Magnetic-birefringence measurements were performed in the nematic phase of the binary lyotropic liquid crystal cesium perfluoro-octanoate and water within 75 mK of the superheating limit. Several results were obtained: (1) The induced birefringence was linear in H for small H, but showed significant deviations from linearity for H>5 T; (2) the elastic constant was found to be very small near the transition, indicating that director fluctuations may contribute a significant multiplicative factor to the average order parameter; and (3) the order-parameter exponent β=0.34±0.06. This last result is examined in the context of a mean-field theory with higher-order terms in the free-energy expansion and in the context of the d=3, N=5 N-vector model.

The diffusion-limited cluster-cluster aggregation model is investigated under conditions which for long times lead to steady-state coagulation. Single particles are added to the system at a constant rate and the larger clusters appearing as a result of the aggregation process are removed according to various rules. Our results show that the dependence of the number of clusters, N(t), on the feed rate κ in a unit volume and the time t can be well represented by a scaling form N(t)∼${\kappa }^{\alpha }$f(${\kappa }^{\beta }$t) with a scaling function f(x)∼x for x≪1 and f(x)=1 for x≫1. The exponents α and β are found to depend on the spatial dimension d, of the system, but within the statistical errors they always satisfy the relation α+β=1 in accordance with the prediction of a generalized rate equation discussed by Rácz (see the companion paper). The values we have obtained for α and β are consistent in two and three dimensions with the corresponding results of the Smoluchowski equation approach but inconsistent in one dimension. This can be considered as an indication of the fact that the upper critical dimension for the kinetics of the diffusion-limited cluster-cluster aggregation model is 2.

A scaling generalization of the Smoluchowski equation is used to treat fluctuation effects in aggregation problems. In particular, we investigate the diffusion-limited cluster-cluster aggregation subject to the condition that single particles are fed into the system at a constant rate, h, while clusters larger than a fixed size are removed. Considering the zero-feed-rate limit as a critical point, we find that h plays the role of an external field conjugate to the order parameter which turns out to be the cluster density. The cluster density obeys dynamic scaling and, because of the finiteness of a kinetic coefficient, the dynamic critical exponents are expressible in terms of a static exponent. The exponents are determined by arguing that the zero-feed-rate process is in one universality class with the A+A→0 diffusive annihilation problem. Our scaling theory is in agreement with available Monte Carlo simulation data.

We present qualitative and quantitative observations on structural instabilities in a cholesteric liquid crystal subjected to static shear. Using a model of a cholesteric that is tilted under shear, we find that, in a Landau–de Gennes coarse-grained picture, buckling instabilities can be created when the strain is larger than a critical value. The analogy with buckling obtained under dilations is sketched, and a comparison is made with the critical wave vector of the undulations. A good agreement is found between the theoretical values, both of the critical wave vector and of the threshold shear values and the experimental ones. New insight can be gained on the mechanism for the formation of hydrodynamical instabilities under shear.

The inverse-spectral-transform method of solution is shown to be applicable to the physically interesting problem of the nonlinear Schrödinger equation with a general ‘‘potential’’ term, ${\mathrm{iq}}_t$+$q_{\mathrm{xx}}$+2[‖q${\Vert }^2$-F(x)]q=0. The method determines the class of solutions that are symmetric or antisymmetric in x. This is done with the help of a modification of the Ablowitz-Kaup-Newell-Segur and Zakharov-Shabat (AKNS-ZS) formalism incorporating an x- and t-dependent eigenvalue parameter ζ, together with a transformation of variables. In certain physical applications, F(x) describes the inhomogeneity of the medium in which nonlinear wave propagation occurs. The functions F(x) for which the equation is amenable to solution by our method are shown to fall into two classes, depending on whether or not ζ is explicitly t dependent. If it is, we show that F(x) must be a general quadratic function of x. An explicit solution q(x,t) is written down and interpreted for a parabolic potential barrier. If ζ is independent of t, we find that localized solutions with static envelopes can exist for certain other functional forms of F(x). Finally, we comment on the extension of the analysis to explicitly time-dependent potentials or inhomogeneities F(x,t).

