A basin boundary can undergo sudden changes in its character as a system parameter passes through certain critical values. In particular, basin boundaries can suddenly jump in position and can change from being smooth to being fractal. We describe these changes ("metamorphoses") and find that they involve certain special unstable orbits on the basin boundary which are accessible from inside one of the basins. The forced damped pendulum (Josephson junction) is used to illustrate these phenomena.

We propose a stochastic generalization of the multigrid method, which reduces critical slowing down in Monte Carlo computations of lattice field theories. For free fields, critical slowing down is completely eliminated. For a ${\phi }^4$ model, numerical experiments show a factor of ≅ 10 reduction, over a standard heat-bath algorithm, in the work needed to get a given accuracy (error-bar size).

We show that in an anomalous gauge-field theory Faddeev's Schwinger term can be removed by a particular renormalization of the Gauss-law operators and we construct a positive-definite Hamiltonian that commutes with these renormalized operators.

A new method for producing the weak-coupling expansion in nonlinear $\sigma$ models and Yang-Mills theories is developed. It assumes only the smallness of the gradient of the field, rather than of the field itself, as the coupling constant $\frac{1}{\beta }\to 0$. The new method reproduces all the known exact results. It agrees with ordinary perturbation theory only in Abelian problems or when the number of space-time dimensions $d\to \infty$. Notably the new scheme reveals that the $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ nonlinear $\sigma$ models in $d=2\mathrm{}$ are not asymptotically free; it also indicates that the leading term of the $\beta$ function of QCD in four dimensions is likely different from its presently accepted value.

As a by-product to the study of muon pairs produced by 255-Ge V/c pions, data from Fermilab yield upper limits on the decay $D^0\to {\mu }^{+}{\mu }^{-}$ and on $D^0-{\overline{D}}^0$ mixing. An unrestricted sample of 122 630 unlike-sign muon pairs allows a 90%-C.L. (confidence level) upper limit of 1.1×${10}^{-5\mathrm{}}$ to be placed on the branching ratio of the charm-changing neutral-current decay $D^0\to {\mu }^{+}{\mu }^{-}$. From a sample of 3973 like-sign muon pairs, the ratio $r=\frac{\Gamma ({\overline{D}}^0\to {\mu }^{+}X)}{\Gamma ({\overline{D}}^0\to {\mu }^{-}X)}$ is determined to be $r<\mathrm{}5.6\mathrm{}\times {10}^{-3\mathrm{}}$ at 90% C.L.

We consider nonstandard electroweak models which are able to explain the observed steplike structure in the cosmic background radiation at $\lambda =1667\mathrm{}\pm 10$ Å as due to radiative decays of massive cosmic neutrinos. In the standard electroweak theory the corresponding radiative lifetime is several orders of magnitude longer than observed, because of the purely left-handed structure of the charged weak currents. We point out that in models which include also right-handed currents, the lifetime can naturally be short enough to account for the astrophysical observations.

The nonlinear $\sigma$ model with the Wess-Zumino term is extended to the low-lying vector meson resonances $\omega$, $\rho$, and $A_1$. These resonances are treated as chiral gauge multiplets in a minimally broken ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\otimes {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_R\otimes {\mathrm{U}\mathrm{}\left(1\right)\mathrm{}}_V$ gauge model. The bulk properties of hedgehog skyrmions are investigated. The results indicate a clear improvement over the conventional Skyrme model.

A sample of $\tau$-lepton decays to ${5\pi }^{\pm }{\nu }_{\tau }$ and ${5\pi }^{\pm }{\pi }^0{\nu }_{\tau }$ observed in the high-resolution spectrometer at the SLAC$e^{+}{e}^{-}$ storage ring PEP, has been used to place an upper limit on the mass of the tau neutrino of 84 MeV/${\mathit{c}}^2$ at the 95% confidence level.

Using the time-of-flight method to determine the velocity of the neutrons from the reaction ${\pi }^{-}+p\to {\pi }^0+n$ at rest we have measured the mass difference $m_{{\pi }^{-}}{m}_{{\pi }^0}$ to be 4.5930 ± 0.0013 ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathit{c}}^2$. From the width of the time-of-flight distributions we conclude that the pionic hydrogen atoms have a mean kinetic energy ${\overline{T}}_{\pi p}<12\mathrm{}$ eV (90% confidence limit) at the time of the charge exchange.

We explore the possibility of whether the anomalous positron peak observed recently in heavyion experiments may be due to a polyelectron complex ($e^{+}{e}^{+}{e}^{-}$). The decay of such a complex with the emission of a photon leads to a positron with a kinetic energy of 341 keV, which coincides with the recently observed anomalous positron peak to within the experimental error. The hypothesis of a polyelectron complex may also explain other features of the phenomenon.

