The percolation properties and upper critical field of a disordered superconductive square network are calculated by use of the de Gennes-Alexander theory. It is suggested that photolithographic techniques be used to build such artificially disordered systems. The critical exponent of the upper critical field is calculated and found to be $k=0.93\mathrm{}\pm 0.06$ on the metallic side of the percolative transition.

A generalized resonance-tunneling equation containing a first-derivative term having the coefficient $\alpha >~0$ is found to exhibit stimulated emission of waves by the resonance. The expected Budden absorption occurs for $\alpha =2N$, $N=0,1,2,\cdots ·$. However, in bands centered around $\alpha =2N+1\mathrm{}$, the modulus of the reflection coefficient can be larger than unity.

A simple numerical reversibility test which proves useful in exposing the chaotic nature of classical dynamical systems is applied to the quantum model of a hydrogen atom in a microwave field. The remarkable result is that, in spite of some apparent chaotic features, the quantum motion proves to be perfectly stable in contrast to the high instability of the classical chaotic motion.

For thermal neutrons we have measured the Fizeau effect to 1.5% accuracy. The quoted accuracy was achieved by use of a newly designed neutron interferometer. Four fast-moving samples, all parts of a single, four-winged, aluminum, rotating propeller, could be made to engage simultaneously in the interfering beams. Our experiment complements and exceeds two recent Fizeau experiments, one of which was performed with cold neutrons and much lower accuracy and the other with a moving medium inside stationary boundaries resulting in a null Fizeau effect.

The method of finite elements converts the operator Heisenberg equations that arise from a Hamiltonian of the form $H=\frac{p^2}{2}+V\left(q\right)\mathrm{}$ into a set of operator difference equations on a lattice. The equal-time commutation relations are exactly preserved and thus are consistent with the requirements of unitarity. We consider general Hamiltonians of the form $H(p,q)\mathrm{}$ and show that the requirement of unitarity uniquely determines the operator ordering in such Hamiltonians. (The ordering procedure involves a set of orthogonal polynomials which are not widely known.) Our result shows that it is possible to treat quantum spin systems by the method of finite elements.

We show that the Fourier transform of very complex spectra gives a sound measurement of long-range statistical properties of levels even in cases of badly resolved, poorly correlated spectra. Examples of nuclear energy levels, highly excited acetylene vibrational levels, and singlet-triplet anticrossing spectra in methylglyoxal are displayed.

The 1D Hubbard model is shown to be an exactly integrable system. A "covering" model of 2D statistical mechanics which I proposed recently was shown to provide a one-parameter family of transfer matrices, commuting with the Hamiltonian of the Hubbard model. I show in this work that any two transfer matrices of a family commute mutually. At the root of the commutation relation is the ubiquitous Yang-Baxter factorization condition. The form of the $R$ operator is displayed explicitly.

Interacting parastrings offer the alternative of constructing string theories directly in four (as well as a number of other) space-time dimensions. These theories are consistent with Lorentz invariance, Lovelace analyticity, and modular invariance. They are also derivable from actions in lightcone gauge. For supersymmetric parastrings, the corresponding actions are supersymmetric.

A nontrivial squared helicity amplitude is given for the scattering of an arbitrary number of gluons to lowest order in the coupling constant and to leading order in the number of colors.

This Letter reports a new experimental search for the family-number-nonconserving decay ${\mu }^{+}\to e^{+}\gamma$. There is no evidence for the presence of this decay mode. The upper limit for the branching ratio is $\frac{\Gamma (\mu \to e\gamma )}{\Gamma (\mu \to e\nu \overline{\nu })}<4.9\mathrm{}\times {10}^{-11\mathrm{}}$ (90% confidence limit).

We present results of calculations which suggest that several of the spin observables for elastic scattering of 500-MeV polarized protons from a polarized ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ target are sensitive to relativistic aspects of nuclear structure.

Decay of xenon atoms with a vacancy in the $K$ shell by the emission of photon pairs which continuously share the transition energy was investigated. The results show the expected dominance of transitions of electrons from the $2s$, $3s$, and $3d$ states, for which the single-x-ray transitions are strongly forbidden. In the energy range of the present measurements the resonance effect due to the intermediate $2p$ (and $3p$) states for transitions of electrons from higher shells has not been observed.

