We introduce an exact enumeration method for calculating the survival probability $P\left(n\right)\mathrm{}$ for the $n$-step random walker on a lattice with randomly distributed high-concentration traps, $c$. Using it we show that our data scale as $\ln P\left(n\right)\mathrm{}\simeq a\rho$, where $\rho ={[-\ln \mathrm{}(1-c\left)\right]}^{\frac{2}{\mathrm{}(D+2\mathrm{})\mathrm{}}}{n}^{\frac{D}{\mathrm{}(D+2\mathrm{})\mathrm{}}}$, when $\rho \gtrsim 10$ in $D=2\mathrm{}$ and $D=3\mathrm{}$ dimensions. This value of $\rho$ corresponds to $P\left(n\right)\mathrm{}\lesssim {10}^{-13\mathrm{}}$.

In order to solve multidimensional tunneling problems that cannot be treated by the normal instanton techniques, we introduce the path decomposition expansion formalism, and show its usefulness by solving three generic examples: the symmetric and asymmetric double well, and the decay problem. The technique allows us to handle excited states and backscattering effects in nonseparable potentials.

Growth is described in terms of an active zone defined as the region where new particles join the existing cluster. This zone is characterized by the probability $P(r,N)\mathrm{}\mathrm{dr}$ that the $N\mathrm{th}$ particle is deposited a distance $r$ from the center of mass. Our Monte Carlo simulations for two-dimensional diffusion-limited aggregation and the Eden process show that, for large $N$, $P(r,N)={\left[{\left(2\mathrm{}\pi \right)}^{\frac{1}{2}}{\xi }_N\right]}^{-1\mathrm{}}\exp [-\frac{{(r-{\bar{r}}_N)}^2}{2{\xi }_N^2}]$, where ${\bar{r}}_N\sim N^{\nu }$ and ${\xi }_N\sim N^{\bar{\nu }}$. We find $\bar{\nu }<\nu$ indicating the presence of two distinctly diverging lengths in these processes.

Schrödinger's equation and the heat equation are connected to one another by analytic continuation, as are the Feynman integral and the Wiener integral. We extend this form of correspondence to the relativistic domain by identifying Poisson processes whose real version gives rise to the telegrapher's equation and which when analytically continued produce the Dirac equation.

An experimental search has been performed for bound systems of neutrons and negative pions, denoted by ${\left({\pi }^{-}\right)}^Z{n}^N$. Such negatively charged nuclear fragments might be emitted in energetic proton-nucleus collisions. Upper limits for production cross sections of $Z=1\mathrm{}$, $N=2-6\mathrm{}$ and $Z=2\mathrm{}$, $N=3\mathrm{}$ systems have been derived by assuming that the lifetime of the bound pion(s) is of the order of that of the free pion or longer.

Two events of ultrarelativistic nucleus-nucleus collisions observed in the Japanese-American cooperative emulsion experiment show large fluctuations of the pseudorapidity distributions of the charged secondaries. The fluctuations are analyzed by use of the power spectrum. A simulation is used to estimate the statistical noise. Fairly strong signals are found in the Si-AgBr event, while the Ca-C event exhibits only weak signals.

A search has been made for isotopes of sodium of mass > 100 amu by studying the isotopic mass shift of the Na $D2\mathrm{}$ transition with use of the photon burst method. An upper limit for the heavy hadron to nucleon ratio of 5 × ${10}^{-12\mathrm{}}$ was found under the assumption of hyperfine splittings comparable to those in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, and negligible fractionation of heavy sodium isotopes. This compares with cosmological model predictions for nuclear matter of ≃ ${10}^{-10\mathrm{}}$.

Auger and x-ray photoelectron spectroscopies indicate that the probabilities for $1\pi \to 2\pi$ shakeup in the C $1s$ ionization of CO and for the $1{\pi }_{\mathrm{u}}\to 1{\pi }_{\mathrm{g}}$ shakeup in ${\mathrm{N}}_2$ are about an order of magnitude greater near the threshold than at energies well above it (the sudden limit). This enhancement is attributed to a conjugate process that is strengthened by the intense core-to-$\pi$ resonance just below the core-ionization threshold.

We report the first quantitative measurements of the effect of a phase-diffusing laser field on a nonlinear optical interaction. Using a nearly Lorentzian laser power spectrum, we have measured the spectral linewidth of an unsaturated two-photon absorption process. We find that the measured width scales as four times the laser width, in agreement with the theoretical predictions of Mollow.