Nuclear magnetic resonance on oriented nuclei has been detected for the first time via the resonant change of the radiation pattern of characteristic $L$ x rays. The magnetic hyperfine splitting $\left|g{\mu }_N\frac{B_{\mathrm{hf}}}{h}\right|$ of ${\frac{13}{2}}^{+}{}_{}{}^{193m}{}_{}{}^{}\mathrm{Pt}$ in Fe was determined to be 111.3 (3) MHz. With $B_{\mathrm{hf}}=-1261\mathrm{}\left(25\right)\mathrm{}\mathrm{kG}$, the $g$ factor is deduced to be (-)0.1158(23). This value differs strongly from the known $g$ factors of ${\left({\nu i}_{\frac{13}{2^{+}}}\right)}^{-n}$ states in Hg, Pb, and Po, suggesting a significant change in the nuclear-deformation parameters of ${}_{}{}^{193m}{}_{}{}^{}\mathrm{Pt}$.

We present calculations of the equilibrium structures and cohesive energies for Si clusters up to the size $n=14\mathrm{}$. No open structures and no diamond-lattice fragments are found. Especially stable structures found for $n=6\mathrm{}\mathrm{and}10$ coincide with experimentally observed magic numbers.

Fully kinetic simulations of high-Mach-number perpendicular shocks demonstrate that electron acceleration in the cross-shock electric field can produce downstream electron temperatures significantly higher than that expected for adiabatic compression.

The density-functional theory of freezing is extended to investigate the crystallization of binary hard-sphere mixtures. As the ratio of diameters $\alpha =\frac{{\alpha }_1}{{\alpha }_2}$ is lowered, the fluid-solid phase diagram for disordered alloys evolves from a spindle shape ($1>\mathrm{}\alpha >0.94\mathrm{}$) into an azeotropic diagram ($0.94>\mathrm{}\alpha >0.92\mathrm{}$) and finally into a eutectic diagram ($0.92>\mathrm{}\alpha >0.85\mathrm{}$). Below $\alpha =0.85\mathrm{}$, nearly complete immiscibility is predicted, in agreement with the empirical Hume-Rothery rule for metallic alloys.

The role of the surface molecular-reaction kinetics in vapor-phase crystal growth is examined via Monte Carlo simulations and shown to give rise to a growth process, referred to as a configuration-dependent, reactive-incorporation growth process, which, depending upon the growth kinetics, can be distinct from the conventional nucleation and continuous-growth mechanisms. Implications of this process for the recently observed oscillations in the reflection high-energy electron-diffraction intensities during molecular-beam epitaxy of III-V compounds are discussed.

Subharmonic frequencies and chaotic behavior have been observed in spin-wave, microwave, parallel-pumping experiments with yttrium iron garnet at room temperature. Above the spin-wave-instability threshold, low-frequency (Å 100 kHz) self-oscillations develop in the power absorbed by the sample and various bifurcation sequences are observed depending on the sample orientation and the wave vector of the primary unstable mode. The results are interpreted with a model of parametric pumping of two spin-wave modes coupled by a nonlinear interaction.

The local mean-field equations are solved for $\mathrm{XY}$ spins on a square lattice with competing nearest-neighbor interactions. For a model with randomly chosen frustrated sites, on lowering the temperature one finds the following sequence of phases: paramagnet; nonuniform ferromagnet; noncollinear, nonuniform ferromagnet; reentrant spin-glass. The reentrant transition occurs via the mechanism of frustrated-spin "melting." For randomly chosen negative bonds it is more difficult to obtain reentrance and to provide a physical explanation.

We report the first measurements of the attenuation of ultrasound in the basal plane of superconducting U${\mathrm{Pt}}_3$. Transverse sound propagating along the $b$ axis shows a marked anisotropy in its temperature dependence when the polarization is rotated in and out of the basal plane. For polarization in the basal plane the attenuation varies linearly with temperature down to 35 mK and the slope scales as the square of the frequency. Our results appear to indicate the presence of an additional attenuation mechanism when compared with recent theories of anisotropic superconductors in the dirty limit.

The Ising spin-glass in a magnetic field is studied for the Bethe lattice. There is an instability that agrees with the replica-symmetry-breaking transition found for the infinite-range model. Correlation lengths are finite on both sides of the transition, but there is a correlation length that diverges at the transition. Some features are different from those of the infinite-range model, and in particular the magnetic susceptibility and internal energy vary smoothly through the transition. An analogy with the localization transition on the Bethe lattice is pointed out.

The thermoelectric power of silicon decreases precipitously when the dimensions of a microcontact are reduced below a critical value. The critical dimension $L$ decreases with rising temperature $T$ and is a measure for an interaction length of electron-phonon coupling. The dimensional reduction inhibits the phonon-drag contribution to the thermoelectric power; the predicted scaling with $L^{-1\mathrm{}}{T}^{-4\mathrm{}}$ is verified for the first time.