A recently introduced algebraic approach to scattering is recast in the language of group contractions and expansions. The expansion describes the deformation of the physical states from one kind of symmetry to another and allows the algebraic derivation of an S matrix. The method is illustrated for scattering models in n-dimensional space of the type SO(n,1) and SO(n,m) with m≥2.

The hyperfine (hf) couplings of all the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ nuclei in the muonated free radical⋅${\mathrm{C}}_6$${\mathrm{F}}_6$-Mu have been measured using a level-crossing-resonance technique. Slow damped oscillations of the muon spin polarization in a large longitudinal magnetic field or frequency splittings in transverse field occur at particular field values at which there is a near degeneracy in the muon fluorine hf levels. Thus a resonantlike effect is observed in the muon-spin-rotation spectrum as a function of magnetic field. The positions of such level-crossing resonances allow an accurate determination of the magnitude and sign of the fluorine hf parameters relative to the muon hf parameter.

Calculations, complete through second order in the collision potentials, are presented for 1s-1s capture by positrons. Some new destructive interference between second-order amplitudes is evident. This destruction interference was not important in capture by protons where one Thomas amplitude is dominant. Nevertheless, the total cross sections for capture by positrons are larger than those for capture by protons at the same velocity because of a kinematical effect.

Degenerate four-wave mixing is examined for arbitrarily strong pump field interactions using a liquid suspension of Brownian microparticles as the active medium. It is shown that pump-generated interactions act to modulate the field-induced translational particle gratings in a novel way which greatly modifies both the steady-state and the transient properties of such media. Of particular interest is the fact that four-wave mixing in suspensions is radically different for the case of an attractive versus repulsive electrostrictive coupling between the microparticles and the pump radiation.

Flow visualization, heat-transprot measurements, and the light-intensity profile as a function of time have been used to study nonlinear propagating waves in ethanol-water mixtures heated from below. The experimental results reveal the main features of the travelling waves predicted by recent theory.

We report studies of Nusselt number N versus Rayleigh number R for a normal liquid ${}_{}{}^3{}_{}{}^{}\mathrm{-}_{}^4{}_{}{}^{}$He mixture with ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ mass concentration c=0.038, confined in cylindrical containers with aspect ratios, Γ (radius/height) of 5.5≤Γ≤10.2. These data were obtained for separation ratios Ψ of -0.2≲Ψ≲0.1. For Ψ>0, the data are consistent with predictions that the slope RdN/dR is small just above the onset of convection and then increases with R. For Ψ≃0, N is a concave function of R with N∝(R-$R_{\mathrm{cs}{)}^{1/2}}$. Contrary to predictions for a horizontally infinite layer, no oscillations at onset were found for Ψ<0. Above the onset of convection when Ψ<0, we observed additional transitions which are beyond the scope of current theory.

We consider the generalized quantum Chirikov map under a resonance condition 2πħ=M/N. This is the quantum-resonance condition discovered by Casati et al. At the resonance, the quantum system reduces to a set of independent N×N unitary matrix eigenequations. We can reduce the evolution operator of the original system as a direct sum of these N×N unitary matrices. We then obtain the eigenstates and eigenenergies (the pseudoenergies) of the quantum map and illustrate their dependences on a number of parameters. We plot these eigenstates in the coherent-state representation and show that they follow closely the Kolmogorov-Arnol’d-Moser curves and other classical orbits.

The electric quadrupole transition 3$p^6$3$d^{10}$ ${\mathrm{}}^1$$S_0$–3$p^5$3$d^{10}$4f (3/2, 7/1) J=2 has been observed in the spectra of Ta xlvi, W xlvii, Re xlviii, Pt li, Au lii, and Hg liii. The excited-level populations of Ni-like gold are calculated by means of a collisional-radiative model and show that the intensity ratio of the electric dipole 3$p_{3/2}$-4${\mathrm{d}}_{5/2}$ and electric quadrupole 3$p_{3/2}$-4$f_{7/2}$ resonance transitions is sensitive to density in the range ${10}^{19}$–${10}^{21}$ ${\mathrm{cm}}^{\mathrm{-}3}$, in qualitative agreement with the present observations.