A theory is presented to explain the statistical properties of the growth of dye-laser radiation. Results are in agreement with recent experimental findings. The different roles of pump-noise intensity and correlation time are elucidated.

Two-dimensional MHD simulations are carried out which demonstrate that the cross-field thermal conduction near the magnetic axis controls the structure of sawteeth in tokamaks. In simulations of discharges with good central confinement, skin currents form at a finite radius causing the safety factor $q$ to fall below 1 away from the magnetic axis. Both normal and compound sawteeth are produced which have many features consistent with experimental observations.

Recent results from the Alfvén-wave heating experiments on the TCA tokamak have confirmed very strong sawtooth activity on the peak electron temperature, with the delivered rf power roughly equal to the Ohmic power. This could be interpreted as being due to a very peaked rf-power deposition profile, in which case it would not correspond to the dissipation of all the Alfvén-wave energy locally at the resonance layers. It is possible that the mechanisms responsible might be the conversion to, and subsequent dissipation of, the kinetic Alfvén wave.

Direct measurements of integrated phase-space densities, e.g., $f(x,v_y,t)$, have been made in an experiment. Using spectroscopically active ions, measurements in a plasma show the ion response, $f_i(\mathrm{x},\mathrm{v},t)$, to linear and nonlinear waves and phase-space particle bunching. Time-resolved measurements show coherent and incoherent phase-space density changes in the presence of waves, indicating that transitions to turbulence and chaos may be studied. The time, space, and velocity-space resolution may allow experimental tests of predictions from the Boltzmann equation.

The dependence of the nonequilibrium partition coefficient $k$ of Bi in Si upon solidification velocity $v$ has been measured with sufficient accuracy to distinguish between proposed solute-trapping mechanisms. For the range of measured velocities, 2-14 m/s, we observe a much more gradual increase in $k$ with increasing $v$ than those previously reported and no evidence for a "saturation" effect, i.e., $\frac{\mathrm{dk}}{\mathrm{dv}}\to 0$ at $k<\mathrm{}1\mathrm{}$. The continuous-growth model of Aziz fits the data quite well; the Aziz stepwise-growth model and the two-level Baker model yield values of $\frac{\mathrm{dk}}{\mathrm{dv}}$ that are too high.

${}_{}{}^{129}{}_{}{}^{}\mathrm{I}$ Mössbauer spectra of $g-{\mathrm{Ge}}_x{\mathrm{Se}}_{1-x}$ alloys display a local maximum in the site-intensity ratio $\frac{I_B}{I_A}\mathrm{}\left(x\right)\mathrm{}$ at the critical composition $x=x_c=0.23\mathrm{}\pm 0.02$. This observation is consistent with the realization of mechanical critical behavior in a covalent network glass recently predicted by Phillips and Thorpe. We identify $x_c$ with the onset of percolation of a specific molecular fragment based on the layered form of $c-\mathrm{Ge}{\mathrm{Se}}_2$.

We study the depletion of a diffusing substance (i.e., of a scalar Laplacian field) near an absorbing fractal, consisting of a random or a self-avoiding walk. We establish a mapping between the moments $〈U{\mathrm{}\left(r\right)\mathrm{}}^n〉$ of the field $U\left(r\right)\mathrm{}$ at a distance $r$ from a point on the absorber and the partition functions of certain star polymers. The scaling with $r$ of each moment is governed by an independent exponent $\lambda \mathrm{}\left(n\right)\mathrm{}$, which we calculate to order ${\epsilon }^2(\epsilon =4-d)$. Nonperturbative results for the limit of high $n$ are also given. We relate the $\lambda \mathrm{}\left(n\right)\mathrm{}$ to the exponents $D\left(n\right)\mathrm{}$ of a fractal measure.

It is shown that the diluted two-dimensional central-force problem belongs to a new class of percolation problems. Geometric properties such as the fractal dimension of the backbone, the correlation-length exponent, and the connectivity are completely different from those of previously studied percolation problems. Explicit calculations of the backbone and the construction of an algorithm which identifies the infinite rigid cluster clearly demonstrate the absence of singly connected bonds, the overwhelming importance of loops, and the long-range nature of the rigidity.