We study a physical system consisting of a low-frequency nonlinear oscillator interacting both with a thermal bath at the temperature $T_1$ and a high-frequency linear oscillator which, in turn, interacts with a thermal bath at the temperature $T_2$ ($T_2$≥$T_1$). The interaction between slow and fast oscillator is nonlinear, thereby influencing the motion of the slow oscillator via fluctuations of a multiplicative nature. By means of a suitable procedure of elimination of the fast variables, a contracted description is obtained, which, at $T_1$=$T_2$, exhibits precisely the same structure as that recently derived by Lindenberg and Seshadri [Physica (Utrecht) 109A, 483 (1981)] from the Zwanzig Hamiltonian. Instead of the transition from the overdamped to the inertial case revealed in our earlier paper [S. Faetti et al., Phys. Rev. A 30, 3252 (1984)] in this series, it is shown that precisely the reverse effect takes place. This is confirmed by computer calculations and the reliability of the computer calculation, in turn, is confirmed in the inertial regime via analog simulation. The theory enabling us to explore the noise-induced transition to the overdamped regime is based on an improvement of the techniques of elimination of fast variables, which produces automatic resummation over infinite perturbation terms. At $T_2$>$T_1$, a space-dependent diffusion term with the same structure as that involved with the multiplicative fluctuation of the ‘‘external’’ kind is proven to be added to the canonical multiplicative diffusion term exhibited by the case $T_1$=$T_2$. Canonical and noncanonical effects, which have so far been the subject of separate investigations, may thus be described via one single picture. It is also shown that, in the purely canonical case, the ubiquitous character of the noncanonical diffusional form, ranging from Ito^-like to Stratonovich-like structure, is lost and a unique form of diffusional equation occurs.

The solitary-wave solutions and their stability in the case of coupled nonlinear field equations describing the proton motion in hydrogen-bonded chains are investigated. First, a model Hamiltonian for two-component solitons in hydrogen-bonded chains is proposed, and the coupled equations of motion for the two displacement fields are derived. The stationary solitary-wave solutions are found from an integral equation formulation by perturbation analysis. For the first time, a convergence proof for the fixed-point iterates of the integral equation is presented. The results show the existence of bell-shaped solitons as well as kinks in an interval of admissible soliton velocities. In the second part of the paper, the nonlinear stability of the stationary solutions is discussed. The Liapunov method is applied and a stability functional is presented. The latter yields stability conditions which are satisfied by the calculated stationary solutions. This proves the existence of stable localized finite-energy solutions in hydrogen-bonded chains which could be responsible for a very effective proton transport.

This paper describes molecular-dynamics simulations of a collision-assisted transfer model of the excess electrons in a rare gas. In this model the effect of an external electric field applied to the fluid is taken into account by allowing the displacement of an excess electron from an atom to another if the modulus of the vector distance between the atoms and the angle between the vector distance and the field have prescribed values. The computed drift velocities are in reasonable agreement with the experimental ones for a large density domain (going from gas to liquid). Then, in spite of the simplicity of the studied model, our computation seems to show that the main features of the electron motion in argon and in other fluids originate in the dynamics of the molecules of these fluids.

A new functional relation for factorizable vertex systems that do not satisfy the so-called symmetry relation is proposed. Together with the unitary condition this relation enables one to obtain the free energy of these systems in the thermodynamic limit. These relations are then used to solve a particular case of the free-fermion eight-vertex model.

In recent years the observation of optical second-harmonic generation (SHG) in nematic liquid crystal (NLC) MBBA [N-(4-methoxybenzylidene)-4’-n-butylaniline] raised again the question of whether NLC’s possess centrosymmetry. Lyakhov et al. [Izv. Akad. Nauk SSSR 45, 917 (1981)] suggested that these observations can only be explained by considering the NLC as noncentrosymmetric and optically biaxial. In this paper it is shown phenomenologically that even with $D_{\infty h}$ symmetry, SHG arising from ee→e, oo→e, and oe→o interactions can occur in an aligned NLC. With curvature strains SHG arising from ee→o, ee→e, oe→o, oe→e, oo→o, and oo→e interactions are all possible. Several experimental observations are satisfactorily explained by the present calculation. The order of magnitude of the effective susceptibilities estimated from a quadrupole-moment mechanism agrees with the values obtained by Arakelyan et al. [Mol. Cryst. Liq. Cryst. 71, 137 (1981)] and by Barnik et al. [Mol. Cryst. Liq. Cryst. 98, 1 (1983)]. One may conclude that it is possible to explain the occurrence of SHG in NLC’s without having to invoke noncentrosymmetry of the system.

Recently a nonlinear Schrödinger equation (NLSE) with an inhomogeneous term proportional to $b\ln \left({\left|\psi \right|}^2\right|a^3)\psi$ has been put forward. It has been proposed to apply it to atomic physics. Subsequent neutron interferometer experiments designed to test the physical reality of such a nonlinearity were not conclusive, thus rejecting it as unphysical. In the present paper it is pointed out that the different length scales $a$ associated with atomic and nuclear physics, for example, lead to different typical energies $b$ for these systems. Guided by the experience with phenomenological NLSE's, the constant $b$ is for the following applications to nuclear physics identified with the compressibility of finite nuclear matter, $C=\frac{K}{9}$, i.e., $b\equiv C$. Thus we obtain consistent qualitative and quantitative answers related to the concepts of microworlds and mesoworlds as well as, e.g., the prediction $130<~K<~250$ MeV. However, this necessitates the interpretation of the respective NLSE as an equation for extended objects.