We write the Frank energy for a discotic liquid crystal taking into account that the twist of the hexagonal two-dimensional lattice is coupled to the distortion of the director. We hence calculate the critical behavior of the Frank energy near the transition from a theoretically predicted nematic phase with sixfold orientational order to the hexagonal discotic phase, and find that the director elastic modes decouple from the ‘‘rotation’’ ones. Moreover, a simple relationship is found between the ‘‘rotation’’ strains and the density of longitudinal edge dislocations.

We investigate the distance dependence of the rate of tunneling between two sites a distance r apart interacting with a thermal bath of phonons characterized by a density of states of the form g(ω)∼${\omega }^{d\mathrm{-}1}$. We show that in such systems, the correction to the tunneling rate is of the form exp[-(r/$r_0$${)}^{3\mathrm{-}d}$] where $r_0$ is a characteristic length. Ohmic dissipation corresponds to d=1 and a Gaussian correction exp[-(r/$r_0$${)}^2$] to the tunneling rate arises as predicted by one of us [P. Phillips, J. Chem. Phys. 84, 976 (1986)].

The algebraic-eikonal approach to electron-molecule scattering is further developed. A simple perturbation method is used to illustrate the coupling of vibrational bands. Furthermore, it is shown explicitly that the differential cross section summed over the final rotational states and averaged over the initial magnetic substates does not depend on the initial angular momentum. Finally this approach is applied to calculate the differential cross section for scattering electrons from the diatomic molecules LiF and KI.

The growth probability measure has been determined for a family of screened growth models with a continuously tunable fractal dimensionality. The distribution of growth probabilities N(P) for clusters of different masses M can be scaled onto a single curve g(x) using the scaling form ln[PN(P)lnM]=ln(M)g(ln(P)/ln (M)). Each point in the scaling function g(x) corresponds to a part of the growth probability measure whose probability P grows as $M^x$ and whose size (number of sites) grows as $M^{g\left(x\right)}$. The function g(x) is related to the function f(α) of Halsey et al. which associates a fractal dimensionality f(α) with that part of the measure which consists of singularities of strength α by g(x)=$D^{\mathrm{-}1}$f(-Dx).

We formulate the dynamics of the Little model at T=0 in simple mathematical terms. We use this to prove that no cycles of length greater than 2 exist in the model. For a subset of systems only 1-cycles exist, and an extensive quantity can be defined.

The boundary between the isotropic phase and the $N_L$ lyotropic nematic phase in a mixture of potassium laurate, ${\mathrm{D}}_2$O, and decanol has been mapped as a function of pressure and temperature. The nematic region is found to be surrounded by an isotropic region in the P-T plane, demonstrating conclusively that the isotropic phase seen at lower temperatures in this system is indeed a reentrant phase. At the phase transition the density of the nematic phase is found to be always less than that of the isotropic liquid.

We have observed in a three-component oil-continuous microemulsion a new percolation phenomenon. The system of interest consists of anionic surfactant-coated water droplets dispersed in oil. The percolation limit ${\phi }_p$ is found to be strongly temperature dependent, while the structure of the microemulsion remains constant. We have proposed a surfactant anion hopping model with a temperature-dependent hopping range. Percolation occurs when the effective droplet volume, as defined by the hopping range, exceeds the hard-sphere close-packing limit of 0.65.

A new self-avoiding walk (SAW) which grows without terminating is introduced as a model of the diffusion-limited growth of linear polymers. The model is in a different universality class than the equilibrium SAW and previously considered kinetic SAW’s with ν=0.774±0.006 in two dimensions and ν=0.56±0.02 in three dimensions. The ‘‘indefinitely growing SAW’’ is shown to emerge as a particular limit of our model.

We report on the first numerical observation of type-II Pomeau-Manneville intermittency in a periodically driven third-order nonlinear oscillator. A discussion of such a transition to chaos in terms of the interaction of a local instability (subcritical Hopf bifurcation) and a global instability (homoclinic bifurcation) of a periodic motion is provided. We investigate the distribution of the laminar lengths and compare our numerical results with the theory. Emphasis is given to the 1/$f^{\delta }$ divergence (δ∼0.67∓0.10) observed in the small-frequency limit of power spectra.