^{\mathrm{-}}$. .AE

For ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{F}}_2$ homonuclear molecules, for six neutral diatomic molecules of the form XH, where X ranges from Be to F, and for the isoelectronic series HF, ${\mathrm{H}}_2$O, ${\mathrm{NH}}_3$, and ${\mathrm{CH}}_4$, it is shown that a substantial part of the accurate numerical calculations reported by Allan et al. [J. Chem. Phys. 83, 4562 (1985)] and by Lee and Ghosh [Phys. Rev. A 33, 3506 (1986)] can be interpreted in terms of basic scaling laws.

The study of the scattering of electrons by ${\mathrm{He}}^{+}$ ions has been extended to the L=3 and the L=4 partial waves below the N=2 threshold of the ion. The ab initio calculations are performed in a pseudostate close-coupling approximation. An 11-state pseudostate basis set is used in the nonresonant energy range and a relatively long-range 14-state pseudostate basis set is used to examine the resonances. Resonance parameters for 19 F-wave and 10 G-wave resonances are obtained with the outer electron extending up to n≃7. Comparisons with other available results are made.

Solutions of the close-coupling equations are obtained for sodium in a four-state approximation (3s,3p,4s,3d) at energies of 22.1, 54, and 150 eV. Generalized oscillator strengths (GOS) deduced from the resulting differential cross sections for the 3s-3p transition are plotted as a function of momentum transfer squared ($K^2$). The resulting GOS do not tend to the exact value of the optical oscillator strength as $K^2$ goes to 0, thus violating Lassettre’s hypothesis. While Lassettre’s theorem is not satisfied exactly, the concepts underlying this hypothesis are still useful at sufficiently high energies.

A general and practical approach is formulated for solving a bound-free coupling problem for an exponentially decaying laser pulse. The method, being essentially of a perturbative type, admits also the existence of an arbitrary number of bound states coupled with the initial state and is suitable for a large class of atomic problems including, for example, near-threshold photoionization of neutral systems.

We show that ordinary coherent light, interacting with a nonabsorbing nonlinear medium modeled as an anharmonic oscillator, is highly squeezed, at least up to the sixth order.

We present a model for a linear amplifier which adds phase-dependent noise to the input signal. This is achieved by preparing the internal modes of the amplifier in a squeezed vacuum. Such a scheme could be used to amplify a squeezed-signal quadrature with reduced added noise compared with conventional schemes. The model discussed could be realized as nondegenerate parametric amplification.

A novel method for producing a high-density, high-temperature plasma medium in which light amplification in the soft x-ray region may occur is described. A cold dense plasma is produced by a slow electrical capillary discharge and subsequently heated by a high-power laser pulse.

A recent treatment of the saturation drift velocity $v_{\mathrm{sat}}$ of electrons in dense, supercritical argon [Leycuras and Levesque, Phys. Rev. A 32, 1180 (1985)] gives positive values of ${\mathrm{dv}}_{\mathrm{sat}/\mathrm{dn}}$ at n/$n_c$=1.2–1.6, whereas the experimental values are negative in both the supercritical gas and the liquid at these densities [Jahnke, Meyer, and Rice, Phys. Rev. A 3, 734 (1971); Huang and Freeman, Phys. Rev. A 24, 714 (1981)]. Other difficulties are mentioned.

We agree with Gee and Freeman that our model could be improved to show better experimental agreement, but we believe that none of the points of the Comment by Gee and Freeman rests on quantitative grounds or justifies modification of the assumption of the model. On the contrary we underscore the reasonable quantitative agreement of our calculated $v_{\mathrm{dsat}}$ and even of ${\mathrm{dv}}_{\mathrm{dsat}/\mathrm{dn}}$ with experiment in the frame of one simple and clear assumption. Moreover, new very strong experimental evidence is given in favor of the localization of excess electrons in fluids and of the molecular-dynamics related drift: the similar density dependence of the inverse of the excess electron mobility and of the half width at half maximum of the ${\nu }_1$ band of ${\mathrm{CH}}_4$ related to the vibrational phase relaxation in methane [Echargui and Marsault-Herail, Mol. Phys. (to be published)]. It is the first time that such a similarity is found with the mobility.

Circular and linear polarization correlation measurements have been carried out for the 3 ${}_{}{}^3{}_{}{}^{}P$ state of He i at an incident electron energy of 60 eV and for electron scattering angles from 35° to 70°. The scattering parameters λ and χ for this spin-exchange excitation process are derived from the complete set of Stokes parameters, and total polarization (‖P‖=1) and coherence (‖μ‖=1) are confirmed. Within the experimental accuracy the measured values agree with recent calculations by Cartwright and Csanak.

We present high-precision measurements of the line shape of coherently backscattered light from a disordered solid which strongly supports the recent vector theory of Stephen and Cwillich, and which cannot be adequately described by current scalar theories. Three different regions have been identified in the experimentally observed line shape which reflect three different types of photon trajectories inside the multiply scattering medium. They are (i) extremely long trajectories which are affected by finite sample size, (ii) trajectories much smaller than the sample dimensions but much larger than the optical mean-free path; for these trajectories the scattering process is essentially two dimensional, and (iii) short trajectories which give rise to an asymptotic falloff which is proportional to the inverse square of the momentum transfer.