The initial value problem for a system of two relativistic scalar fields in two space-time dimensions is solved. One of them has a self-interaction of the sine-Gordon type, while the other is massless and moves in a background geometry which has a dynamical evolution of its own. The system has soliton solutions and is shown to be completely integrable using the inverse scattering method. The appropriate linear equations are found by thinking of the problem as the isometric embedding of a surface in a three-dimensional Euclidean space.

Flux bundles with nonzero transverse winding numbers, in spontaneously broken non-Abelian gauge models or electrodynamics with anomalous magnetic moment interactions, collapse to strings of vanishing transverse size and vanishing classical energy per unit length. This self-focusing phenomenon, which occurs independently of the strength of coupling constants and other Lagrangian parameters, yields the first example of soliton solutions as distributions, extended only within a manifold of lower dimensionality than space-time.

The characteristics of six trimuon events observed in the new large-angle neutrino detector at Fermilab are described. The leptonic system appears to take an inordinate fraction of the incident neutrino energy if new hadrons are presumed to be the origin of these events. A similar effect seems to be present in the dimuon events previously observed. The events find a natural interpretation as the products of cascade decay of a new lepton (the $M$ particle) through a lower-mass neutral lepton (the $L^0$ particle).

The experimental data on neutrino-induced trimuon production are compared with the results of a cascade model involving two heavy leptons. The agreement between theory and experiment is excellent.

We explain neutrino-produced trimuon events with a gauge model incorporating heavy leptons $M^{-}$ and $M^0$ with the cascade-decay chain $M^{-}\to M^0{\mu }^{-}\overline{\nu }$ and $M^0\to {\mu }^{-}{\mu }^{+}\nu$. Comparisons with trimuon data are made for $M^{-}$ and $M^0$ masses 7 and 3.5 GeV, respectively. This mechanism predicts same-sign dimuons at five times the trimuon rate.

We have measured the relative cross sections of ${\pi }^{+}$ and ${\pi }^{-}$ electroproduction from protons and neutrons, and combined them in a way which permits a new, detailed comparison with the quark parton model of the nucleon. We confirm the expected behavior with $\frac{1}{\omega }$ of the quark charge ratio and the quark fragmentation function.

The prominent side peak observed in nuclear reaction data induced by massive heavy ions such as Ar, Kr, and Xe is observed to be dominated by quasielastic processes and these processes are interpreted theoretically in terms of the distorted-wave Born approximation (DWBA). Variations of peak location with energy and projectile mass and charge are well reproduced by sample DWBA calculations for particle transfer. Quantal and classical contributions to the angular widths are discussed.

Measurements of the total cross section differences ${\sigma }_T\left({}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}\right)-{\sigma }_T\left({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\right)$ and ${\sigma }_T\left({}_{}{}^{44}{}_{}{}^{}\mathrm{Ca}\right)-{\sigma }_T\left({}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\right)$ are reported for positive and negative pions. Optical-model calculations are used to extract values of the rms neutron radius difference for each isotope pair. For ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$-${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ the deduced radius difference agrees with the results of recent $\alpha$-particle and proton scattering experiments but is smaller than values predicted from Hartree-Fock calculations.

Opto-acoustic high-resolution spectroscopy of the $v=1\mathrm{}\to 2$ vibrational-rotational transitions of the ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}$ states of NO is reported. Accurate frequencies for the 1→2 band centers for both the ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}$ states are obtained. The opto-acoustic detection technique has allowed Zeeman spectroscopy of the excited-state transitions.

Close-coupling calculations of cross sections for rotational transitions have been performed using the full static Hartree potential surface plus a local approximation to the exchange interaction. While simpler approximations to the interaction potential are adequate for the total integrated cross section, accurate treatment of short-range interactions is essential for the momentum-transfer cross section. We find a resonance feature with II symmetry at about 2 eV only in the static-exchange-model calculations.

Because of the binding of the atomic electrons, the Compton line is asymmetric in shape and its center of gravity differs from the position to be expected for free electrons. Using a new Compton fluorescence method, this difference has been determined experimentally for a number of elements and primary wavelengths and it is compared with theoretical predictions. The agreement is satisfactory.

Molecular dynamics calculations in two dimensions for particles interacting with a repulsive "step" potential show melting-curve maxima and minima as well as solid-solid phase transitions. These features are similar to those observed in the phase diagram of cesium and cerium.

Electron-nuclear double-resonance (ENDOR) spectra at 1.5 K of ${\mathrm{Cr}}^{5+}\left(3\mathrm{}{d}^1\right)$ on tetrahedral ${\mathrm{As}}^{5+}$ sites in K${\mathrm{H}}_2$As${\mathrm{O}}_4$ show lateral Slater protonic configurations. The $d_{x^2-y^2}$ function couples with the two near protons. The reorientation of this unit in the four possible lateral configurations occurs in the paraelectric phase. The observed reorientation times are discussed.

A large temperature-dependent transition in the magnitude of the ambient axial electric field inside a vertical copper tube has been observed. Above a temperature of 4.5 K the ambient field is 3 × ${10}^{-7\mathrm{}}$ V/m or greater. Below 4.5 K, the magnitude of the ambient field drops very rapidly, reaching about -5 × ${10}^{-11\mathrm{}}$ V/m at 4.2 K. We believe that these effects results from the presence of a surface electron layer on the inside wall of the tube which provides a temperature-dependent shielding effect.

Dispersion and damping characteristics of surface exciton polaritons in ZnO have been measured by nonlinear optical technique. Optical mixing was used to excite surface exciton polaritons while surface roughness was used to couple the surface waves out. The results were used to deduce characteristic parameters of bulk excitons in ZnO.

Fourier-transformed experimentally determined valence Compton profiles of trigonal, polycrystalline, and amorphous Se are presented. For trigonal and polycrystalline Se, the experimental results are reproduced quantitatively by a self-consistent orthogonalized-plane-wave calculation. The results are discussed in terms of one- and two-electron densities. Because of the surpriseinly large differences between the amorphous and crystalline results we believe that the Fourier-transformed Compton profile is a powerful probe for the microstructure of semiconductors.

There is a connection between nonlinear partial differential equations that can be solved by the inverse scattering transform and nonlinear ordinary differential equations without movable critical points (e.g., Painlevé transcendents). We exploit this connection to reduce the second equation of Painlevé to a linear integral equation. We also describe a class of nonlinear ordinary differential equations that can be exactly linearized by this method.

The algebra of the weakly vanishing Hamiltonian generators of localized translations, rotations, and supersymmetry transformations of supergravity theory is found. I argue that supergravity is the square root of ordinary general relativity in the same way as the Dirac equation is the square root of the Klein-Gordon equation and the Ramond-Neveu-Schwarz model is the square root of the spinless string.

We have observed six trimuon events produced by neutrinos in the new large-angle neutrino detector (NEULAND) at Fermilab with the momenta and charges of almost all muons determined. The properties of these events strongly suggest that their origin is not hadronic but may be in the lepton sector.

We suggest that the conservation of muon number is associated with a local gauge principle and that small nonconservation effects develop from the spontaneous breakdown of the gauge symmetry. Experimental consequences of the scheme, stemming from the spontaneous genesis of off-diagonal neutral currents, are discussed in detail.