Analytic expressions of the convection diffusivity tensor in fully developed isotropic turbulent flow are given and used to evaluate the broadening of a cloud of marked particle pairs perpendicular and longitudinal with respect to an initial separation. Both turn out to remain different because of the difference between $〈v_{\perp }^2〉$ and $〈v_{\parallel }^2〉$. Parameter-free expressions for the variances ${\sigma }_{\perp }$ and ${\sigma }_{\parallel }$ yield the dependence on the Reynolds number and other flow parameters in addition to the known scaling behavior $\propto {\tau }^{3-\gamma }$.

The nonlinear evolution of the Rayleigh-Taylor instability of a thin sheet in three dimensions is studied numerically. Results show that erosion of mass at the top of the bubble is similar to that found in two-dimensional simulations, but mass flow into spikes is slower in three dimensions.

A quasi-steady-state lower-hybrid current-drive operation is demonstrated in the Alcator $C$ tokamak at densities up to ${\bar{n}}_e\simeq 1\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The current-drive efficiency is measured experimentally over a wide range of densities and magnetic fields. The radial distribution of high-energy x rays indicates that the current-carrying electrons peak near the plasma axis.

Experimental observations of the bootstrap and Pfirsch-Schlüter currents, predicted by neoclassical transport theory, are presented. Detailed measurements of the parallel plasma currents in a toroidal octupole agree, within the separatrix, with theoretical predictions. Observations of the spatial structure, collisionality, and toroidal field dependence of the complete current and the ion portion of the current are discussed.

We report the first observation of line emission resulting directly from charge-exchange recombination of medium-$Z$ elements injected into a PLT discharge. Transitions due to the radiative cascade immediately following charge-exchange of He-like Al and Sc were observed. One of the newly observed lines, AlXI 3209 Å, offers a convenient spectroscopic and medium-$Z$ charge-exchange diagnostic due to its long (air) wavelength. Spatial scans provided information on the profile of the neutral beam in the plasma.

Raman backscatter of intense laser light from an inhomogeneous plasma in the presence of a self-generated magnetic field is studied by means of simulations with use of a 1½-dimensional particle code. The magnetic field results in a significant blue shift in the frequency of the backscattered light. Emission levels show a dependence on magnetic field that is consistent with linear mode conversion of the scattered light wave.

Using kinetic simulations we find that Raman backscattering can exist for laser intensities a factor $2\pi$ lower than the density gradient ($\nabla n$) threshold and that Thomson scattering can account for backscattering signals even lower. In addition, kinetic, collisional simulations show that laser intensities ≳3-10 times the electron-ion collisional threshold are needed for significant Raman absorption. Collisions can also reduce the heated electron temperatures for $\nabla n\ne 0$.

The interaction of low-frequency ac electric fields with the anisotropic polarizability of rodlike polydiacetylene macromolecules is used to excite slow (<50 cm/sec) transverse elastic modes in gels made up of a network of these molecules. The specific coupling of the ac field excitation and the birefringence detection to the network allows direct measurements of the fraction of the sample for which there is an elastic restoring force (the "infinite cluster").

A dislocation-mediated model is presented for restacking phase transitions that have been observed in a variety of lamellar (liquid crystalline) systems. The model explains the existence of nonhexagonal crystalline (smectic)-$B$ phases in terms of dislocation-induced tilting of hexagonally packed layers. Ordered dislocation arrays explain both the symmetry and the amplitude of observed modulations. It is likely that the model will also be applicable to modulated lipid-water phases.

Smectics $A$ and $C$, tilted discotics, and the smectic-$\tilde{C}$ phase are shown to have finite shear moduli for shears applied in directions which have no translational order (liquid directions): This is the signature of a glass. This modulus is generated purely by dynamical fluctuation effects. It leads in smectics $A$ and $C$ to a violation of the basic rule of conventional hydrodynamics which asserts the equality of the numbers of hydrodynamic modes and fields.

Overlayers of C, N, and O on Mo(001) have been studied by 500-eV ${\mathrm{K}}^{+}$ -ion scattering. The energy distributions and their dependence upon incident angle are found to depend strongly upon coverage and annealing temperature. Enhanced specular scattering is extremely sensitive to changes in adsorbate ordering observed by low-energy electron diffraction. The enhancement is explained by a novel scattering mechanism discovered by computer simulation.