Recently, a simple analytical formula has been put forward giving the relative nuclear (charge root-mean-square) radii as functions of mass number and binding energy per nucleon. To that end, inverse methods in conjunction with the famous $A^{\frac{1}{3}}$ dependence of the nuclear radii were employed. The main point of the present Brief Report is to show that the same goal may be accomplished without leaving the framework of inverse methods (leading even to slightly more realistic value of the amplitude than the previous one). Detailed calculations are presented for the isotopes of ${}_{42}{}^{}{}_{}{}^{}\mathrm{Mo}$, ${}_{66}{}^{}{}_{}{}^{}\mathrm{Dy}$, and ${}_{56}{}^{}{}_{}{}^{}\mathrm{Ba}$.

With the use of a Green's-function method, the scattering states of the one-dimensional Dirac equation are obtained. The potential is assumed to be a sum of $\delta$ functions of arbitrary strengths and positions on a chain of finite length.

The time dependence of recombination luminescence of 760-2300-torr krypton excited by ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ fission fragments has been measured and a delay has been clearly observed. The measured delay time is inversely proportional to pressure and is 2.6±0.4 μs for 760 torr, which is in qualitative agreement with the calculated thermalization time for electrons.

An earlier Born-approximation calculation of collisional electron detachment from ${\mathrm{H}}^{-}$ is extended with the use of improved bound- and free-state ${\mathrm{H}}^{-}$ wave functions. Present results confirm the previous conclusion [T. C. Genoni and L. A. Wright, J. Phys. B 13, 461 (1980)] that the difference between the resultant atom motion and the center-of-mass motion of the outgoing ion complex (H+$e$) cannot, in general, be ignored. In addition, differential cross sections calculated using closure and an average-momentum-transfer approximation are shown to be in excellent agreement with calculations employing an explicit summation over final target-atom states.

The alignment of the $2p$ state by Compton scattering is investigated. Here, Compton scattering is understood as the inelastic scattering of large-momentum photons, electrons, or ions. At the peak position of the $2p$ Compton profile the alignment parameter $A_{20}$ has its maximum possible value, +0.5.

The Kr $3d_{\frac{5}{2}}:3\mathrm{}{d}_{\frac{3}{2}}$ branching ratio has been measured between 97 and 200 eV photon energies using monochromatized synchrotron radiation from the Tantalus storage ring. The branching ratios have been obtained both from the Kr $3d_{\frac{5}{2},\frac{3}{2}}$ photolines, and from the Kr $M_{4,5}{N}_1{N}_{2,3} \left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ Auger lines in the low- and high-photon-energy ranges where the direct photoelectron measurements are very difficult. The agreement between results for the two methods is very good. In contrast with the Xe $4d_{\frac{5}{2}}:4\mathrm{}{d}_{\frac{3}{2}}$ branching ratio, the Kr $3d_{\frac{5}{2}}:3\mathrm{}{d}_{\frac{3}{2}}$ ratio is almost a constant and very close to the statistical value of 1.5 throughout the energy range studied. Our results are not in good agreement with the theoretical relativistic random-phase approximation results which predict a variation of the $3d_{\frac{5}{2}}:3\mathrm{}{d}_{\frac{3}{2}}$ ratio of 1.4-1.7 between 100 and 120 eV, due to an initial decrease in $3d$ cross sections to 105 eV followed by a slow increase. Our results show that the $3d$ cross sections increase immediately above threshold.

An explanation of the peaks of probability distributions of chaotic nonlinear maps is given, as well as an algorithm for calculating the locations of those peaks. This analysis also provides insights into the nature of periodic and aperiodic behavior in nonlinear maps.

The chaotic regime of systems which go to chaos via quasiperiodicity is studied, with the aim of establishing universal scaling laws for the invariants like the Lyapunov exponents, fractal dimensions, etc. Despite the complicated interventions of periodic windows, the envelopes of these quantities appear to agree extremely well with the theoretical predictions. This agreement is tied to the smooth development of the underlying invariant manifold.

Three different results for the nonanalytic dependence of the shear viscosity on shear rate have been given. This discrepancy is resolved by an independent calculation based on the nonlinear Navier-Stokes-Langevin equations. The relationship to previous calculations and reasons for the differences are described.